Codex Atlanticus691 pages
- Blank verso with faint show-through of machinery
- Lifting pump with lead-sealed valves and an optical sighting tube
- Five small geometric figures on a near-blank verso
- Faint mechanisms with numbers and fractions (verso)
- Equal objects appear smaller with distance
- Equal objects appear smaller with distance (verso)
- Geometry, a pavilion frame and mechanical sketches
- Wire-drawing machine, cranes and lifting devices
- Faint ruled lines and compass circles (verso)
- Sheet of machine sketches with circle-squaring figures
- Faint sketches revealed by restoration (recorded as blank)
- Mechanism with paired end-boxes and a central rocking arm
- Geometry, calculations and machine studies
- Faint geometric and mechanical drawings, no writing
- Sheet of mechanical and geometric studies (no text)
- Hoisting a great weight and the squaring of triangles
- Perspective and geometric studies
- Squaring the circle: hexagons, bi-angles and proportional circles
- Milling machine and column studies
- Bombard Ballistics and Pulley Geometry
- Geometry, a mirror problem, accounts, and an upright bombard
- Mean proportionals, roots and the quadrature of circles
- Bombards, a timber vault, columns, and polyhedra
- A wheeled gun-engine, cube-root line, and a horse
- Firing props to collapse a wall; cube-root scale
- The Image of the Sun in a Spherical Mirror
- Continuous proportion and the doubling of the cube
- Quadrature of the triangle, proportion tables and perception
- Water-driven mills and the weight of falling water
- The science of shadow: rays, angles and degrees of darkness
- Grain mill, furnaces, and a concave burning mirror
- Pyramids in cylinders and cubes, with dies and a cutting template
- Proportional figures, an instrument for refraction and a cutting tool
- Blank Verso with a Small Show-Through Drawing
- Blank Verso with Faint Circular Pen Lines
- Geometric Figures, the Horizon, and Architectural Sketches
- Hoisting Wheels, a Mile-Gauge Gear, Sums, and Rain-Light
- Machine studies: a wooden plane, boring machine and gearwork
- Faint Sheet: Head, Frieze, Interlace Knots, and a Jotting
- Fortress Design: Concealed Sally-Ports and Defenses
- Eddies of Water and Air, and a Tangent-Angle Construction
- Measuring Distances by Sighting with the Eyes
- Notes on percussion and obliquity, with instrument sketches
- Ravelins and crossing lines of artillery fire
- Squaring circles and lunes; the motions of a twisted cord
- Squaring the circle: dividing portions and 'quadrable' figures
- Bird-flight notes and De ludo geometrico figures
- Coloured shadows, cord-weights, and De ludo geometrico
- Blank verso of the building-plan sheet
- Red-chalk perspective of a fortification detail
- How the size of a light governs a body's shadow
- Blank Verso with Recto Text Showing Through
- Blank verso with faint show-through of architectural forms
- Geometric square construction and a radial wheel mechanism
- Blank verso with faint geometric show-through
- Blank verso with faint show-through of a framed structure
- The sling: a giant stone-throwing engine
- Crossbow Release Mechanism and Lock Components
- Bombard, winding gear and faint column studies
- A spring lifting instrument, shown right and wrong
- Blank verso of folio 148
- The great crossbow, with bombard and torsion engines
- Blank verso of folio 149
- Bombard without a stock, a wedge-lifting device and perspective solids
- Doubling the cube: two cubes, one double the other
- Similar triangles and the proportion 1, 2, 4, 8
- Geometric star figures and a short column of figures
- Red-chalk studies of wheel-and-axle devices
- Constructing the triangle of a triangular balance
- On movers, impetus, and the parts' desire for their whole
- Wheeled bombard carriage with a screw-lowered axle-beam
- Faint geometric figures and looping lines (verso)
- Near-blank leaf with a tiny animal sketch (verso)
- Toothed wheels, proportional circles and gear contact
- Red-chalk mechanism with lettered parts and a scaled diagram
- The Motion and Foam of Sea Waves
- The Roman Harbour of Civitavecchia
- How a flat board falls through the air
- On the Nature of the Surface: Boundary of Body and Air
- The Division of Fractions
- Which of Two Equal Beams Is Easier to Drag?
- Centres of Gravity of Pyramids, Prisms and Cubes
- Proportion of Equal Squares Equals Their Heights
- Definitions of the circle and quadrature of curved surfaces
- Dividing one circle into nine equal circles
- Blank verso, invisible before restoration
- The Curvature of the Earth: How Far Two Men See the Horizon
- Studies of the Balance: Weight, Friction, and Gravity
- Squaring the Semi-Annulus, with Dome and Vault Studies
- The Six Cases of Squaring Crescents and Lunes
- Propositions on Equal Lunes, Crescents and Circles
- The four elements weighed, with number tables and water chapters
- Innate heat besieged by cold, with two riddles
- Quadrature of lunes and equal-area curved figures
- Squaring the circle: lunules and equivalent surfaces
- Blank verso, invisible before restoration
- Quadrature studies: lunules, biangles and a cross
- Blank verso, invisible before restoration
- Twenty-two quadrature figures, with memoranda and sums
- Squaring the Circle: Lunes and Inscribed Figures
- Highland Lakes from Landslides, and Surface Geometry
- Balancing Pyramids: Centers of Gravity on a Beam
- Truncated pyramids and wedges: volumes and weights
- Squaring the circle: lunes and a critique of Archimedes
- Doubling the cube, circle constructions, and a weighted chain
- Blank leaf: geometry showing through from the recto
- How the Eye Sees Things Placed Before It
- Blank leaf with the eye diagram showing through
- Angle of Incidence at a Spherical Mirror
- Blank leaf with reflection lines showing through
- The centre of a suspended body lies below its support
- Proportion of circle-portions; tracery and vault designs
- Squaring lunes and curvilinear triangles; calculations
- Lunes and circle-portions; the river Arve near Geneva
- Gearing note: a wheel and pinion of 24 and 6 teeth
- Profile head, circle-grid rosettes and a note on proportion
- Circle and square: doubling, portions and proportion
- Concave mirror from a circle-segment: equal angles
- Reflection geometry: incident line and reflected ray
- Squaring the Circle by Rosette Portions
- Rosette and Circle Diagrams (No Text)
- Two Mean Proportionals and Cube Roots
- Mean Proportionals by Similar Triangles
- Circle Sectors and Solid-Figure Studies
- Memoranda: Cornelians, a Physician, an Ambassador
- Doubling the cube and squaring lunes and circles
- Lune and circle quadrature, dated 7 July 1514 at the Belvedere
- Proportions of circle portions in nested and intersecting circles
- Squaring the circle: lunes, inscribed squares and circles
- Squaring lunes: converting curved surfaces into squares
- Weight of suspended bodies; definitions of point, line, surface
- Arch thrust, a moving body and its mover, with sums
- Proportions of circles: portions, bisangles and squaring
- Proof that 84 portions less 12 equal 72
- Squaring the circle with lunes, and a note on a craftsman
- Heavy bodies toward the earth's center, with circle figures
- Studies in squaring lunes: crescents made rectilinear
- Squaring of lunes continued, with a theorem on the square
- Quadrature of the circle: portions and lunes
- Quadrature studies: lunes and proportional circles
- Squaring curved figures: lunes and circles inscribed in squares
- Squaring curved figures, continued, with a measuring-wheel note
- Squaring the circle, an inheritance problem, and perspective studies
- Weights, plumb-lines, and squaring the circle
- Squaring circles, lunes and curved figures
- Squaring the circle: lunes, rosettes and curvilinear octagons
- Quadrature studies and the plan of the Stable of the Magnifico
- Squaring curved figures: lunes, circles and transformed spirals
- Machine-part sketches with measurements in braccia
- Squaring the Circle: Lunes, Sectors and Perforated Circles
- Quadrature of Lunes and Circles
- Kinds of Motion, with a Winch and an Ornamental Candelabrum
- Verso with a Small Hatched Triangle, Otherwise Blank
- Dividing Circles Between Parallel Lines
- Circle-square proportions and construction of square roots
- Faint circle studies with a compass construction (verso)
- Quadrature of lunes and curvilinear surfaces
- De ludo geometrico: squaring curved surfaces
- Finger motion and the squaring of curved triangles
- The three centres of a tapering rod (pyramid)
- Bell mechanism: pivot braced against the tower walls
- Blank verso, devoid of writing and drawings
- Quadrature of the circle: inscribed circles, lunes, and roots
- Squaring circular portions: two small figures
- Studies in the quadrature of the circle and lunes
- Studies on squaring the circle: lunes and nested circles
- Dividing lines and circles into equal parts; squaring the circle
- Beam balanced by six counterweights
- A Balance Compared to a Bellows Crossbar
- Nine cords supporting a beam: how force is shared
- Squares equal to curved figures, and a recipe for false jasper
- Quadrature of the circle with bi-angles and inscribed polygons
- Stacked spheres, 'excess of excess', and a wheel mechanism
- Dividing a square into any number of equal squares
- Squaring the circle: lunes and circle-square proportions
- Squaring circles by portions and curvilinear figures
- Squaring the circle through the hexagon and proportionality
- Circles worth half the greatest circle; a money reckoning
- Squaring the circle: circles, squares and octagons
- The greatest quadrilateral in a right triangle
- Mechanical Instruments and Geometric Figures
- Forces between two weights and a stringless arch
- Squaring the circle: two tables of proportionality
- The Aliquot Parts of Six and the Circle of Bisangles
- Dividing the Circle by Six: Hexagons, Triangles and Squares
- The Table of Proportionality and the Squaring of Portions
- Calculations with a Loggia Sketch and Ornamental Letters
- Why a Painted Face Seems to Follow the Viewer
- Percussion, Resistance and the Powers of Ten
- Squaring the Circle: Lunes and Equal Curved Figures
- Two Circle Diagrams on the Quadrature of the Circle
- Flattening the Eighth Part of a Sphere into a Square
- Centre of gravity of a suspended weight and the balance
- Squaring lunes and semicircles, with vault studies
- Squaring the circle, a pulley, and two building elevations
- Squaring the Circle: Lunes and Circle-Portions
- Balances, Levers and the Oval Equal to a Circle
- Geometric Construction with Calculations and Memoranda
- Strength of beams: length, thickness and weight borne
- The science of light and shadow: primitive and derivative
- Beam mechanics: how a smaller angle bears more weight
- Quadrature of the Circle: Lunes, Squares and Diameters
- Squaring the circle: sectors, chords, and Archimedes' rule
- Axioms on quadrable and non-quadrable surfaces
- The hexagon and the sixfold division of the circle
- Cords and pulleys: tangency and the centre of gravity of an arc
- Beam, potential lever, and divisibility to infinity
- Quadrature of lunes and transformation of areas
- The diagonal divides its square into equal halves
- Solid Geometry of Pyramids, Cones and Cylinders
- Lettered Geometric Constructions (Verso)
- Circular sectors, portions, and doubling a circle
- Measuring an unknown distance with similar triangles
- The triangle as the most perfect figure; number tables
- Triangle's inscribed and circumscribing circles, and the lune
- Capacity of polygons and the surfaces of cylinder and sphere
- Household expense account, with faint geometry and a horse's head
- Lines of natural and accidental obliquity; descent and impetus
- Definitions on circles in double proportion and squaring the circle
- Parallelepipeds and the doubling of the cube
- Studies of the Balance: Natural and Accidental Figures
- Center of Gravity of a Pyramid Suspended from a Balance
- Book of Equivalence: Squaring Circular Sectors and Portions
