Codex Atlanticus565 pages
- Odometer and pedometer: machines that measure distance
- Large Excavating Machine and Earth-Moving Weights
- Large Hoisting Machine and Ditch Measurements
- Water-wheel driven by a river to grind mills
- Faint mechanisms with numbers and fractions (verso)
- Machine for drawing iron into cannon barrels
- Column of Figures with Faint Mechanical Sketches
- Geometry, calculations and machine studies
- Automatic Goldbeating Hammer Driven by Geared Wheels
- Studies of Levers, Pulleys, Gears and Proportion
- Wire-drawing machine and the power of percussion
- Weighing materials, poisoning trees, and a water clock
- Water clocks and a meditation on measuring time
- Hoisting a great weight and the squaring of triangles
- Squaring the circle: hexagons, bi-angles and proportional circles
- Column of calculations with small mechanical sketches
- Seven cannon and falcon barrels with their dimensions
- Five culverins of graded size with their dimensions
- How water rises and flows under pressure: cisterns and canals
- Mean proportionals, roots and the quadrature of circles
- Weighing the force of a blow: percussion experiments
- Firing props to collapse a wall; cube-root scale
- A wheeled war-engine and the Pavian mill
- The Law of the Balance: Beam, Arms and Counterweight
- Gear Trains, a Bombard Hoist, and Time Reckonings
- 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
- Friction and counterweight in balanced weights
- A gear train to multiply motion, force and heat
- Water-driven mills and the weight of falling water
- Studies of machinery and a bombard carriage
- Compound pulley-blocks and a crossbow-spanning device
- Anti-scaling defence engine for a bastion
- Columns of household accounts in lire, soldi and denari
- Winding Machine, Balanced Weights and Calculations
- Silk-Doubling Machine and a Perspective Instrument
- Hoisting Wheels, a Mile-Gauge Gear, Sums, and Rain-Light
- Balances, weights and motion, with sums and expense notes
- Gear-trains and a bombard, with multiplication tables
- Measuring Distances by Sighting with the Eyes
- Fortress towers and bastions, with a column of sums
- 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
- How the size of a light governs a body's shadow
- Fortress Design: The Castellan's Total Surveillance
- Compound lever press and the multiplication of force
- 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
- Toothed wheels, proportional circles and gear contact
- Scattered numbers and multiplications
- Mechanical studies with a multiplication (300 x 25)
- Gearing, hung weights and a press, with a multiplication
- Combinations of numbers and a treatise-plan on percussion
- A sheet of arithmetical calculations, with a small plan
- Wage Accounts for Benedetto and Ioditti; a Stone-Saw
- On the Nature of the Surface: Boundary of Body and Air
- Studies of Falling Water Drops, Splashes and Motion
- Rules for Compounding and Dividing Fractions
- Fraction Arithmetic and Methods of Moving Earth
- The Division of Fractions
- Rules for Multiplying, Adding and Subtracting Fractions
- Friction of a Pivot and the Balancing Counterweight
- Proof of the Counterweight Calculation for a Pivot's Friction
- Computing the Counterweight of a Pivot's Friction
- Weights of the elements and the crest of a wave
- Friction of bodies equals a quarter of the weight
- Plan of Milan: Gates, Distances and the City's True Centre
- Definitions of the circle and quadrature of curved surfaces
- Dividing one circle into nine equal circles
- Descent and Soaring of Birds, the Echo, and Rivers Moving Gravel
- The four elements weighed, with number tables and water chapters
- Water issuing under pressure from spouts
- Counterweight for a lever's friction, with a dissection note
- Friction, counterweight and the elements of machines
- Twenty-two quadrature figures, with memoranda and sums
- Squaring the Circle: Lunes and Inscribed Figures
- 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
- The centre of a suspended body lies below its support
- Balancing composite arms of a balance against each other
- The lever law: weight against distance from the fulcrum
- Squaring lunes and curvilinear triangles; calculations
- 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
- Squaring the Circle by Rosette Portions
- Two Mean Proportionals and Cube Roots
- Mean Proportionals by Similar Triangles
- Circle Sectors and Solid-Figure Studies
- Doubling the cube and squaring lunes and circles
- Proportions of circle portions in nested and intersecting circles
- 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
- Studies in squaring lunes: crescents made rectilinear
- Flat tube-ceiling, a beam hoist, and radial arch diagrams
- Quadrature of the circle: portions and lunes
- Quadrature studies: lunes and proportional circles
- Squaring the circle, an inheritance problem, and perspective studies
- Weights, plumb-lines, and squaring the circle
- The Nile's source and the great rivers of Asia
- Squaring the circle: lunes, rosettes and curvilinear octagons
- Squaring curved figures: lunes, circles and transformed spirals
- Circle-square proportions and construction of square roots
- Quadrature of lunes and curvilinear surfaces
- Mostly blank verso with a later column of numbers
- Weights on rods hung by cords; centres of gravity
- Balances, cord bends, and pulleys multiplying weight
- Proportion exercise: equalizing the ratio of 6 to 2
- The three centres of a tapering rod (pyramid)
- A rod on two cords: shifting one cord toward the middle
- How a cord's angle changes the load on it
- Quadrature of the circle: inscribed circles, lunes, and roots
- Studies on squaring the circle: lunes and nested circles
- Dividing lines and circles into equal parts; squaring the circle
- Balances, counterweights and the compound lever
- Equilibrium of Balances and Systems of Pulleys
- Balances of Proportional Weights and Divided Beams
- 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
- Squaring the circle: circles, squares and octagons
- The greatest quadrilateral in a right triangle
- 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
- 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 the Circle: Lunes and Circle-Portions
- Geometric Construction with Calculations and Memoranda
- Strength of beams: length, thickness and weight borne
- Quadrature of the Circle: Lunes, Squares and Diameters
- Squaring the circle: sectors, chords, and Archimedes' rule
- Quadrature of lunes and transformation of areas
- Pulley blocks: the cord must run perpendicular to the axle
- Block and tackle: trading weight for time and speed
- The Strength of Supports and the Scaling of Loads
- Why Lightning Bends: Motion from Dense to Rare Air
- Solid Geometry of Pyramids, Cones and Cylinders
- 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
- Water through apertures, falling weights, and images in crystal
- Definitions on circles in double proportion and squaring the circle
- Parallelepipeds and the doubling of the cube
- Grid of Balance Diagrams with Weight and Distance Values
- Book of Equivalence: Squaring Circular Sectors and Portions
- Quadrature studies: doubling pyramids and equipartition of sectors
- Circles in quadruple proportion and curvilinear triangles
- Mining a fortress angle; the earth's motion and the moon
- Quadrature of lunes and curvilinear surfaces
- Light and the Diminution of Objects with Distance
- Diagrams of Light Rays and the Boundary of the Luminous
- Studies of the Balance and the Centres of Weights
- The Balance: Choosing the Site of Weights by Proportion
- Squaring of lunes: proofs on crescent-shaped figures
- Squaring of lunes, continued: lending triangles
- Mining fortress walls: undermining and sap tunnels
- Solar rays through apertures, with sums and accounts
- Turning curved surfaces into straight; arcs, chords, sagittae
- Geometric construction with columns of calculation
- The arithmetic of growing, shrinking and equal proportions
- Studies of the balance: centres of gravity and arm ratios
- Weights on inclined planes: resistance, friction and the fulcrum
- Rods loaded with numbered weights: balance studies
- A rod hung by two cords: how its weight is shared
- Squaring the Lune: Transformations of Curvilinear Figures
- Curvilinear Geometry: Sectors, Lunes and the Limits of Squaring
- Windlass and cord mechanics with quadrature of lunes
- Transmuting triangles and squaring lunes, with cord statics
- Geometric versus arithmetic change of a proportion
- Forces in a cord wound on a rod, and pulley blocks
- Raising the irrigation from Lake Brivio: a canal scheme
- Surveying the Brivio canal to the Travaglia mill
- First treatise: triangles in semicircles and the quadrature of lunes
- Quadrature of Lunes and Circular Sectors
- Weights on a Beam Suspended by Two Cords
- Quadrature of Lunes and Curved Figures
- Two Mean Proportionals and the Cube Root
- Pyramids and cubes: proportion, weight and the doubling of the cube
- The science of the balance: weights, arms and pivots
- Balance schemes and canopied frames
- The falling water-vein and the descent of dropped bodies
- Water Raised by Counterweights and the Fall of Water
- Studies of Pulleys, Gears and Springs
- Motion, Ballistics against Walls, and a Surveying Square
- Numeric tables and a radiating geometric construction
- Accelerated fall and the force of falling water
- Experiments on Falling Bodies; Measuring the Sun
- Geometry of Superimposed Circles and Sectors
- The Strength of Beams and Supports
- Strength of a beam and the balance of suspended rods
- Dividing lunes and squaring curved figures
- Pulleys, cords and balances: how weight multiplies through tackle
- Broken lever versus continuous lever; the force of falling water
- Statics of the balance: weight, equilibrium and oblique descent
- Pivot friction of a crane worked out in fractions
- Geometric equivalences and ornamental circle studies
- Curved-figure geometry: biangles, sectors and the hexagon
- Squaring curved figures: lunes, rings and circle proportions
- Lunes, Sectors and the Squaring of Curved Surfaces
- Dividing a Circular Portion into Equal, Similar Parts
- Plans of a house with land measurement and calculations
- Plans and notes for a gentleman's house
- Proportional division of a line in a mechanical figure
- 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
- A Catalogue of Quadrable Curved Figures
- Cloth-napping machines, springs and gears
- The balance: friction at the fulcrum and the limits of weighing
- Weights in the balance: friction and the impossibility of measure
- Transmuting curved surfaces into rectilinear ones (lunes)
- Lunes squared by proportion, and the percussion of balls
- Moving Earth and Heavy Loads: Levers, Carts, Oblique Motion