- Circular Portions in Sixteen Sectors, and Their Squaring
- Squaring the Circle and Circling the Square
- Equating Circular Figures by Lending and Removing Areas
- Joined circle sectors and a sphere resting on a sphere
- Quadrature studies: doubling pyramids and equipartition of sectors
- Balances and weights, with prophecies and a note on flight
- Circles in quadruple proportion and curvilinear triangles
- Squaring a square with curved figures; ornament and a pulley
- Surveying: measuring mountain heights and leveling land
- Surfaces of the cylinder, a theatre curtain cord, and the oblique beam
- Letter to his family, July 1507, among lune quadratures
- Quadrature of lunes and curvilinear surfaces
- The Five Terms of Perspective: Point, Line, Angle, Surface, Body
- Diagrams of Light Rays and the Boundary of the Luminous
- The Balance: Choosing the Site of Weights by Proportion
- Squaring of lunes: proofs on crescent-shaped figures
- Squaring of lunes, continued: lending triangles
- Solar light through square, cross and round apertures
- Turning curved surfaces into straight; arcs, chords, sagittae
- Geometric construction with columns of calculation
- Studies of the classical orders: architrave, arch and pedestal
- Weights on inclined planes: resistance, friction and the fulcrum
- Squaring the Lune: Transformations of Curvilinear Figures
- Curvilinear Geometry: Sectors, Lunes and the Limits of Squaring
- Mechanical and hydraulic studies on a faint sheet
- Sluice-gate construction with quadrature-of-the-circle notes
- Near-blank verso showing the recto through the sheet
- Windlass and cord mechanics with quadrature of lunes
- Transmuting triangles and squaring lunes, with cord statics
- Geometric versus arithmetic change of a proportion
- First treatise: triangles in semicircles and the quadrature of lunes
- Quadrature of Lunes and Circular Sectors
- Convergence of Light and Shadow: the 5/8 Penumbra
- The Science of Light and Shadow on Spherical Bodies
- Quadrature of Lunes and Curved Figures
- Squaring the Lunules; a Night Water-Clock
- Two Mean Proportionals and the Cube Root
- Pyramids and cubes: proportion, weight and the doubling of the cube
- Triangular prisms and pyramids: weight proportional to the axis
- Center of gravity of solid bodies
- Motion, Ballistics against Walls, and a Surveying Square
- Euclid's Staff and the Impact of a Ball on Fresh Earth
- A Canal Lock, Pyramid Sections, and Notes on Shadows
- Numeric tables and a radiating geometric construction
- Pulleys, levers, and beams suspended by cords
- Weighing a beam held by a slanting cord
- The nature of weights: simple rods and beams
- Suspended rods: squaring the simple rod for its load
- The nature of light on opaque and transparent bodies
- Geometry of Superimposed Circles and Sectors
- Dividing lunes and squaring curved figures
- Faint verso, only partly visible before restoration
- Archimedes, On Floating Bodies, Book II (Latin copy)
- A cone-segment floating in a fluid (Latin proof)
- Statics of the balance: weight, equilibrium and oblique descent
- Geometric equivalences and ornamental circle studies
- Curved-figure geometry: biangles, sectors and the hexagon
- Blank verso, devoid of writing and drawings
- Squaring curved figures: lunes, rings and circle proportions
- More squaring of lunes, with a sluice-gate and a maxim
- Lunes, Sectors and the Squaring of Curved Surfaces
- Dividing a Circular Portion into Equal, Similar Parts
- Squaring Lunes by Transposing Surfaces
- Lunes, Wedges and the Circle on the Hypotenuse
- Transmutation of Straight-Sided into Curved Surfaces
- Notes on a Proportional Compass, with a Tool List
- Weights on cords over pulleys, in proportion
- Doubling the cube, with cube-roots and a stamping press
- Doubling the cube: diagonal sections and mean proportionals
- Squaring the Lunes; Flame, Air, and a Note on the Medici
- Squaring Circles and Lunes by Superposition
- Quadrature of Lunules and the Flight of Birds
- A Catalogue of Quadrable Curved Figures
- Conception: the circumscribed is smaller than the circumscribing
- Transmuting curved surfaces into rectilinear ones (lunes)
- Lunes squared by proportion, and the percussion of balls
- Geometry of lunes and surfaces, with a note on safe falling
- Squaring the circle: kinds of curved surface, lunes and triangles
- Proportions of squares, triangles and lunes
- Lunes, Circles and Squares: Geometry of Equal Areas
- Struck-Out Circle-and-Semicircle Note
- Squaring the circle: circles, bi-angles and curvilinear triangles
- Quadrature studies: transforming curved and straight surfaces
- Bi-angular surfaces and the curvi-hollow square
- Circle-segment geometry, the tides, and maxims on motion
- Table of squares, lunes, and figures equated by curvature
- Squaring circular segments by adding and removing triangles
- Proportion of Circles and Squares from Their Diameters
- Doubled Circles and a Bird Steering in the Wind
- Squaring Curvilinear Figures into Equal Rectilinear Areas
- Lunes and circles: similar figures and division of the arc
- Quadrature of lunes and circles: equal-area figures
- Geometric Figures Composed from Portions of Circles
- Interlaced Knot Designs and Circle-Portion Figures
- Squaring the Circle: Lunes, Squares and Circle-Portions
- Euclid's five postulates and eleven common notions
- Right angles, part and whole, and a lettered triangle
- Squaring the circle: sectors, lunes and inscribed squares
- Quadrature studies and a note on Leonardo's treatise
- The Lune of Hippocrates and circle-doubling
- Blank verso with show-through of the recto
- Geometry of Circles, Squares, and Circular Rings
- Cube with an inscribed pyramid, and roots multiplied
- Transmuting circle portions; the equilateral triangle
- The aliquot part of numbers; circles divided into portions
- Motion of waves and currents; the angle of contingency
- Squaring the lunes; measurements of San Paolo, Rome
- Quadrature of the Circle: Lunes and Squarable Figures
- Geometric Doodles, Knots, and a Latin Scrawl
- Simple and Composite Motion; Impetus as a Wave
- Rolling ball: motion on the ground versus through air
- Quadrature of the circle: turning 36 biangles into 42
- Transmuting 36 biangles into 42 by a geometric method
- Lunes and biangles: quadrature figures, with a French address
- The game of geometry: circle transformations and sphere optics
- Definitions of the sphere after Euclid and Theodosius
- Quadrature of lunes: circles, squares, and hexagons
- Quadrature series of lunes and circular portions
- Simple and compound shadows from two lights
- A sequence of thirteen numbered geometric figures
- Sheet of interlace knots, two heads and geometric studies
- Cones from cylinders and the ballistics of bombards
- Dividing a circle and its double: lunes and inscribed square
- Blank verso with faint show-through (before restoration)
- Polygons in circles, spiral, and area equivalences
- Blank verso with show-through of circles and spiral
- The squaring of lunes and circular figures
- Blank verso with show-through of lune figures
- Squaring lunes: rectangles, sectors and semicircles
- Every body fills the air with its likeness, as mirrors do
- Why the sun's rays cannot fully illuminate the earth
- How air condenses and sustains a bird in flight
- Number calculations, polygons and a sublimation recipe
- Scaling problem, balances and a boat with a paddle-wheel
- Quadrature of lunes and an instrument for reflected light
- Geometry of lunes: proportional division of circles
- Studies of lunes and semicircular portions
- Lunes, triangles and circle-to-square proportion
- On the definition of surface
- Quadrature of lunes with a note on the sea's tides
- Quadrature of lunes: area equivalences of circles and squares
- Axioms on parts reunited to remake their whole
- Complaints against the German mirror-makers at the Belvedere
- Areas of circles as squares of diameters, and lantern studies
- Curvilinear figures of equal area drawn from a circle
- Curved pyramids and the rolling of circles
- Rectangles of equal area, Euclid, and surd roots
- Squaring the circle through sectors and lunes
- Blank restored verso with offset traces of geometry
- Squaring the circle: lunes, portions and the inscribed square
- The painter's life, colour contrast and a coupled-column design
- Geometry and arithmetic exercises with wave studies
- Blank restored verso with offset from recto studies
- Angle of contingence to a circle; the eye and inverted vision
- Equilibrium of a triangular figure divided about its axis
- Angle of incidence in a concave mirror and compass constructions
- Dividing lines and circles with a single compass opening
- Shadow of a sphere under star-shaped light, with quadrature figures
- Shadows cast by a sphere, and the squaring of the lune
- The science of weights: gravity, levity and the spheric body
- Optics glossary: rays, mirrors, reflection and refraction
- Geometry glossary: points, lines, angles, triangles, figures
- Solid geometry: cube, sphere, cone and polyhedra
- Circles, tangency and the quadrature of lunes
- Machine sketches with a 'body born of perspective'
- Mostly blank verso with a single mechanism sketch
- Compass rosettes and lunes, with a record of the king's salary
- Squaring curvilinear figures: lunes, rosettes and a hexagon
- Squaring Lunes and Sectors; Proportion of Triangles
- Squaring Lunes and Rings; Circular Sectors
- The Triangular Balance: Finding Its Centre
- Lever and Counter-Lever: Definitions and Right Angles
- Pyramids cut by parallel planes; triangle centres of gravity
- Centres of gravity, a waterfall, hexagons and proportions
- Why one light casts two shadows behind one body
- Quadrature of lunes and proportions of circles
- Quadrature of lunes; circles in double proportion
- Widening the Base of a Truncated Pyramid
- Tables and Cylinders: Transforming Solids of Equal Volume
- Quadrature of the Lune
- Lunes, Triangles and Pyramids Compared
- Mensuration of a Circular Ring
- Lettered Solids and the Geometry of Vision
- Geometry of Vision: Visual Triangles on a Surface
- Vaulted trusses, with notes on hot water and capillary rise
- Squaring lunes and circles, with a note on wind vortices
- Earth's Gravity and the Quadrature of Divided Circles
- Quadrature of Circles: Doubling Circles and Squares
- Squaring Curvilinear Triangles, Lunes and Circle Portions
- Squaring the Lune of the Hexagon and Crescents
- Triangle proposition, square roots and household grocery accounts
- Quadrature of lunes, cylinder geometry and a bitter letter to a brother
- Squaring a rectangle: the gnomon and Euclid's Elements
- Squaring a quadrilateral by equal removals from the diagonal
- Weighted wheels and toothed gears for perpetual motion
- Domed churches, columns, and a theorem on a divided line
- Six wheels mounted on a single pole
- Weighted wheel and a rosette of overlapping circles
- Water raised by counterweights and finding its level
- Lunule construction and curvilinear surfaces
- An orbicular pyramid equal to a rectilinear figure
- Light and shadow on spheres, with sphere geometry and a comet
- Squaring the sphere's surface and branch ramifications
- Resolution of geometric fractions and a water wheel
- Gearing, screws, water-wheels; dividing a line into parts
- Power of Water Falling on Mill-Wheels at Various Obliquities
- The 'Wheel of Increase' and Faint Geometric Constructions
- Rods Bending Under Weights, and the Circle Defined
- Graduated triangle with columns of calculations
- Bombard powder, the line of motion, and loaded arcs
- Two ways to dig a ditch: a labour-and-earth calculation
- Topography of Lake Como and the Alpine Valleys
- Reclining nude and faint marginal notes
- Transforming a cube; centres of gravity and lever devices
- How the eye sees spheres and plane surfaces
- Cone-and-circle figures lettered d b a and m p o n
- Quadrature of the circle by sectors and octagon
- Constructing a Curve with Movable Templates
- Doubling the Cube: Cube Roots and Proportional Means