- 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
- Table of squares, lunes, and figures equated by curvature
- Proportion of Circles and Squares from Their Diameters
- Doubled Circles and a Bird Steering in the Wind
- Squaring Curvilinear Figures into Equal Rectilinear Areas
- Quadrature of lunes and circles: equal-area figures
- Geometric Figures Composed from Portions of Circles
- Squaring the Circle: Lunes, Squares and Circle-Portions
- Winds and Projectile Motion: The Path of an Arrow
- Euclid's five postulates and eleven common notions
- Squaring the circle: sectors, lunes and inscribed squares
- Quadrature studies and a note on Leonardo's treatise
- The Lune of Hippocrates and circle-doubling
- 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
- Quadrature of the Circle: Lunes and Squarable Figures
- 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
- Two fables: the vain razor and the restless stone
- Load shared among the cords suspending a horizontal rod
- Loaded rods and the double rod balanced by cords
- Oar and wing faster, slower, or equal to the water and air
- The law of the balance: arms, weights, and friction
- Quadrature of lunes: circles, squares, and hexagons
- Quadrature series of lunes and circular portions
- Debt memo, Arno place-names and arithmetic jottings
- Number calculations, polygons and a sublimation recipe
- Scaling problem, balances and a boat with a paddle-wheel
- Geometry of lunes: proportional division of circles
- Studies of lunes and semicircular portions
- Lunes, triangles and circle-to-square proportion
- 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
- Areas of circles as squares of diameters, and lantern studies
- Curvilinear figures of equal area drawn from a circle
- Rectangles of equal area, Euclid, and surd roots
- Squaring the circle: lunes, portions and the inscribed square
- Geometry and arithmetic exercises with wave studies
- Blank restored verso with offset from recto studies
- Weight of a bar suspended by two cords
- Balancing a composite rod against a simple rod
- Angle of incidence in a concave mirror and compass constructions
- Dividing lines and circles with a single compass opening
- Shadows cast by a sphere, and the squaring of the lune
- Levers and cords raising beams; reflex motion and balances
- Organizing diggers to excavate a mile of ditch
- Digging a ditch: pyramidal gangs and an excavator
- Mostly blank verso with a single mechanism sketch
- The earth clothed and stripped of its provinces
- Squaring curvilinear figures: lunes, rosettes and a hexagon
- Squaring Lunes and Sectors; Proportion of Triangles
- Squaring Lunes and Rings; Circular Sectors
- Triangular Balances and Weight Calculations
- The Triangular Balance: Finding Its Centre
- The Science of Friction and the Cart Wheel
- Centres of gravity, a waterfall, hexagons and proportions
- Quadrature of lunes and proportions of circles
- Quadrature of lunes; circles in double proportion
- Lunes, Triangles and Pyramids Compared
- The Friction of a Counterweight on a Balance
- Mensuration of a Circular Ring
- Squaring lunes and circles, with a note on wind vortices
- Quadrature of Circles: Doubling Circles and Squares
- Triangle proposition, square roots and household grocery accounts
- Domed churches, columns, and a theorem on a divided line
- Lunule construction and curvilinear surfaces
- An orbicular pyramid equal to a rectilinear figure
- Resolution of geometric fractions and a water wheel
- Rat breeding, sun-moon-earth eclipses, and hand muscles
- The 'Wheel of Increase' and Faint Geometric Constructions
- Studies on Friction: Its Laws, Kinds, and Counterweights
- Excavating a great ditch: the labour and arithmetic of moving earth
- Calculating the Labour of Digging a Ditch
- Rods Bending Under Weights, and the Circle Defined
- Graduated triangle with columns of calculations
- Ornamental vases, perspective studies, a word list and sums
- Two ways to dig a ditch: a labour-and-earth calculation
- Wheel-diameter calculation and a recipe for making indigo
- Balances and Weight-Calculations, with a Cloth Memo
- River flow in narrow channels; the strength of columns
- How the eye sees spheres and plane surfaces
- Bolted frame with a note on bolt-heads and a multiplication
- On the speed of ropes in pulley tackle
- Spring mechanisms, a wheel-lock striker and river pile-work
- Sheet of calculations with faint sketches
- Faint verso with a word fragment and figures
- Quadrature of the circle by sectors and octagon
- The wine-and-water problem and infinite divisibility
- Doubling the Cube: Cube Roots and Proportional Means
- 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
- Definitions of double and subdouble ratio
- Balance Arms, Friction and Counterweights
- 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
- How many equal segments fit into a sixth of the circle
- The sixfold division of the circle proved by its bisangles
- 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
- 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
- Levers and Counterweights for Raising Beams
- Unrolling the Surfaces of Cylinders and a Pyramid
- Squaring lunes and portions of circles
- Squaring lunes; and a maxim on natural wit
- Suspended-beam weights and a book memorandum
- Squaring circular segments and lunes
- Squaring the ring: quadrature of circles and annuli
- Triangles between parallels and circular portions
- The eye, the pupil, and images of the sun on the sea
- Geometry: proportional division and circle contact points
- Geometry of tangent points, with sketches of springs and devices
- Balances and weights: the centres of gravity govern the beam
- Triangular balance and proportional distribution of weights
- Cannon on a carriage, with calculations and a divided circle
- Transforming rectangles: widening and shortening
- Squaring the circle: lunes reduced to triangles and squares
- Semicircles divided into equal sectors
- Lunes in quarter-and-eighth proportion, with a letter draft
- A catalogue of lunes: the quadrature demanded without arithmetic
- Box for excavating a ditch bottom, with fines ledger and tables
- Rotational rebound of struck spheres, with divisions of the circle
- Squaring the circle by twelve inscribed circles
- Measuring the sun and moon's size from their distance
- The Moon in Eight Phases and the Sun Reflected on Water
- 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
- Successive halving and the vessel of wine and water
- Pyramids of incident and reflected light rays
- Squaring of figures and transformation of quadrilaterals
- A method for measuring the course of the sun
- Diminution of figures and solids along a beam of rays
- Percussion of heavy bodies, a wheel system and aphorisms
- Altimetry, accounts, and studies of a leaf and flower
- Algebraic place-values, a trajectory, and a column of woven rings
- Squaring the circle by arc-division and equivalent pyramids
- Inserting two mean proportionals; the cube root
- Constructing the Cube Root by Two Mean Proportionals
- The Blow of a Staff Struck at Two Points
- Squaring the Circle: Lunes and 'Circles with a Foot'
- Circles in Quadruple Proportion and 'Shield' Figures
- Light Rays Through Apertures; Weight on Cords
- Geometry of circles, semicircles and their segments
- Two fables, with geometry, motion and lightning notes
- Columns of arithmetical calculations
- De ludo geometrico: squaring lunes and curved figures
- The tides as the breathing of the Earth
- Solar Rays, Squaring the Circle, and a Letter to a Friend
- The Mazzocchio: A Faceted Torus in Perspective
- Squaring lunes and curvilinear triangles
- Firing angle of artillery, with pen and pencil sums
- Columns of Divisions and Fractions, with a Church Plan
- Truss Arches and Domed Churches; Pen Trials and Sums
- General rules of blow and force: loaded beams and a lifting screw
- Three Balances of Equal Nature
- A beam hung by cords at equal angles carries equal loads
- Motion through right and obtuse angles: load on suspending cords
- What weight is; forces on beams hung from angled cords
- Inclined beams with counterweights, levers and calculations
- Geometry: lettered figure with proportional ratios
- Geometry: squaring curved-sided figures
- Squaring curved figures: circles, lunes, sectors and annuli
- Geometric constructions with a column of arithmetic
- The balance: dividing the arms among four weights
- 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
- Circular Building Plan with Rooms, a Device and Sums
- Monetary accounts and a curve construction
- Loom mechanism: warp beams, reed and levers
- Areas of Circles, Lunes and Squares, with a Portal Study
- How to Divide 2/3 by 3/4, and Why the Cross-Rule Misleads
- Blank verso (invisible before restoration)
- Toothed wheels, a weight-wheel, and interlace knots
- Weights on balances, with tables of powers of two
- Quadrature studies: squaring circles, rings and lunes
- Water emptying from two vessels; the rise of rivers
- Similar Portions of Circles in Sixteenfold Proportion
- Inscribed Hexagon and the Squaring of Circle Portions
- Circles, squares and the geometry of lune-figures
- A rule for chained-fraction proportion problems
- Solving 'a fraction of what number' problems
- Working a Tower in Water, with Studies of Area Equivalence
- Balance Diagrams with Studies of Circular Proportion
- Geometrical Figures Keyed to Euclid
- Overbalancing wheel with rolling weights, gears and a siphon
- Great water-bucket wheel for perpetual motion (778v)
- Machine studies with a column of figures (779v)
- Note on the pope's chamberlain; geometric solids (780r)
- Well-bucket hoist with pulley, winch and gear ratios
- Friction, Balance and Centres of Gravity
- The balance: arms, weights, and the point of equality
- Quadrature of sectors, lunes and crowns; proportion of circles
- Screw-driving lever, tent frame, and notes on motion
- Light and shadow, the balance, and sunbeams through clouds
- Figure Studies and Solids, with a Note on Ratios
- Volume of a pyramid and the doubling of the cube
- Columns of calculation and oxen dragging wheels of varied size
- Sizing a man's wings from a bird's span and weight
- Cubing a Cylinder: Cube Roots by Proportional Rectangles
- Mill machinery, a friction study, and pyramid geometry
- Friction in Pivots and Wheels; the Perfect Round on a Plane
- Column of Numbers on a Near-Blank Sheet
- Lever Hoist for Raising a Weighted Box
- Water rising from reservoirs pressed by equal weights
- Lever linkages of bone and sinew, with household accounts
- On force and weight, with crossbow force problems
- Wing proportions and an articulated wing linkage
- Geometry of triangles, circles and squares; proportions
- Masonry arch study with weights of a pillar and tiburio