- The quadrature of lunes and circular sectors
- Squaring figures bounded by a single curved side
- Transforming triangles and dividing lines by proportion
- Triangles, circles and the rule of three for irrational lines
- Squaring curvilinear figures with lunes
- Squaring the circle: lunes, circles and squares
- Verso catalogued blank; geometry shows through from the recto
- Spiral in a star polygon, a vortex study and a mechanism
- Two restored paper fragments recorded as blank
- Definitions of double and subdouble ratio
- Motion through acute and right angles
- Graduated Arm and Pulley Weight Tracing Concentric Arcs
- Crowded Sheet of Studies: Vaults, Ships, Circles and Star Figures
- Compressing a cylinder: how its base widens as its height falls
- Squaring the cylinder: transforming solids into equal squares
- Memoranda for Milan, with geometric figures after Apollonius
- Radial line construction within a circle
- Geometric division of a circle into sectors and segments
- How many equal segments fit into a sixth of the circle
- The sixfold division of the circle proved by its bisangles
- Making a curved figure equal to a straight-sided one
- Curve equal to straight, with maxims on knowledge
- Balance-arm mechanics, an axle-pin recipe, and a lune figure
- Faint pencil sketches: vessels, a perspective study, an interlace panel
- Dividing and Equalising Circles
- Quadrature Studies: Circles, Lunes and Portions
- Hexagons, Triangles, and Portions of the Circle
- Division of Quantities into Equal Parts
- Derived Shadows and the Squaring of Curved Figures
- The Largest Square Inscribed in a Right Triangle
- Squaring Lunes and Circles: Geometric Games
- Geometric Projections with a Memorandum on Florence
- Doubling the cube, with plans for a palace and garden aviary
- Squaring the lunes of the hexagon and the square
- Circles as squares of their diameters; dividing a lune
- Red-Chalk Profile Head with Geometric Figures
- Unrolling the Surfaces of Cylinders and a Pyramid
- Squaring lunes and portions of circles
- Squaring lunes; and a maxim on natural wit
- Squaring circular segments and lunes
- Squaring the ring: quadrature of circles and annuli
- Triangles between parallels and circular portions
- Quadrature of Lunes and Curvilinear Figures
- Double Circular Sector
- Geometry: proportional division and circle contact points
- Geometry of tangent points, with sketches of springs and devices
- Cannon on a carriage, with calculations and a divided circle
- Transforming rectangles: widening and shortening
- Squaring the circle: lunes reduced to triangles and squares
- Blank side of a fragmentary leaf, with recto showing through
- Semicircles divided into equal sectors
- Lunes in quarter-and-eighth proportion, with a letter draft
- A catalogue of lunes: the quadrature demanded without arithmetic
- Impact of colliding spheres, with geometry of solids and circles
- Rotational rebound of struck spheres, with divisions of the circle
- Derived shadow on steps and slopes, and light through apertures
- Dividing a portion of a circle into equal parts by halving
- Squaring lunes and dividing semicircles, with flight notes
- Squaring the circle by twelve inscribed circles
- Definitions of arcs, chords, sagittae and circle-portions
- Lever and Counter-Lever: Weights Carried by an Angled Cord
- Squares and Roots, with Small Geometric Figures
- Geometry of lunules, octagons, and the quadrature of figures
- Transforming pyramids and cylinders: height versus base
- Transmutations of a slab: simple and composite changes
- A method to measure any distance by triangulation
- Pyramids of incident and reflected light rays
- Sunlight through an aperture; mirror and reflected rays
- Squaring of figures and transformation of quadrilaterals
- Diminution of figures and solids along a beam of rays
- Circles, inscribed figures and incident rays on a ring
- Beams on two cords: equal angles, equal support
- Raising a beam by a cord: lever weights at every degree
- Geometric definitions, the bow's force, and loads on beam and column
- Squaring the circle by arc-division and equivalent pyramids
- Squaring lunes: geometrical versus mechanical quadrature
- Dividing circular portions; the arc and irrational chord
- Difference between two circular portions
- Inserting two mean proportionals; the cube root
- Constructing the Cube Root by Two Mean Proportionals
- The Blow of a Staff Struck at Two Points
- Sheet Without Text: Faint Geometric and Mechanical Sketches
- Squaring the Circle: Lunes and 'Circles with a Foot'
- Circles in Quadruple Proportion and 'Shield' Figures
- Geometry of circles, semicircles and their segments
- Two fables, with geometry, motion and lightning notes
- The science of derived and primitive shadow
- Geometric construction of radiating lines and arcs
- Circular sheet with a web of intersecting chords
- Oblique balances, compasses, and the squaring of lunes
- De ludo geometrico: squaring lunes and curved figures
- Quadruple circles, with a timber frame and wheel
- Divided bar for wheels, jointed mechanism, and a ramped structure
- Propositions on weight and the descent of falling bodies
- Interlaced knot-work of star-rosettes and knotted medallions
- Geometric interlace (knot) design
- Pricked interlace pattern (verso of the knot design)
- Perspective study of a mazzocchio ring
- Perspective construction of a foreshortened circle
- Solar Rays, Squaring the Circle, and a Letter to a Friend
- Perspective Study of a Faceted Ring
- Interlaced Geometric Star Medallion
- Star Polygon on a Cut Polygonal Sheet
- Blank Verso of the Star-Polygon Fragment
- Interlocking Prisms: A Three-Dimensional Solid
- The Mazzocchio: A Faceted Torus in Perspective
- Blank Verso of the Mazzocchio Sheet
- Squaring lunes and curvilinear triangles
- Instrument and method for measuring any distance
- Truss Arches and Domed Churches; Pen Trials and Sums
- Motion through right and obtuse angles: load on suspending cords
- Geometry: lettered figure with proportional ratios
- Geometry: squaring curved-sided figures
- An instrument to measure the size of the Earth
- Squaring curved figures: circles, lunes, sectors and annuli
- Geometrical diagrams of circles, squares and sectors (verso)
- Port of Civitavecchia, church plans, and laws of the balance
- Domed churches, a hoisting crane, and quadrature studies
- Geometric constructions with a column of arithmetic
- The angle of contingency and proportional triangles
- Studies of polyhedra: bodies of many faces
- Cords bear more weight as their angle to the beam sharpens
- Sharper cord angle bears double the beam's weight
- Concave burning mirror: rays reflected to a focus and its profile
- Monetary accounts and a curve construction
- Geometry of incident and reflected rays
- Screw jacks and geometric sketches
- Birds in the Wind, Reflection in a Sphere, and Circle Diagrams
- Areas of Circles, Lunes and Squares, with a Portal Study
- Weights on balances, with tables of powers of two
- Tides and river mouths, with circle-quadrature figures
- Quadrature studies: squaring circles, rings and lunes
- On local motion and percussion; a diagram of rayed lozenges
- Draft letter to a lord about a troublesome German craftsman
- Similar Portions of Circles in Sixteenfold Proportion
- Sector Subdivisions and a Square Equal to a Curved Figure
- Inscribed Hexagon and the Squaring of Circle Portions
- Circles, squares and the geometry of lune-figures
- Squares, triangles and circles inscribed and circumscribed
- Working a Tower in Water, with Studies of Area Equivalence
- Balance Diagrams with Studies of Circular Proportion
- Geometrical Figures Keyed to Euclid
- Rays from a Light Source and from the Eye to a Circle
- Blank verso with faint show-through lines (777v)
- Note on the pope's chamberlain; geometric solids (780r)
- Letter to Ser Giuliano and notes on pyramid geometry
- The curvature of flowing water and its sphere
- On the Point, and the Quadrature of Lunes
- Nothing and the Void; Earthquakes and Lune Quadrature
- Superimposed Surfaces, Tender Jottings and Moral Prose
- Profile Head of a Youth and a Pyramid in Perspective
- The eye, the pupil, and the visual pyramids
- Near-blank verso with recto diagram showing through
- Angles of contingency on the sphere; concentric-circle diagrams
- Faint geometric figures on an unwritten verso
- Draft letter, Plato's Great Year, and star polygons
- Theory of the balance: arms, appendicles and centres of gravity
- Squaring circular segments, crowns and lunes
- Blank leaf, invisible before restoration
- Quadrature of sectors, lunes and crowns; proportion of circles
- Mirror Optics, Geometry, and Hydraulic Devices
- Verso: Circle Figure and Show-Through of the Sphere Machine
- Setting out a screw thread on a cylinder, with a scent recipe
- Studies of two solids: a ribbed cone and a triangular pyramid
- Dividing a line in three; walking, oxen and river control
- Figure Studies and Solids, with a Note on Ratios
- Flame, Rising Air and the Geometry of Narrowing Triangles
- Proportional division of a triangle by parallel cuts
- Volume of a pyramid and the doubling of the cube
- Faint architectural study: column and ruled frame
- Motive power and distance; a bisecting transversal
- Cubing a Cylinder: Cube Roots by Proportional Rectangles
- A Sector of a Circle
- Mill machinery, a friction study, and pyramid geometry
- Sheet of mechanisms with a toothed wheel and pinion
- Lever Hoist for Raising a Weighted Box
- Reflection in mirrors and the brightest point on a sphere
- Faint geometric solids and inscribed figures
- Geometry of triangles, circles and squares; proportions
- Motion of falling bodies, friction, and percussion
- Circle divided into six sectors with device studies
- Geometry: doubling of areas and solids, an octagon from a square
- Squares Inscribed in Circles: Areas and Proportions
- Statics of Beams: Levity, Gravity and the Pulley
- Faint Leadpoint Studies with a Quadrant of a Circle
- Faint Mechanical Sketches Revealed by Restoration
- Grinding-Wheel Machines and a Line of Verse
- Rotor mechanism; a circle divided into three equal arcs
- Suction pumps from Imola and lettered figures
- Reflection: where light rebounds at equal angles
- Quadrature of Triangles with Two Curved Sides
- Dividing a circular sector; a note on lightning
- Pyramids, cylinders and squaring the circle
- Practice of Geometry, the Balance, and the Course of Rivers
- An antique-style fireplace, with pavilions and a cube in perspective
- Ray diagrams through a lens-like figure
- Constructions of triangle, square, pentagon and hexagon
- A heavy sphere descending an inclined plane
- Reducing a solid to a perfect cube; a red-chalk mechanism
- Halved cube and square; a red-chalk mechanism
- Statics of balance beams and loaded inclined bars
- On the force of a falling body's blow
- Star-pattern geometric studies with a balance note
- Stone-Shot against Mud-Covered Mantlets
- Pyramids of light: concave mirrors, apertures and forked shadows
- Vision through apertures and bodies interposed before the eye
- Twin Wheels Coupled by Pins, One Turning, One Fixed
- Partitioning the Hexagon Inscribed in Its Circle
- Squaring Curved Figures and a Weight on an Incline
- Geometry of triangles, a balance, water swirls and a house plan
- Four mounted fragments, verso (declared blank)
- Octagonal figures, interlaced constructions and numbers
- Waves, impetus and the centre of gravity of a wedge
- Rivers, waves and tides; circle geometry and the impact of balls
- Circles and squares, weights in balance, and the deluge of birds
- Definitions of the plumb-line, with circle-in-square figures
- A screw press with a double nut
- Chords, arcs, and the equal angles of reflection
- Geometry: transforming cubes, pyramids and solids
- Reverse of folio 1009, catalogued as blank
- Recto of folio 1010, catalogued as blank
- Central-plan church studies with a lettered circle
- Octagon construction, a balanced scoop, and fire rockets