- Verso of the wing leaf, with columns of figures
- Land-yield reckoning, abacus problems and bridge sketches
- Crucibles, a geared millstone and a goose-foot oar
- Duomo di Milano account register with fraction exercises
- Thrushes flying against the wind, with a wing study and a jest
- On the proportion of force and motion; crossbow questions
- Mechanical studies: bar-cutter, pump and Heron's fountain
- Press mechanism and a draft letter on financial want
- Page of arithmetical calculations (not in Leonardo's hand)
- Geometry: doubling of areas and solids, an octagon from a square
- Squares Inscribed in Circles: Areas and Proportions
- Toothed Wheels and Spindles: Diameters and Tooth Counts
- Household Accounts, Reckonings and Notes on Bird Flight
- Wheels as Balances and the Law of Block-and-Tackle
- Reflection: where light rebounds at equal angles
- Notes on the windlass, water pressure and communicating vessels
- Wheels, axles and levers for hauling a cart
- Elasticity of bent wood and interlocked timber roof frames
- The Mediterranean basin and the making of valleys
- Surveying instruments, a sum, and military devices
- Pyramids, cylinders and squaring the circle
- Earthwork Reckoning for Digging a Ditch
- Machine for Lifting Earth from an Excavation
- Mechanism of Semicircles Swapped by Pulling Cords
- An Astronomical Gear-Train Calculation
- Practice of Geometry, the Balance, and the Course of Rivers
- Survey of the River Adda for the Naviglio Canal
- Wheelwork studies with a figure marked 'Time'
- Rules for an experiment on a falling weight striking a ball
- Proof that a water-wheel cannot make water raise itself
- A train of fifteen wheels and pinions multiplying by twenty
- Reducing a solid to a perfect cube; a red-chalk mechanism
- Statics of balance beams and loaded inclined bars
- Design for a striking water-clock
- Stone-Shot against Mud-Covered Mantlets
- The Species of Objects Fill All the Air
- River-valley map with accounts, arithmetic and pulley sketches
- Partitioning the Hexagon Inscribed in Its Circle
- Magic Squares, Riddles and Parlour-Trick Experiments
- Balance beams and graduated weights, with arithmetic
- Balances and the excess of weights along the beam
- Friction on the Balance: No Weight Can Exactly Match Another
- Rotating Screw-Reservoir, Pulleys, and Weight Calculations
- Levelling Instrument and Balance Experiments
- Canal gradients and a series of balance-beam schemes
- Bucket machine for raising water from a well
- Octagonal figures, interlaced constructions and numbers
- Force, time and space diagrams; the spheres of the elements
- Percussion of spheres, arithmetic, and a large winged mechanism
- Mechanical Loom: Gear Train and Treadle Timing
- Rays converging on a lit surface, a balance and arithmetic
- Balances with weights, universal pivots, and calculations
- Lifting machines, a Latin grammar table, and a multiplication
- Chords, arcs, and the equal angles of reflection
- Geometry: transforming cubes, pyramids and solids
- Workshop mills and a grinding machine with part dimensions
- A glass-vessel spinning engine and the wear of its pivot
- Gear trains, a column-lifting rig, and a beam-loading rule
- Octagon construction, a balanced scoop, and fire rockets
- A wheeled machine, with lists of cities and Florentine names
- Circles and Squares of Double Capacity
- Circle-and-quadrant figures and area equalities
- Digging Ditches: Spade-Work, Earth Weights and Gangs
- Organizing Diggers: Barrows, Windlass and Labour Sums
- The balance rule for finding a counterweight
- On the squaring of the oval figure
- Earth-moving: filling boxes and excavator schemes
- Improving the great hoist; excavation worker schemes
- Toothed wheels and screws for lapidary machines
- Gem-polishing mills, pivots and concave mirrors
- Quadrature of circles and lunes
- Squaring the circle by transmutation of surfaces
- A striking water-clock that sounds the twenty-four hours
- On the pivots: keeping them steady and how thick pivots wear
- How the sun heats and lifts the sphere of water, with calculations
- Calculating the tiles in all four faces, with mechanical sketches
- Spring-and-Gear Mechanism with Squaring Sums
- Rotating spring device, room measurements, and sums
- Egg Riddle and a Multiplication, with Faint Sketches
- Sheets of Arithmetic over Male Profiles (not by Leonardo)
- Geometry of triangles and circles, with balance notes
- Dividing a Pyramid in Septuple Proportion
- Copper-melting furnace and embryonic umbilical studies
- Interlace knot designs, with a casting note and a doubling series
- Sheet of arithmetical calculations with small mechanical sketches
- Earth-moving machine and the arithmetic of excavation
- Balance-beam weight studies with numeric tables
- Balance and opposed counter-weights (verso)
- Clock wheels and a steam device among small mechanisms
- System of wheels stepping by powers of ten
- Spring device and wheeled mechanisms, with sums and a memory
- Self-tipping excavator cart, with a draft letter
- Studies for squaring a curved surface
- Studies of friction, ball bearings and point contact
- Machine with Rollers and Lantern Pinions; a Calculation
- Arrow-launching war engine with firearms and reckonings
- Geared machine with tooth counts and calculations
- Parabolic compass and geometric construction
- Bladed windmill, augers and a note on a buckler
- Geometric fan diagram with proportional divisions
- Mould Core and Mantle for Casting the Horse; Number Table
- Clock gear-trains, an escapement and a colour recipe
- Household inventory, the power of two bows, and a note on Nothingness
- Winch with toothed wheels and a suction pump
- Heat and steam devices with a rotating machine
- Perpetual-motion vessels and cord-suspension studies
- Distillation apparatus, a spade, geometric solids and calculations
Codex Arundel107 pages
- Balance-arm weights, and the opening of a new collection
- Balance arms and weights hung from angled cords
- Three kinds of oscillating motion; weights on oblique cords
- Descent on oblique lines, centre of gravity, and balancing by proportion
- Weights on angled cords: real arms, potential arms, and their loads
- Lightening of a weight on its support; a cord pulled by two powers
- Weights Hung on Angled Cords, with a Rule-of-Three Problem
- A short method for measuring distance
- Combining and subtracting squares and circles
- Summing a progression and finding square roots geometrically
- Balance arms, centres of gravity, and a refutation of Alberti
- Theory of proportion; the four powers and the nature of gravity
- The kinship of weight, force and percussion
- Balances with friction: equilibrium on equal and unequal arms
- A proportional compass, a dyers' cauldron, and rules of motion
- Triangles on a common base: areas as their heights
- Arcs are not proportional to their chords and sagittae
- The angular balance and equal weights on unequal arms
- Equilibrium of balances with unequal arms and weights
- The three centres of gravity of a heavy body
- Mirrors and the simulacrum, with a note on Roger Bacon
- Concave burning mirror: angle of incidence and the converging light pyramid
- The science of the balance: weights, arms and the centre of the world
- Axioms of power, weight, and proportion (f. 79r)
- Impetus against percussion, and land measures
- Loads on Cords and Beams; Dividing Numbers by Proportion
- Distributing a load between the cords of a suspended beam
- Index for a treatise on rivers, with a wing and calculations
- Efficiency defects of the earth-moving wheel machine
- The infinite variability of percussion
- On 'nothing', the arithmetical zero, and Vespucci's geometry book
- Measuring the pouring vessel's motions: one mile per hour
- Water rebound, a semicircle problem, and Salai's expenses
- The Four Accidental Powers and Crossbow Ballistics
- Multiplication Table with Figure and Perspective Studies
- Division of the Greater Inequality: Ratio Theory
- Transformations of Pyramid, Cube, Cylinder and Slab
- Seventeen problems on reshaping cubes, cylinders and slabs
- 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
- Semicircle perimeters and cone-cylinder surface proportions
- Finding cube roots by means of broken numbers
- Folio 200 verso: near-blank with recto show-through
- Centres of gravity of weights hung from cords
- The centre of gravity of weights on a beam, by rule
- Book I of the Waters: point, line, body, and the sun
- A digger's labor: earth moved by shovelfuls per hour
- Numerical calculations
- Turning cubes into boards by irrational proportion
- Cube, board and cylinder in equal proportion
- Balance of the Lever and a List of Household Expenses
- The Divided Lever Exerts Greater Force
- Studies in fractions and proportional means
- Surface versus volume: cube roots and doubling the cube
- Cube roots, solid surfaces, and man compared with the earth
- How objects set obliquely in a river dam up its current
- Balances, wheel motion and hauling; with calculations
- Extending, Shortening and Uniting Rectangles
- Arithmetical calculations; blank facing leaf
- Equal Motions from Unequal Force; the Sound of Flies
- On weights: lever and counter-lever in equilibrium
- The Visual Pyramid and How It Narrows With Distance
- Perspective, the Visual Pyramid, and the Praise of Archimedes
- Begun in Florence, 1508: preface and weights on the balance
- Oblique descent of weights and the centre of gravity of a square
- Weights on beams and cords, and the mover's power
- Accidental weight in angled cords, and the potential lever
- Elements of mechanics: shared loads and how cords break
- Centers of Gravity of Squares, Brackets and Triangles
- A Brief Method for Measuring a Distance
- Summing a Progression and Finding Roots Geometrically
- The angular balance and the law of unequal arms
- Postulates on rods and balances of equal arms
- Theory of ratios; the nature of gravity and levity
- Simple equality of balances and the arithmetic of friction
- Geometric constructions: circle in a square, squares within squares
- The cone of light, the angle of incidence, and a burning mirror
- Proportion of powers and weights (f. 79r, backlit)
- Impetus and percussion in inverse proportion
- Sharing two weights along a beam hung from three cords
- Weights on wheels and the fall of heavy bodies
- A rule-of-three sum and an index of chapters on water
- Leaf with geometric sketches and columns of calculation
- The rebound of a struck body: impetus and percussion
- Point, line and surface as 'nothing'; a weighted wheel
- A reed-wheel for a four-part canon, with liquid-motion notes
- Ratios of Proportion: Double, Triple, Quadruple, Quintuple
- Transforming Solids: Pyramid, Cube, Cylinder and Slab