- Note of twenty florins, with geometry and machine sketches
- Cutting a file, materials by weight, and a line construction
- Circles and Squares of Double Capacity
- Circle-and-quadrant figures and area equalities
- Rebounds of Moving Bodies; Solid Figures Defined
- The balance rule for finding a counterweight
- Counterweight demonstrations, cubes, and artillery bores
- On the squaring of the oval figure
- Geared drums, presses and the quadrature of a lune
- Quadrature of circles and lunes
- Squaring the circle by transmutation of surfaces
- Faint dividers and geometric sketches on a near-blank verso
- Geometry of triangles and circles, with balance notes
- Ray diagram for concave and convex mirrors
- Dividing a Pyramid in Septuple Proportion
- Light-ray and shadow angle diagrams, with a maxim of Anaxagoras
- Studies for squaring a curved surface
- Studies of friction, ball bearings and point contact
- Studies of lunes, circle sectors and quadrature
- Circle inscribed with a five-pointed star
- Parabolic compass and geometric construction
- Geometric fan diagram with proportional divisions
- Optics: the images of bodies fill every point of the air
- Compass construction: circle with a scalloped rosette of arcs
- Bombard on a wheeled carriage with mechanical studies
- Distillation apparatus, a spade, geometric solids and calculations
Codex Arundel197 pages
- Descent on oblique lines, centre of gravity, and balancing by proportion
- How a Suspended Weight Varies with the Angle of Its Supports
- Potential and Real Levers; a Body Falling Through Water
- Elements of Machines: the Weight at a Cord's Angle
- Centres of gravity of squares, trapezia and triangles
- Centres of gravity of the triangle and the pentagon
- A ball rebounding within a circle: the gentlest percussion
- Moon-spots, and proportionalities for the angle of incidence
- Constructing the angle of incidence within a circle
- On the angle of incidence: the best-lit point of a circle
- Finding the angle of incidence on a spherical mirror
- Angle of incidence on a spherical mirror
- A short method for measuring distance
- Combining and subtracting squares and circles
- Summing a progression and finding square roots geometrically
- Reflection in a convex mirror: locating the image
- The Angular Balance and Centres of Gravity
- Rods, Cords and the Balance of Equal Arms
- Triangular Balance Problems and a Semicircle Riddle
- The folds of the limbs' joints, with a spiral line
- Proportional figures and water likened to the body's blood
- Groynes in a river bend and a lettered proportion figure
- Geometric construction for the origin of a reflected ray
- Power proportioned to its load, with geometric and tube studies
- Triangles on a common base: areas as their heights
- Compass-drawn figure of interlinked circles on f.52v
- Similar triangles and the angle of incidence in mirrors
- Natural perspective mixed with accidental perspective
- Arcs are not proportional to their chords and sagittae
- The bird's eye and the angle of incidence on a sphere
- Heavy bodies falling to the centre of the world
- The angular balance and equal weights on unequal arms
- The three centres of gravity of a heavy body
- Geometrical constructions and a note on double proportion of motion
- Concave burning mirror: angle of incidence and the converging light pyramid
- Largely blank sheet with faint show-through (ff. 73v, 78r)
- Surfaces of solids and the squaring of the lune
- Graphite sketch of a columned frame on a wheeled base
- Faint geometric figure amid show-through writing (ff. 75v-76r)
- The bounce: percussion versus impetus in falling bodies
- Angle of rebound equals angle of incidence
- Percussion gives height, impetus gives distance
- Proportional grid and a fan of construction lines
- The law of equal angles for incident and reflected rays
- Which concave mirror kindles fire fastest
- Why Heavy Bodies Descend: Gravity and the Balance
- Finding the Point of Reflection on a Spherical Mirror
- Reflection angles at a circle, with geometric constructions
- The nature of mirrors: rays and pyramids of species
- Which prop best supports a loaded beam; lever forces
- Optical Notes on How Lines, Angles and Shadows Meet the Eye
- Geometric Figures: Polyhedra, Squares and Cylinders
- Finding the centers of gravity of a cone and its pyramids
- Faint radiating-line constructions with an arc
- Geometric construction on a perpendicular through n m r q
- Centres of gravity of a body and its parts
- Centers of gravity of wedges and pyramids
- 'Nothing', percussion, and the centre of gravity of a semicircle
- Nearly blank spread with three geometric box figures
- On 'nothing', the arithmetical zero, and Vespucci's geometry book
- Boundaries of bodies, the point, and weights on cords and a wheel
- Straight river-beds, river bends, and a bird riding the wind
- Water waves, reflected light rays, and a well-bucket hoist
- A reed-wheel musical canon, drums, and studies of liquid motion
- Profile heads, a balancing nude, and the impetus of a bombard
- Braziers, a study of the motions of fire, and a curve made square
- The pouring vessel: motions resolved into a right triangle
- Measuring the pouring vessel's motions: one mile per hour
- Small circle figures on a near-blank spread
- Water rebound, a semicircle problem, and Salai's expenses
- Multiplication Table with Figure and Perspective Studies
- Transformations of Pyramid, Cube, Cylinder and Slab
- Seventeen problems on reshaping cubes, cylinders and slabs
- Boiling water and vapour, and the definition of the point
- The point, the surface, and the elements
- On Solids, Motion, and the Nature of Time
- Time, Geometry, and Definitions of Line and Angle
- Falling Water, Heavy Bodies, and the Balance
- Gravity, levity, a sunlight mirror, and musical drums
- Net of a sphere in six triangles, with figures and sums
- Two mean proportionals and the doubling of the cube
- Finding Two Mean Proportionals Between Given Lines
- Transforming a cube into a square slab of given height
- Cubes and slabs turned into pyramids and cylinders
- Studies of pyramids, prisms and spheres
- Friction of weights drawn along inclined paths
- Gain and loss of friction on different slopes
- The pupil of the eye, and a struck cube that rounds
- Measuring a ship's speed with a mercury clock and a right angle
- Errand lists, definitions of point and line, and measuring motion
- Centres of gravity of pyramids, wedges and the tetrahedron
- Mechanical elements: beams, wheels and the pull of gravity
- Balances and the line of gravity to the center of the world
- Squaring the circle, with cylinders, cones and spheres
- Semicircle perimeters and cone-cylinder surface proportions
- Finding cube roots by means of broken numbers
- Geometric study: intersecting circles and inscribed triangle
- The sun's heat, the point, and the birth of gravity
- Book I of the Waters: point, line, body, and the sun
- Turning cubes into boards by irrational proportion
- Cube, board and cylinder in equal proportion
- Heavy Liquid Moves Light: Water and Air in an Inverted Vessel
- Faint geometric constructions on a near-blank verso
- Centres of gravity of pyramids and circular segments
- Centre of gravity of a pentagon and of circular segments
- Perpendicular bisector of two points and the definition of the circle
- A moving figure gains as much space as it loses
- Perspective, refraction, and the visual pyramid of the eye
- Surface versus volume: cube roots and doubling the cube
- Cube roots, solid surfaces, and man compared with the earth
- Propositions on visual pyramids and rays
- Reversed pyramids and images seen upside down
- Squaring the Triangle and Transforming Squares
- Constructions from a Point Outside a Line
- Cones on oblique bases and the equality of triangle sections
- Extending, Shortening and Uniting Rectangles
- Right triangle with an inscribed square
- Faint Device Sketches: Pegged Disc and Frame
- Definitions of point, line, surface and body; the First Book of Waters
- On the weight of water and the centre of the world
- Nearly Blank Leaf With a Faint Circular Sketch
- Falling to the Centre of the World; Earth Moved by Water
- Oblique descent of weights and the centre of gravity of a square
- Weights on beams and cords, and the mover's power
- Centers of Gravity of Squares, Brackets and Triangles
- Rebound of a Moving Body After Percussion
- The Moon's Spots and the Angle of Incidence
- Finding the Angle of Incidence on a Circle
- Finding the Angle of Incidence on a Spherical Mirror
- A Brief Method for Measuring a Distance
- Summing a Progression and Finding Roots Geometrically
- Angle of Incidence on a Convex Mirror
- On the Moving Body and Its Mover: Kinds of Motion
- The Restless River: Erosion and the Making of Clouds
- Crossing-line figure with marginal sketches (untranscribed)
- A faintly glimpsed geometric figure; facing leaf blank
- A figure of linked circles within a great circle
- Similar triangles, a common chord, and mirror incidence
- Proportions of arcs versus their chords and sagittae
- Falling bodies about the centre of the world; a two-bucket well
- Geometric constructions: circle in a square, squares within squares
- The cone of light, the angle of incidence, and a burning mirror
- Surfaces of sphere and cylinder, and the quadrature of lunes
- The balance: obliquity of arms and the pull toward earth's centre
- Large converging-ray diagrams (ff. 88v-84r, backlit)
- Concave mirrors: convergence of reflected rays
- Impetus and percussion: motion between equal angles
- Why heavy bodies descend: the medium, not the centre
- Equal angles of incidence and reflection at a circle
- Which prop best supports a loaded beam
- How the eye judges lines, angles and shadows
- The nature of mirrors and the reflection of visual rays
- Diagrams of luminous spheres and cones of rays
- Centres of gravity of a cone and its inscribed pyramid
- Point d placed on the perpendicular o b p
- Ray-fans, arcs and geometric sketches (untranscribed)
- Levers, counter-levers and the science of balances
- The balance analysed: real and potential arms and appendages
- Leaf with geometric sketches and columns of calculation
- The centre of gravity of a body and its parts
- Points, lines and surfaces as 'nothing'; a semicircle's balance
- Point, line and surface as 'nothing'; a weighted wheel
- Why river beds run deepest at the centre; a soaring bird
- A reed-wheel for a four-part canon, with liquid-motion notes
- A sealed brazier, notes toward fusion, and a right angle in a circle
- Compound motion: the right triangle of fall and cross-motion
- Transforming Solids: Pyramid, Cube, Cylinder and Slab
- The boiling of water and the geometry of the point
- On Time, the Point, the Line, the Angle and the Surface
- Falling Water, Heavy Bodies, and the Balance's Angles
- A sphere unfolded into six triangles, among machine sketches
- The Two Mean Proportionals Between Two Lines
- Densely Written Leaves with Small Diagrams
- Transforming Cubes, Slabs, Pyramids and Cylinders
- Faint geometric sketches: circles, triangles and a box
- A hanging weight passes wholly into its support; friction on a slope
- Geometric figures and boxes (transmitted light)
- Mechanical elements: loaded beams and wheels
- Geometry of the semicircle, cylinder and cone
- A method for cube roots using fractions
- Geometric line construction with a marginal list
- The Golden Chain: Heat, Cold, Gravity and Levity
- Reducing a Cube to a Cylinder of Equal Content
- Prophecies: Grain, Grafts and Threatening Censers
- Centres of Gravity of Pyramids and Circular Segments
- A Line Equidistant from Two Given Points
- Surfaces, Volumes and Cube Roots; Doubling the Cube
- The visual pyramid: how bodies radiate their images
- Framed circles, arcs and an untranscribed note
- Geometric constructions with compass and straightedge
- The science of shadows: simple, compound, and their crossings
- Geometry: subdivided triangles, pyramids and conic figures