- On Time, the Point, the Line, the Angle and the Surface
- The Two Mean Proportionals Between Two Lines
- Transforming Cubes, Slabs, Pyramids and Cylinders
- A hanging weight passes wholly into its support; friction on a slope
- Geometry of the semicircle, cylinder and cone
- A method for cube roots using fractions
- Centres of Gravity of Weights Hung on Cords
- Reckoning a Labourer's Rate of Moving Earth
- Reducing a Cube to a Cylinder of Equal Content
- The Divided Lever versus the Whole: Force and Lift
- Centres of Gravity of Pyramids and Circular Segments
- Surfaces, Volumes and Cube Roots; Doubling the Cube
- Obstacles that dam a river's current
- A square inscribed in a right triangle
- Mechanical sketch and calculations; facing leaf blank
- Perspective: the diminution of the visual pyramid over distance
Codex Forster I57 pages
- Thinning a Board Without Changing Its Volume
- The Proportional Compass and Its Screw-Nut
- Constructing the Square Root of 10
- Enlarging and Shrinking a Square Board
- Cubing an irregular six-faced body from twelve lines
- Cubing a cylinder by lending and restoring
- The cube and its transformation into a cylinder
- 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
- Dodecahedron, Solids, and Turning a Cube into a Pyramid
- 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
Codex Forster II116 pages
- Folio 1r: Columns of Figures with Red-Chalk Sketches
- Folio 1v: Triangle on an Equivalent Rectangle, with Sums
- Folio 2v: Columns of Multiplication Figures
- Memorandum of faces to draw; a column of figures
- Red-Chalk Sketches, Figures, and a Name
- Detail of a Spring Mechanism
- Columns of numbers in continued proportion
- Continuous and discontinuous geometric proportion
- Notes on greater and lesser proportion
- 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
- Permuted and Compound Proportion
- Disjunct proportion: the series 6, 8, 9, 12
- Equal proportionality of various kinds
- Reversed (perverse) order of proportion
- Gear-train sketch with pen note and red-chalk figures
- On motion: force, weight and distance in throwing a stone
- On tensioning strings tuned in octaves
- Three spheres: the earth with mountains, and numbers
- Arithmetic proportions, and a note to send for wheat
- Proportion of powder and barrel in a small firearm
- Multiples 3 6 9 with a diagram of the earth's sphere
- Two mountains rising from the earth's circumference
- Equal Division of a Rectangle: a Equals b
- Equal Divisions of Straight and Curved Rectangles
- Greater and lesser inequality; air resisting a man's arms
- On motion: air resistance and the fall of weights of 16 and 1
- A Balance That Lifts Infinite Weight
- Mechanical device, a flower, and calculations
- Mechanical device, gear-trains, and arithmetic
- Mould for casting a bombard
- On Motion: the Bombard that Casts its Ball Farthest
- On Motion: a Crossbow Casting Weights of Differing Thickness
- Page of multiplications and calculations (fol. 61r)
- Prophecy of the shoemakers amid columns of figures
- On impact: a rule for the powder charge of projectiles
- Emblematic devices and notes on figures' gestures
- Architectural moulding profiles with calculations
- Weight of suspended beams shared among their cords
- Weights on a pair of connected suspended beams
- Dividing a beam's weight among added cords
- Beam on three cords loaded by three weights
- Falling bodies keep equal intervals; a roof section of the Castle
- Three Suspended Rods: Combining Movers and Counter-Levers
- The Crossbow: Blow and Motion Given to the Arrow
- Trading time, force, motion and weight to lift a load
- Centre of gravity of a suspended triangle divided in nine
- Balance Beams and the Sesquitertian Ratio of Weights
- The Weight of the Balance Arms Must Be Counted
- Water Tenfold the Volume of Lead; a Geared Counterweight Device
- The Quadruple Pulley and the Cubic Rule for Cord Loads
- Eight Pulleys on a Beam: Doubling of Power Along a Cord
- Two Pulley Systems: How Four Pounds Loads the Top Cord
- A Loaded Beam and the Strength of Its Span
- Two Suspended Rods and the Division of a Load
- Confirming the Balance Proof with Weights 4 and 2
- A loaded cord and its counterweight: correcting the 32 for 4
- Two tested horizontal rods and the rule for a loaded cord
- Balancing Three Weights with Two Counterweights
- Placing an 8-Pound Counterweight Against Three Loads
- Balance beam with weights in double proportion
- Placing four weights on the experimental balance
- Positioning three weights on a suspended rod
- Triangular balance: a worked example with weights 3, 6, 1
- Seven triangular-balance cases worked out in numbers
- Finding the weight positions without knowing the fulcrum
- Which of two weights sits nearer the balance's pole
- Greatest and smallest weights are set opposite the middle
- The triangular balance stays steady in any orientation
- Triangular balance of three equal arms
- Composite and simple rods in equilibrium
- Squares inscribed obliquely within squares
- Finding the Centre of Gravity of Seven Suspended Weights
- Four Suspended Rods with Weights: A Simpler Balance Case
- Suspended Rods: Locating the Center of Gravity of Weights
- Four Balanced Rods: Center of Gravity Always at Line m n
- A 15-Pound Load on Three Cords: Dividing Weight by Proportion
- General Method for the Center of Gravity of Weights on a Rod