- A square inscribed in a right triangle
- On point, line and body; first book of the waters
- Perspective: the diminution of the visual pyramid over distance
- Pulley mechanism, solids, and candlesticks (transmitted light)
- Musical canon wheel, timpani, and notes on the motion of liquids
Codex Forster I71 pages
- Title Page: On the Transformation of Bodies
- Thinning a Board Without Changing Its Volume
- The Proportional Compass and Its Screw-Nut
- Constructing the Square Root of 10
- Cutting One Regular Solid from Another
- Enlarging and Shrinking a Square Board
- Cubing an irregular six-faced body from twelve lines
- Reducing a dodecahedron to an equal cube
- The order of the five regular bodies
- Cubing a cylinder by lending and restoring
- Cylinders joined in a line to form one long cylinder
- The cube and its transformation into a cylinder
- Direct and reflected light entering a cavern
- A board lengthened to a set limit without change of thickness
- Twenty-eight problems on transforming a board's dimensions
- Twelve transformation problems for a solid board
- The three dimensions and six workings of a solid
- Lengthening a compressed board without changing thickness
- Geometric construction of square and cube roots
- The Five Regular Bodies and the Infinite Cutting of Angles
- Dodecahedron, Solids, and Turning a Cube into a Pyramid
- Reducing a Dodecahedron to a Cube by Pyramids
- Volumes of Pyramids and Wedges as Equivalent Slabs
- Making a Proportional Slab from a Cube by Three Lines
- Completing the Proportional Slab with the Judicial Lines
- Turning a Cube into an Irrationally-Proportioned Slab
- Reducing a Cylinder to a Square Slab
- A Pyramid Holds One Third of Its Cylinder
- Making a Cylinder from a Square Slab
- Thinning a Square Slab and Its Growth in Area
- Lowering a pyramid while widening its base at equal volume
- Widening or narrowing a pyramid's base at constant volume
- Turning a pyramid into a slab of given length and width
- A square slab of given thickness made from a pyramid
- Converting a cylinder to a tall pyramid, and pyramid to cylinder
- Squaring a pyramid's base and proportional division of solids
- Turning a Cube into a Taller Pyramid of Equal Volume
- Cutting Many Lines in a Given Proportion
- A Pyramid Fills a Slab a Third of Its Height
- From a Square Slab to a Pyramid of Equal Volume
- Making a Cube from a Tall Pyramid, and Its Converse
- Cube to a Low Pyramid, and Pyramid to a Cube
- Solid geometry: pyramid in a cube and squaring a pyramid base
- Pyramid, cylinder and cube each a third of one another
- Equal-volume pyramids and a construction for doubling the cube
- Turning a cylinder into a squared board of given thickness
- Cylinder-to-board conversion continued, with alternate methods
- Exchanging the dimensions of a board without losing width
- Transforming a stretched board into a cylinder to find its thinning
- Squaring a rectangular board to a given width
- Making one cube from two equal cubes, and squaring a board
- Subtracting one cube from another, and summing two cubes
- Turning a cylinder into a square board, and back again
- Reducing a square board to a cylinder of given length
- Reducing a Cylinder's Length: How It Thickens
- Turning a Cube into a Cylinder of Given Thickness
- A Cylinder of Given Length from a Cube
- Converting a Quadrilateral Cylinder into a Cube
- Transforming Boards into Tetragons and Cylinders
- Adding Two Rectangles into a Single Square
- Reshaping a rectangle to swap its length and breadth
- Stretching a rectangle sideways to find its lost length
- A rectangle's thickness when stretched to a set length
- Turning a square into a rectangle of a given breadth
- From rectangle to square and back, after Euclid II
- From an outside point, a line cutting an equal segment
- Geometry: locating a point equidistant from two given points
- Geometry: the line through two equal circles' intersections
- Turning a rectangle into a square, and changing its sides
- Transmutation of solids: cylinders, cubes, and pyramids
- On Weights, and How to Measure a Tower's Height
Codex Forster II48 pages
- Folio 1v: Triangle on an Equivalent Rectangle, with Sums
- Folio 2r: Rectangles in a Semicircle; Note on Capacity
- Right angles from perpendiculars and crossing lines
- Two equal circles that generate a perfect square
- The lune equals the square: equal figures leave equal remainders
- On perspective: apparent size and the proportion of light and shade
- True proof of the square: four equal circles on one circle
- Geometry, a Prophecy 'Of Kid-Goats', and Stray Notes
- Sand heaps, a divided circle and a number series
- Three spheres and a cube with its octuple
- Geometric progression 1 3 9 27 in arcs
- Number Progressions and a Weight on Pulleys
- Hollow Parallelepiped and Number Progressions
- The Cube: Faces, Corners and Edges
- Disjunct proportion: the series 6, 8, 9, 12
- Parallelepiped with a diametral cut, with accounts for Arrigo
- Halved parallelepiped and cube, with a note on a bedstead
- Rotating beam, inclined planes and an irregular pentagon
- Rod set diametrically across a circle
- Multiples 3 6 9 with a diagram of the earth's sphere
- Two mountains rising from the earth's circumference
- A moral maxim beside a set of concentric circles
- Equal Division of a Rectangle: a Equals b
- Perspective Studies of Hollow Parallelepipeds
- Water Jet from a Double Pipe
- Equal Divisions of Straight and Curved Rectangles
- Right and oblique solids: parallelepiped, cube, triangle
- Note on the friction of the timbers at a b
- Canal bridge, a wheel, and a square within a ring
- Balance with weights and a square inscribed in a circle
- On the bombard: degrees of velocity as fractions of a circle
- Velocity of bombards: fire, powder and weight of the ball
- Bombard diagram with measures of motion and a quadrant
- Pile-Driver Raised by a Man with Pulley and Rope
- Strength of square, triangular and right-angled screw teeth
- Centre of gravity of a suspended triangle divided in nine
- Wheel for Perpetual Motion: Proof of Impossibility
- Where a Suspended Rod Hangs: Centre and Obliquity
- Constructing the triangular balance
- Constructing the quadrangular balance
- Making a triangular balance
- A perfect circle touching a plane at a single point
- Triangular balance of three equal arms
- Squares inscribed obliquely within squares
- On Friction: Contact Area and the Wearing Compass Point
- On Friction: Why No Perfect Circle Can Be Drawn
- Double-proportion balance and centres of solid figures
- Weights of Pyramids on Equal Bases
Codex Forster III32 pages
- Square frame of four crossed rods, a circle at each crossing
- Pinwheel or vaned wheel (girandola)
- Part of a building; two pyramids hung at their centre of gravity
- Hexagon in a circle and sketches for building works
- Indeterminate Sketches: Hatched Form and Line Studies
- Ground Plan with a Note on Canals Behind the Houses
- Studies of Circles and Wheels, Possibly Mechanisms
- Jointed semicircles and a circle inscribed in a square
- Every angle of a triangle as centre of intersecting circles
- Pyramid suspended at its centre of gravity; circles
- Why a man sliding on ice does not fall
- Beam rotating in a quadrant: balancing a against b
- Bolt-Latch Rod and Vault Geometry Schemes
- Concentric Circles Crossed by Bundles of Rays
- Faint Rectangle on a Blank Page
- On the Doubling of Lights, with Sketches
- Recipe for aqua fortis and for casting a copper figure
- Superimposed Squares and Concentric Circles
- Simple Cube and Eightfold Cube
- A knife cutting a ball
- A square and a cube, with a note on showing a model
- Pythagorean theorem: squares with inscribed circles
- Pythagorean proof on sides 6, 8 and 10
- Finding the area of a circular segment
- Finding the surface of a sphere
- Finding the volume enclosed by a sphere
- Finding the area of a circle
- Finding a circle's centre from a chord and its sagitta
- Sketch of a leaf and a faint indeterminate figure
- Studies of 45-degree angles and two framed figures
- A beam rotating through a quarter-circle
- Geometry of a screw thread and its pitch
Codex Madrid I48 pages
- Gear-Tooth Contact, Leverage and Friction
- Proportioning Gear Teeth Between a Large and Small Wheel
- Linkages that Convert Lifting into Sliding Motion
- Springs, a Screw and a Quarter-Circle Among Machine Elements
- Springs and counter-levers acting on an iron catch
- Force as Line and Arc: an Eightfold Proportion
- The balance: equal weights and the angle of the cords
- Lifting a heavy body: spiritual and material levers
- Bending a body by a cord: powers of the motors a b c d e
- Rule to find the centre of the arc of right angles
- Dragging a weight of 12 with friction; the lever rule continued
- General rule for bending a heavy body about its pole
- Tapered Rollers, a Cord-Breaking Ratio, and a Mirror Template
- How Angled Cords Carry Extra 'Accidental' Weight
- Loads in the Three Cords of a Suspended Beam
- Loaded Struts and the Sharing of Weight on Supports
- The general rule of loaded cords proved on the triangle
- A glossary of geometry for the science of weights
- Screw and windlass: obliquity of the thread and lever proportions
- Statics of the balance: how a hung weight divides between two cords
- How a struck cube dilates into a circle
- The centre, the struck cube, and a man's leap
- Levers and Counterlevers: Real and Potential Arms
- Weights on Cords and a Screw for Forcing Things Apart
- Real and Potential Arms of the Balance; a Graduated Wheel
- Angles and Rectangles of the Balance: Real, Semireal, Potential
- The Three Right Angles of the Balance
- Teeth and their alignments in meshing wheels
- On teeth and toothed wheels: the square-tooth construction
- Dividing wheels into teeth and sizing wheels to pinions
- Heaps of falling powder and circular waves in a struck vessel
- Raising a beam: lever, counter-lever, and center of weight
- Finding the center of gravity of a triangular pyramid
- Force-pyramids and the true centre of gravity
- Balance puzzles and the centre of gravity of a quadrilateral
- Loads on Raised Members, an Arch's Thrust, and a Warning to Architects
- Centre of gravity of a triangle and a hanging pillar
- The three species of centres within a heavy body
- Centre of gravity of a triangular prism; dragging a beam
- Distribution of a hung weight between two angled cords
- Defining the line of motion and the line of gravity
- Accidental weight, called force; balance diagrams
- Cords, a struck cube, and the corded triangle a b d
- Transverse motion of a weight; lifting a long load by its centre
- Gravity toward the centre; balls falling by different slopes
- Descending balls and the dragging of beams
- Weights on cords and the collision of thrown balls
- Rule of Weights and the Compound Motion of a Toothed Wheel
Codex Madrid II118 pages
- Spanish title-page: treatises on fortification, statics and geometry
- Definitions of lines, angles and triangles
- Faint cutaway of a domed building with squared plan
- Faint cutaway of a domed building
- On Perspective: the eye and images on a wall
- Square Roots by a Semicircle, and the Fortress of Piombino
- Estimating the earthwork: cutting the hill and moat
- Dimensioned section of the hill and moat
- Quadrature (volume) of the pyramid
- Geometric Proof: Figures Equal to Their Squares
- A repeated impulse driving a suspended weight
- A Triangular Pyramid Is Half the Square Pyramid
- Pyramids Divided into Equal Triangular Solids
- Double the Height, Eight Times the Solid
- Sapping Trenches That Show the Enemy Fewest Angles
- Continuous and Discontinuous Proportionality
- On Proportion: Its Names, Members, and Three Species
- Commensurable and Incommensurable Quantities
- Proportionality vs Proportion; the Three Proportional Means
- Continuous and Discontinuous Proportionality
- On Proportion: Continuous and Discontinuous Proportionality
- Reducing Any Solid to a Cube
- Multiplying an Unknown Line by the Rule of Three
- On simple, composite, and decomposed local motion
- Near-blank recto (folio 54r) with show-through of a geometric solid
- Dividing a wedge into three equal pyramids
- A windmill, a wedge's centre of gravity, and mean proportionals
- A prism divided into equal pyramids
- Constructing a line equal to a segment's remainder
- Transmuting squares and rectangles into equal figures
- Near-blank verso with show-through of geometry
- Squaring circular portions into triangles
- Ten-pointed star with crescent lunes
- Squaring circular sectors and figures
- Quadrature proofs and the light of the moon
- On the mathematical sciences and their offspring
- Squaring Triangles and the Volume of Pyramids
- Solids on Square and Triangular Bases; a Retort on Birth
- Angles of the Balance and the Diagonal of a Cube
- The Center of Gravity of a Pyramid
- Dividing the Cube into Pyramids; the Two Mathematical Sciences
- The Pyramid as One-Third of the Cube; the Order of the Sciences
- Dividing the Cube into Six, Three and Other Fractions
- Similar Triangles in Quadruple Proportion; the Cube in Six Pyramids
- Scaling of Squares, Triangles and Pyramids by Multiplication
- General Rule for Cutting a Wedge
- The Wedge Cut and the Pyramid as One-Sixth of the Solid
- Dividing the cube: a tetrahedron is one-sixth of it
- The eye adjusting to light, and muscles in exertion
- Squaring the oval: a circle equal to an oval figure
- Faces changing with a man's emotions and toil
- Colour perspective in shadow; lowering a rectangle to a set height
- Recipe for imitation jasper and agate; a geometrical area proof
- Transforming rectangles and a theorem on equal triangles
- Wind striking a wheel; further rectangle constructions
- Squaring the Gnomon and Equal Curved and Straight Parallelograms
- Circles Quadruple to One Another and the Proportion of Lunes
- Surfaces of Double and Quadruple Proportion Superimposed
- Quadrature of lunes: crescents equal to rectilinear areas
- Curved-sided triangles equal to a straight-sided figure
- Common measure of line a c and a doubling number series
- Equating a Curvilinear Right Angle, and a Retractable Bridge
- Faint sketch for laying out a screw thread
- Marking out a screw thread by hand
- Squaring the circle by 196 sectors
- Volume of a truncated pyramid and squaring the circle
- Squaring the sectors of quadruple circles
- Proving two surfaces equal without motion
- Turning a straight pyramid into a curved one by motion
- Postulates and common notions for a geometry of surfaces
- Rule of proportion for equating parts of unequal circles
- Surfaces in triple ratio: uncovered areas and squaring
- Squaring a curvilinear triangle from lunes and segments
- Conceptions on the equality of superimposed surfaces
- Bisecting any angle and the mean proportional of circles
- Quadrature of curvilinear figures by superimposed segments
- On the equality of unequal surfaces; squaring the lunula
- Turning triangles between rectilinear and curvilinear form
- Squaring the Circle: the Science of Equalization
- Squaring Curved Triangles by Ratios of Circles
- Equal Areas by Cutting and Shifting Parts
- Squaring Curved Triangles from Circles in Double Ratio
- Curvilinear Triangles Equal to Any Rectilinear Triangle
- Squares and Triangles Made Equal Between Parallels
- Squaring a Curvilinear Figure Equal to a Rectilinear One
- Triangle and Square Between Parallel Lines
- Cutting a Ninth of a Circle Between Two Parallel Lines
- Portions and Sectors in Proportion
- Squaring the Triangle of Three Curved Sides
- Lunes, Quadruple Portions, and the Root of Ten
- Squaring Lunes and Dividing Circular Portions into Sevenths
- Dividing the Lune and Squaring a Fraction of a Square
- Squaring Curved Figures; a Note on Etching Plates for Print
- Pyramids and Wedges Bisected by Semicircle Peripheries
- Diagrams of Equal Lunes and Divided Circles
- The Cube's Diagonal in Sesquialteral Proportion
- Dividing a Cube into Pyramids and Their Weights
- Circle divisions and a hatched triangle (geometry)
- Circular sectors, semicircles, and crescents made equal
- Two equal semicircles divided into equal parts
- Transforming circular segments with fractional ratios
- Dividing circular portions into 3 and 5 similar parts
- The tip of a pyramid: squaring and cubing its fractions
- Squaring and dividing curved-sided triangles (falcate)
- Angles inscribed in a circle; squaring curved-sided pyramids
- Squaring the lune; equating curved and rectilinear triangles
- Field survey: a polygon plotted by bearings and distances
- Sheet of geometric studies: lunes, vaults and radial plans
- Motion on an incline; curved-figure and radial-plan studies
- Dividing a Semicircle into Curvilinear 'Pyramids'
- Cutting a Third from a Semicircle Between Parallels
- Superposition of Equal Surfaces, Curved and Straight
- Kinds of Percussion, a Kite's Descent, and Squaring a Curve
- Constructing an Equilateral Triangle on a Given Line
- Euclid's common notions: the axioms of equality
- Quadrilaterals, parallel lines, and the five postulates
- The circle, semicircle, segments, and kinds of triangle
- Euclid's definitions: point, line, surface, and angle
Codex Urbinas (Treatise on Painting)50 pages
- The Book of Painting: Whether Painting Is a Science
- Painting Versus Poetry, and the Principles of Painting
- The Book of Painting: Title Page and Opening Chapter
- Painting Compared to Poetry, and Its First Principles
- Painting's Principles: Plane Surface, Shadow, Perspective
- Astrology Born from the Eye; the Painter Disputes the Poet
- Painting as a Mental Science; Painter, Poet, and Musician
- Painting a Mental Science of Shadow, Light, and Form
- Why Miniatures and Paintings Need Different Finish
- The Brightest Part of a Reflection, and the Red of Flesh
- Three motions in a man's leap; the endless aspects of a limb
- The Compound Derivative Shadow and Its Boundaries
- How Primitive and Derivative Shadow Are Joined
- The figures of derivative shadow and its swift motion
- When a shadow lags, matches, or blurs beyond its body
- Reflection, augmented shadow, and simple shadow's darkness
- Greater light, greater shadow; death of the derivative shadow
- Three natures of derivative shadow; the sphere's simple shadow
- Light and Shade: Shadow Cast on a Sphere, with Diagrams
- The Darkest Shadow and the Largest Luminous Angle
- Where the First Light and First Shadow Fall on a Sphere
- Reflected Light and the Shadow Under Building Eaves
- Equal Shadows from Luminous Bodies of Different Sizes
- Lighting a Shadowed Sphere; Colour of Painted Shadows
- An Opaque Surface Between a Black and a White Object
- When a surface is evenly lit: three geometric demonstrations
- The brightest point on a screen: shadow and light pyramids
- How a man's shadow changes as he moves or bends
- Degrees of shadow and light cast by a window on a body
- Light of window and sky-horizon falling on a shaded sphere
- Angles of least light and the shadow directed to one point
- Horizon circle and window: light lines crossing at its middle
- Every shadowy body lies between a dark and a bright pyramid
- Crossing lights on a sphere; when the eye can see no shadow
- The Shadow of a Sphere and When the Eye Can See It
- Darkest Point of a Sphere Lit by the Sky-Hemisphere
- Edges of Light and Shade; the Highlight That Moves with the Eye
- Which parts of a sphere are most and least illuminated
- How Equal Arcs of the Sky Light a Sphere Evenly
- Why the Shadowed Sphere Is Darkest Where It Sees Most Earth
- How Greater Light Lights a Greater Part of the Sphere
- Placing Shadows and Lights on a Faceted Body
- Light on an Octagon's Faces by the Angle of Incidence
- Why Forks Bulge Outward: A Three-Circle Proof
- On the Horizon: the Nile's white distance and the perspective pyramid
- The horizon of sky and earth in perspective
- Why the horizon never sits at the eye's height
- The horizon on a spherical earth and at sea
- Book on Painting: Whether Painting Is a Science
- Painting versus Poetry; First Principles of Painting
Codex on the Flight of Birds5 pages
Paris Manuscript A31 pages
- Finding roots and measuring areas by geometry
- Measuring a tower by its shadow; strength of bundled ropes
- Leaning beams and canes: geometry of the right angle
- Perspective Propositions and the Bisected Right Triangle
- Dividing the Circle: Inscribing Regular Polygons
- Dividing the Circle and Building an Octagon from a Square
- Triangle Subdivisions, Concentric Circles, and Eyeglasses
- Dividing triangles by their midpoints into proportional parts
- Inscribing a hexagon and pentagon; area of a quarter-corona
- Nested squares and circles in geometric ratio
- A triangle in a rectangle always fills half its area
- Squares and circles that hold four equal copies of themselves
- Screw threads, a weighted bellows, and compass constructions
- Geometry: radius of an arc, a perpendicular, and a self-stopping door
- Geometry: dividing a line and inscribing a hexagon
- Geometry: dividing lines and finding an arc's radius
- Geometry: constructing a triangle, a square, and a pentagon
- Geometry: naming and grading the degrees of angles
- Measuring a rope's length with proportional triangles
- Measuring the earth's center and the size of the sun
- Measuring the sun's height and distance from two hilltops
- Blow and weight: balls in corners and a cube-doubling method
- Inclined-plane motion, bending beams, and hurled bodies
- Perspective Screens: the Square, the Line, and the Point of Diminution
- Measuring the Diminishing Visual Pyramid with a Rod
- How the Eye Sees Simply: Flat versus Curved Perspective Screens
- Geometric Figures for Perspective and Foreshortening
- Inscribed Polygons Tilted into Perspective
- Perspective diagrams: octagon, gridded circle, and vanishing point
- Equal figures on a semicircle; the twenty-times rule
- Finding the eye's height and distance in a perspective square
Paris Manuscript B18 pages
- Painted Fruits and Vegetables with Ornamental Letters and Plans
- Vault geometry, a glass-bell casting and river-crossing floats
- Ducal garden pavilions and a square-bastion fortress
- Octagon constructions and a lockable square house
- Dividing the circle, a geared mechanism, a lamp and a violet
- Constructing a pentagon and an equilateral triangle
- Flower study, a pentagon construction and soldering lead roofs
- Finding circle centres, an octagon, and a divided triangle
- Machine for raising columns, and how an arch loads its columns
- Dividing a circle into equal parts; a crossbow and composite beams
- Dividing a circle into seven, and a chamber of eight mirrors
- Constructing a nonagon; a cross-lap timber joint and river-bank roads
- Latin Arms-Names and Dividing a Circle
- River spur, weir facing, a stone auger, and fast earthworks
- Measuring heights and distances with a ground square; fire trebuchet
- Measuring a river's width; barrels rolled down a slope in defence
- Centralised temple: plan and dome, with a twelve-faced variant
- On the Nature of Force; Weight of a Beam Between Two Walls
Paris Manuscript C15 pages
- How light and shadow fall on bodies: primitive and derivative shadow
- How shadow varies when light is larger than or equal to a body
- Forked shadows from a pyramidal opaque body
- Uniform shadow, and shade sharper far from the light
- Why bodies near the horizon look larger; sunlight through a chink
- Small light gives sharp shadows; the speed of a cast shadow
- Graded light along the penumbra of a large light source
- Shadows Cast by Four Lights and Four Bodies
- Overlapping Shadows Doubling in Darkness
- Rays Through an Aperture and the Kinds of Shadow
- On Shadow: Primary and Derivative Light on Spheres
- Cast Shadows and Their Central Axes
- Cast Shadows and the Blue of Distant Things
- When a Shadow's Shape Follows Body or Light Source
- Mixing Two Shadows: Perfect and Imperfect
Paris Manuscript D2 pages
Paris Manuscript E51 pages
- Cones in a cube, squaring the circle, and weights on planes
- Backgrounds of Painted Figures and a Perspective of the Four-Sided Wall
- Cords Hanging Between Pulleys and the Pull of the Sag
- How a Hanging Weight Divides Along a Cord and an Angle
- Force and Accidental Weight: the Lever, the Spring, and Rectangles
- Geometry: Superposed Equal Surfaces and Transforming a Square
- Geometry: Pyramids, the Cube's Three Roots, and Pythagoras
- Mechanics, Paradise of Mathematics: Wax Shaped into a Pyramid
- Geometry: doubling a sphere and dividing a triangle by proportion
- Geometry: proportional parts of a triangle cut parallel to its base
- Geometry: turning a square into a rectangle of given length
- Geometry: bisecting a triangle with one cut parallel to its base
- Squaring the circle by rectifying the semicircumference
- Ring-Pipes Bisected by Their Diameter
- Squaring the surface of a sphere by rectilinear motion
- The true rule for squaring any portion of a circle
- Compound motion applied to squaring a circular sector
- Squaring surface a b c d in ten staged figures
- Six rules for the quadrature of the circle
- The Perfection of the Cube; Friction of Pulleys on Their Axles
- Squaring the Oblique Triangle; Measuring the Sphere of Water
- Dividing a line into equal parts by a triangle
- The pyramidal shadow and kinds of derivative shadow
- The three natures of derivative shadow
- Squaring a circular sector; balance and pulley mechanics
- Apparatus for a great ventilator, and pulley-cord levers
- The Descent of Birds: Simple and Compound Obliquity
- A bird outracing the wind along a square's diagonal
- A bird twice as fast as the wind: oblique gliding
- A classification of motions: straight, curved, and spiral
- How a Bird Climbs on the Wind Without Beating Its Wings
- The Bent Wingtip: Condensing Air and the Circle c d b r
- Bird flight: wing feathers, landing, and steering in the wind
- Measuring a river's width by triangulation
- Solid Geometry: The Cube Divided into Pyramids
- On Gravity: Locating the Balance's Fulcrum
- Weight and force: the potential lever and infinite division
- On the cord: a weight at the center of a horizontal rope
- On weights and cords: real and potential angles
- On gravity and the cord: levers, counter-levers and angles
- Demonstration of the weight of the arched cord
- Where the arched cord separates from its pulley
- Gravity: the intercentric line through a suspended weight
- On weight: the central line of gravity in suspended bodies
- On weight: oblique cords and the axis of the force triangle
- Dividing a suspended weight between two cords by geometry
- The plumb-line of a weight resting on a slope
- The question of weights on inclined planes
- The Friction of Weights on Sloping Surfaces
- On Friction: Level, Sloping, and Calculated
- The Center of Gravity of Uneven Bodies
Paris Manuscript F22 pages
- The Convex Mirror: Why Reflection Has No General Rule
- The figure of the elements: refuting Plato's solids
- Five Regular Solids: Why a Cube Rolls More Than a Pyramid
- Is a River's Surface Spherical? Water Along Arc and Chord
- A wind-rose of directions and obliquities for the water book
- Order of the book: describing water jets by the four winds
- Motions of Water and the Doubling of the Cube
- Centre of Gravity of Pyramids and Quadrature of the Cube
- Water outlets of different shapes and their discharge
- A half-cylinder into a half-cube, and an agate recipe
- Transforming a cube into a rectangular prism
- Making a cube from a quadrilateral prism
- Cubes double one another: the diagonal cut
- Doubling the cube: a mental, not instrumental, proof
- To make a cube double or half another
- Perspective: the axis of the angle of incidence on a cylinder
- Do Bodies Weigh More in Air Than Under Water?
- Angle of Contingency; Why the Sea Seems Higher than Land
- The Sun's Image in Curved Mirrors; Defining Half-Obliquity
- The Light of the Moon and the Forms of Solar Rays
- Why the Sphere of Water Is Perfectly Round
- Why Two Vertical Towers Lean and Topple Together
Paris Manuscript G52 pages
- Tree-trunk swellings, a parallelepiped, and impact of motion
- The heart as a muscle, a triangular pyramid, and Mombracco stone
- Head of a Horse; a Horse Running Through Water
- On Proportion: Doubling Circles and Squares
- Geometry of the Triangle; Ropes in Pulley-Blocks
- On Trees: How Foliage Rounds Off at a Distance
- Perspective of a rhombus and the reading of light and shade
- On painting: bodies should not be outlined
- Quadrature of the spherical surface
- Weights on inclined planes and quadrature of the hemisphere
- Weight on Two Cords; Squaring and Cubing the Sphere
- Doubling of Concentric Circles and Squares
- Self-Feeding Oil Lamp; Division of a Pyramid
- Squaring the surface of a sphere, and cubing the solid
- Squaring the lunes; a water-driven template machine
- A mercury siphon clock; drawing a circle through concurrent lines
- Instruments for shaping templates and a rasp lathe
- Water-wheel machine for polishing a concave form
- The power of the voice, and constructing very large circles
- Geometric constructions for large arcs, and a furnace varnish
- Divisions of Solids: Pyramids Within Cubes
- Subdividing a great disc into 57,600 squares, and its gilding cost
- Geometry: Squaring Lunes with Triangles, Circles and Ovals
- Geometry: Sinuous-Sided Triangles Equal to Straight Ones
- Parity Rules, and Squares Equal to Lunes
- Geometry: Dividing a Circle's Circumference into Equal Parts
- Geometry: Squaring the Circle with Irregular Lunes
- Geometry: Crescents Proved Equal to Triangles
- On the Squaring of the Semicircle
- The Four Kinds of Parallel Space
- Squaring the Circle by Cone, Cylinder and Sphere
- Why a Cone's Surface Cannot Equal Its Base
- Cones and the surface of their base circle
- Rolling a cone and a cylinder out onto a plane
- Toward the quadrature of the circle: sphere, cylinder and cone
- Unrolling the cone and squaring the circle
- Squaring Lunes: Circle Sectors, an Inscribed Square and Equal Areas
- On the Cubature of the Sphere
- Resolving the Spherical Body into Pyramids
- Rectifying the Surface of a Shield-Shaped Body
- Rectifying the Hemisphere and Half-Oval
- On Quadratures: Squaring the Sphere and the Cone
- Colliding Winds; Doubling Squares, Circles and Lunes
- Squaring the circle: lunes and doubled circles
- Why drawn iron wire curves and twists
- Experiment of the Balance: Rest About the Fulcrum
- Equal Weights on Equal Slopes Stay Balanced
- Covering a sphere of four braccia with parallel plates
- Roller machine with pyramidal beams for shaping plates
- How Wind Forms, and Why a Cloud's Shadow Outruns It
- Squaring the circle; a water-raising machine and pulleys
- Mechanical measurements, a ruler, breathing, and mathematics
Paris Manuscript H6 pages
Paris Manuscript I47 pages
- Dividing a line and turning a triangle into a parallelogram
- Perpendiculars, parallels and squares built on a given line
- Squares on a divided line and tangents to a circle
- Squares on a divided line, with worked numerical examples
- Rational and medial products on a divided line
- Dividing a line: the gnomon and the square of the whole
- Bisected line extended: rectangle plus square equals square
- Squares on a line divided into 8 and 4 (Euclid II.7)
- A line extended, and the square on 16 (Euclid II.8)
- Proving Pythagoras: the 3-4-5 triangle and squares on the sides
- Equal squares on an isosceles right triangle: a congruence proof
- The gnomon and Thabit's theorem ('De Tebit')
- Products as areas: squares, rectangles, gnomons, Pythagoras
- Multiplying lines to form rectangles
- Dividing a line and its square into three parts
- Fourth: a line of 12 divided into 4 and 8
- Line of 12 split into 8 and 4, with diagonal construction
- Corollary of the fourth: square split into two rectangles
- Dividing lines, gnomons and decomposed squares
- Line divisions and figures of the Pythagorean theorem
- Right-angled triangles and the doubling of a square
- Perpendicular from a circle's centre onto a chord
- Two chords crossing off-centre inside a circle
- Intersecting circles, with the rule of branching trees and waters
- Geometry: Tangent Circles and Groups of Crossing Lines
- Circle Constructions and a Water-Filled Pipe
- A Pipe Projecting Water, and Lines Drawn to a Circle
- Quadrilaterals Inscribed in Circles
- Geometry of angles inscribed in circular segments
- Circular-segment dispute with knot and chain sketches
- Circle theorems: chords, secants, tangents and Pythagoras
- Cubes on a triangular prism, Pythagoras, and tangent-secant circles
- Tangent and secant of a circle; the Pythagorean theorem
- On luminous rays and the power of their extremes
- Circle and square; infinite slowness and speed of motion
- Optical study: rays converging on a circle (a, a, b)
- Shadow of a Pyramid, with a Friction Study
- Pendulum and beam: indeterminate figures
- Geometry: circles, squares, Pythagoras and cubes
- Why a sphere seen with two eyes never looks perfectly round
- Bouncing as reflected motion; a wheel divided into sectors
- Where a loaded wheel and rings suffer the most strain
- Multiplication sums and an indeterminate figure
- On the proportion of motions, powers and resistances
- Latin adverbs and small geometric sketches
- Allegory of Il Moro with geometry and a prophecy of jackdaws
- Lunes of a square in a circle, with a profile head
Paris Manuscript K127 pages
- Two equal semicircles and a circle divided by curved lines
- Parallelogram within a parallelogram; three joined parallelograms
- Rectangle cut by its diagonal, with two complements
- Polygons and triangles compared by side and area
- Circular segments in continuous proportion
- Three polygons with matched homologous sides
- Pentagon divided into three triangles
- Two pentagons and three measured triangles
- Triangles and a segment: a proof of proportionality
- Faint study of proportionally divided line segments
- Faint geometric figures: squares, triangles, diagonals
- Line segments divided in continued proportion
- Circle-arcs, segments and joined rectangles
- Joining Equal Angles; Parallelograms on Triangles
- Equal Rectangles with Reciprocally Proportional Sides
- Dividing a Long Line in the Same Proportion as a Short One
- Cutting Any Part from a Triangle with One Compass Setting
- Mean Proportional Found by Parallels in a Triangle
- Right Triangle in a Semicircle and the Mean Proportional
- Right Triangle with Proportional Measures, and a Rhombus
- Two Triangles Have Six Angles, or Three Pairs
- Three Triangles, Two Sharing a Single Base
- Fifth Figure: Converse of the Preceding
- Two Triangles Within a Triangle, Cut in Proportion
- Triangle with Interior Lines and Equal Angles Marked
- Faint charcoal geometry: triangle with a five-pointed star
- Proportion in a double triangle cut by a parallel
- A triangle cut by a parallel to its base
- Parallelogram decomposed into triangles and rectangles
- Parallelograms side by side between two parallels
- Rectangle superimposed on a square; three segments
- Two Quadrilaterals in Proportion
- Two Triangles in Discontinuous Proportion (Euclid, Book VI)
- Table of Proportional Numbers
- Segments Divided in Ratio
- Three Triples of Segments: Indirect Proportion
- Three Triples of Segments: Direct Proportion
- Converse and ostensive proportion
- Compounded and separated proportion
- Proportion figure valid for two conclusions
- Cutting equal parts from the greater magnitudes
- Compounded proportion (congiunta)
- Multiple ratios (multiplici)
- Multiple and Submultiple Ratios on Divided Lines
- Ratio Tables Serving Algebra (Sets 201 and 212)
- The Four Operations on a Proportion (Series 191)
- Proportional Points Along Ruled Lines (Series 171)
- Ratio Table and the Alternate Proportion (Series 161)
- A Line Divided into Equal Multiples (Series 151)
- Proportions among labelled line-segments (a-d)
- Proportional segments with bracketed group sums
- Line-segments in quintuple proportion (quincupla)
- Segments L and h as multiples of a and b
- Grid of proportional line-segments (K, h, g...)
- Unmeasured proportion grid: lettered segments only
- A Line Divided at Points a, b, c
- A Line with the Dividing Point c
- The Eighth Rule: Multiples in Continued Proportion
- Line-Segments in Proportion: c Drawn Twice
- Divided Lines d-h-e-K with Proportional Parts
- Table of the fifth proportion and quadruple ratio
- Table of the multiples of multiples
- Table of the fourth proportion with quadruple ratios
- Table of multiples: double, triple and sextuple ratios
- Table of the second proportion
- The augmentative lever, with named curves
- Euclid, Book V: the definitions of part and multiple
- Equal triangles and the squares upon their bases
- Figures for the Pythagorean theorem
- Squaring the oval solid; a note on Aristotle
- The lenticular solid is one third of its cylinder
- Parallelograms on equal bases between parallels are equal
- Triangles on the Same Base Between Parallels Are Equal
- A Parallelogram Is Double a Triangle on the Same Base
- Quarter Circle with an Inscribed 32-Sided Polygon
- Turning a rectangle into an equal-area square
- Geometry of Lunes: Semicircles, Sectors, and Triangles
- Faint geometric sketch: polygon inscribed in a circle
- Hexagon inscribed in a circle
- Constructing a pentagon inscribed in a circle
- Triangles in two internally tangent circles
- Blank leaf with faint contact impressions
- Tangent and secants to a circle from an external point
- Circle with Tangent and Secant; an Analogous Figure
- Combining Several Squares into One
- Semicircle on a Rectangle's Base plus Height; a Pythagorean Figure
- Triangle Divided by its Altitude; Squares on Two Sides
- Obtuse Triangle with Perpendicular on a Produced Side
- Joining a Larger and a Smaller Square
- Geometric Algebra: the Ninth and Tenth Demonstrations
- The Eighth Demonstration: Squaring 8 + 4 + 4 into 256
- The Seventh Demonstration: Squaring 12 = 8 + 4 into 144
- The Sixth Demonstration: Squaring 6 + 4 into 100
- The Fifth Demonstration: Squaring the Line 6 = 4 + 2
- The Fourth Demonstration: A Square of 12 Split into 48 and 96
- Dividing a Line, Rectangle and Square into Numbered Parts
- Defining the Straight Line and the Four Kinds of Angle
- Straight versus Curved Lines, and the Center of the World
- The Circle as a 'Parallel' Figure; Equal Triangles on a Base
- Squaring the Circle: Sixteen Sectors Rectified
- A Partitioned Rectangle and Circular Rings
- Lune and sector figures, with a note on the ox-bristle
- Squaring an annular band against a triangle
- A lune made equal to a circular sector
- The doubled lune, squared like the last
- Straightening the curve of a semicircle
- The roots of numbers marked along a line
- Transmuting an obtuse triangle into a right triangle of equal area
- Cutting from a larger triangle an area equal to a smaller one
- Triangles on the same base are proportional to their heights
- Two triangles double a third are equal in area
- Triangles of equal height are proportional to their bases
- Cutting from a sharp-angled triangle a part equal to an obtuse one
- Dividing a Semicircle into Proportional Parts
- The Rule of Subtracting Four to Divide a Semicircle
- Of What Number Is Four the Three-Quarters?
- The Three Centres of a Pyramid
- Trisecting a Circular Portion, Concluded
- Trisecting a Circular Segment by Construction
- Dividing a circular segment into four equal parts
- Equalizing opposed triangles by swapping their bases
- Making two unequal triangles equal in area
- Proof that inverse base-height ratios give equal triangles
- Triangle of Curved Sides: Counting Similar Triangles
- Water Courses, a Fountainhead, and Arcs in a Square
- The Swiftest Channel Section Is a Half Circle
- A sphere equal to the pupil is always seen as half
Paris Manuscript L22 pages
- The pupil, the blowpipe, and a divided quadrilateral
- Triangular figures, a water-filled vessel, and a driven wedge
- Ropes on pulleys, a labelled casing, and rectangular figures
- Friction on the inclined plane
- Beams, Lattice-work and Lettered Broken Lines
- Spherical Weights on Inclined Planes; a Two-Hammer Bell
- Proof of the Obliquity of Gun-Embrasures
- The Laws of Impact and Reflected Motion
- Why an Oblique Shot Fails to Pierce a Wall
- The Dents Left by a Ball Striking at Angles
- The Splayed Embrasure Hardest to Storm
- Comparing Embrasures: Wide Mouth versus Wide Within
- Geometry of artillery fire: shots kept within the angle
- Military architecture and a diagram of artillery fire
- Why doubling a figure needs more than doubled power
- Flax dedicated to death and corruption
- Geometric diagrams with untranscribed notes
- Finding the cube root of 81 by a rectangle rule
- Rule of power; plan of the fortress of Urbino
- Windmill Parts, a Divided Square and a Compartmented Beam
- Land-Measure Units and a Water-in-Sunlight Experiment
- A Column Under Load, a Subdivided Square and a Colour Note
Paris Manuscript M86 pages
- Opening leaf: ornamental 'M' with geometric figures
- Classification of triangles by angle and side
- How the three triangles derive from three quadrangles
- The long tetragon and the two kinds of rhombus
- The rhomboid defined; parallel lines
- Equal triangles and the axiom of whole and part
- Geometry sketches: triangles, a rhombus, and nested figures
- Euclid's five postulates
- Parallel lines from opposite ends of the world, after Ptolemy
- Continuous and Discrete Quantity Compared
- The Five Postulates of Geometry
- Transversals Across Lines, Arcs and Circles
- Perpendiculars, a Subdivided Square, and 'On Local Motion'
- Decomposing the Square: Gnomon and Supplements
- Commensurable Sides and Square Numbers
- Naming the Angles of Isosceles Triangles
- Square Numbers and Continued Proportion
- Isosceles Triangle by the Common Notion of Equals
- Thabit: Triangles Built on Intersecting Circles
- Commensurable Quantities and Their Common Measure
- Segments Marked with Numbers and Letters
- Point, segment and triangle constructions with circled figures
- Segments and a circle with the axiom on equal magnitudes
- Continuous and discontinuous proportion; dividing a line
- Dividing a line from an external point; the straight line defined
- Experiments with triangular paper cut-outs; Euclidean notions
- Superposed triangular cards and equality of remainders
- Squares, roots and surds; a triangle with extended sides
- The nine common notions (Euclidean axioms)
- Right angle in a semicircle; angles on a line
- Squaring segments and forming rectangles from products
- Geometry is infinite; the arithmetic of discontinuous quantity
- Plane geometry: triangles, a rhombus, and line segments
- Geometry of rectangles and squares with computed areas
- Note on opposite angles formed by two crossing lines
- Constructions on angles, triangles and a circle
- Squares on a triangle's sides and an 'irrational' height
- Rational and irrational lengths from a semicircle
- Isosceles Triangles and an Extended Base
- Opposite Angles Where Two Lines Cross
- The Seventeenth: Right Triangles with a Line to the Base
- The Triangle Inequality: When Two Sides Fall Short
- Refuting Unequal Sides in Nested Isosceles Triangles
- Constructing a Triangle from Three Given Lines
- Constructing an Angle Equal to a Given Angle
- Roots, Medial Lines and the Number 108
- Comparing the Angles of Similar Right Triangles
- Isosceles Triangles: Angle a Exceeds Angle d
- Commensurable Surfaces and Medial Lines
- Congruent Triangles by Equal Base and Angles
- Coalternate angles between parallels dc and fK
- Coalternate interior angles are equal
- Refuting the equality of coalternate angles
- Diagrams of parallel lines and interior angles
- Constructing a parallel through a point
- Proportional rectangles with root magnitudes
- Irrational roots, triangle angles and polygons split into triangles
- The exterior angle of a triangle equals the two opposite angles
- Angles about a point and the exterior angles of polygons
- Exterior angles of a triangle and the five-pointed star
- Squares on a right triangle and parallelograms between parallels
- Parallel lines cut by diagonals and equal parallelograms
- Rectangle divisions, a triangle in a semicircle, paired numbers
- Parallelograms between parallels and the equality axiom
- Squares and a trapezoid between parallels
- Constructing a square equal to a triangle
- Triangles of equal height and equal-area parallelograms
- Equal Arms by the Circle: an Equals ar
- Oblique motion still grows in arithmetical proportion (prism figure)
- Pyramidal Proof That Motion Grows in Arithmetic Proportion
- Range of a Culverin and How to Measure It
- The pyramidal law of accelerating fall
- Two Surfaces of Equal Area but Different Shape
- Parallel figures compared, and the law of motion
- The Crossbow's Diminishing Force and a Subdivided Triangle
- Two graduated staves bowing equally under weights 1 and 8
- A tree's branches sum to its trunk's cross-section
- The Five Regular Solids, with a Tercet
- How angled barriers divide a projectile's impact
- Page of notes with small diagrams (text not transcribed)
- Dividing a triangular "pyramid" into two equal weights
- Removing weighted pieces of a pyramid by squared fractions
- When two curved lines meet: parallel arcs and "curved pyramids"
- How Infinite Lines Can Meet at a Single Point
- Parallel Curved Lines and Concentric Circles
- Angles Around a Point Equal Four Right Angles
Ashburnham I (ex-Ms A)19 pages
- Opening leaf: mirror-script with a circle-and-center figure
- Cone rising from a circle to a single point
- Crossing cones of vision with balance and angle figures
- Line, plumb and triangle figures with directional arrows
- Suspended Geometric Figures for Centres of Gravity
- Perspective Study of an Interior with an Oculus
- Linear Perspective and the Diminution of Forms
- Faint Perspective Constructions and Offset Impressions
- Perspective Projection of a Square and Circle with a Star Figure
- Rays radiating from a circle; study of light or vision
- Perspective study: a square and circle projected to a point
- Weight on a balance arm swung through a graduated arc
- Projection of spheres to a plane; optics of light and shadow
- Geometry of Shadow: Three Spheres under a Luminous Semicircle
- Shadow within a Cylinder beneath a Luminous Arc
- Geometric Diagrams of Proportion
- Full page of Leonardo's mirror-script prose
- Isometric triangle grid with stepped solid and knots
- Rosette of overlapping circles with interlace friezes