- Suspended Rod: Working the Weights by Multiplication
- Three Weights on a Rod and the Law of the Lever
- Finding the pole of a balance from its two weights
- Suspended beam and a ball on an inclined plane
- Distributing 12 pounds onto the three cords of a beam
- Centre of the cords divides the beam as 4 is of 6
- Equal loading of three equidistant cords on a beam
- Midpoint of the cords divides a beam by its opposite weights
- Balance rod: proving the equality of suspended weights
- Rod on eight cords: equal sharing of a weight
- Ball on an inclined plane: time and velocity of descent
- Suspended beams and the velocity of falling weights
- A rod on a support: equal effort to raise or to lower
- Rods hung by cords: the cord nearer the centre bears more
- Three cords sharing a beam's weight in equal parts
- Distributing four pounds among three cords on a beam
- A general method for the load on each cord of a beam
- Dividing a load among a rod's suspension points by proportion
- Five paired rods with stepped weight ratios
- Balancing rods by sub-double and sub-quadruple ratios
- Weights suspended from a disc by three cords
- Load shared between two cords on a suspended rod
- Six suspended rods: a 'universal rule' of weights
- Weight of a rod shared between two suspending cords
- Rod on two cords: weight change with unequal spacing
- Proportional rules for the weights on two cords
- Symmetric versus one-sided motion of the cords
- Weights on cords, and the acceleration of falling bodies
- How a suspended rod shares its weight between two cords
- Balance with arms in double proportion, tested by experiment
- Double-proportion balance and centres of solid figures
- Equal arms and the spaces from centre to pole of a balance
- Balance beam a m n o p: reducing weights to the pole
- The true centre of gravity of a balance's arms
Codex Forster III21 pages
- Two bells of equal weight but double size sound lower
- Strength of a beam set vertical, horizontal and oblique
- Joined horizontal rods with numbers; a maxim on experience
- Casting proportions: earth to metal, wet and dry
- Proportion Between a Thrown Stone's Motion and Its Mover
- Column profile with proportional relationships
- Balanced bars, added sums, and a court-hall measurement
- Divided bars and weight-boxes with paired numbers
- On the Doubling of Lights, with Sketches
- 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
- Geometry of a screw thread and its pitch
- Calculating the power of a screw and lever
- Force of pulley blocks, with arithmetical notes
- Calculations for a tackle: rope drawn versus load raised
- A twenty-wheel pulley train and its windlass
Codex Madrid I63 pages
- On Wheels: Gear Trains and the Matching of Teeth
- Gear-Tooth Contact, Leverage and Friction
- Proportioning Gear Teeth Between a Large and Small Wheel
- Screw versus wheel: equal work by two men in one hour
- Compound levers built from toothed wheels and pulleys
- The Crossbow: Force, Weight and the Flight of Bolts
- Primary and Derivative Force; a Four-Wheel Gear Train
- Force as Line and Arc: an Eightfold Proportion
- Descent of arrows and their penetration into the ground
- The spinning machine: bobbin, flyer and the twisting of thread
- A spinning machine for eighteen women: wheels and gearing
- Onset of Sliding Friction and Oblique Pulling
- 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
- Cords Under Accidental Load; 'Tested' Beam Experiments
- Weights on cords and levers: a general rule of proportion
- The general rule of loaded cords proved on the triangle
- Balance-beam experiments and a rule of division
- Acceleration of falling bodies: velocity gained, time lost
- Counterweights on a balance and the infinite
- Force and motion of the lever and screw
- Friction reduced toward infinity; a giant calculation
- 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
- Gravity, Resistance, and the Beginning of Motion
- Levelling and Measuring a Tunnel Bored Through a Mountain
- Dividing wheels into teeth and sizing wheels to pinions
- Measuring the force of the screw and its triple friction
- Raising a beam: lever, counter-lever, and center of weight
- The pyramidal power of the balance arms
- Balancing unequal arms by inverse proportion
- General rules of the balance
- How a weight loads its support
- The Perfect Balance and a Black-and-White Water Experiment
- How loaded beams bend under weight
- Sharing a beam's load between its two supports
- A balance instrument and beams resting on beams
- Force, weight, motion, time; water jets from tubes
- On the counterweights of clocks
- Centre of gravity of the pyramid; levers, beams and loads
- Sharing a load among balance cords by the rule of proportion
- Finding weights from their spacing; bounce of a rolling ball
- Cords, a struck cube, and the corded triangle a b d
- Two Cords of Unequal Thickness Sharing One Weight
- The Simple Beam of a Balance and Where Its Weight Lies
- Rule for Computing How a Beam Distributes Its Load
- Load shared between two cords supporting a beam
- Rule of weight: added length unloads a support
- Cords sharing a beam: equal and proportional loads
- Balance-arm diagrams: proportional weights and pulleys
- The general rule of weights on the arms of the balance
- Beginning of the book: support strength and lever balance
- Load carried by pulleys and little wheels on a shared cord
- Folding wooden joints for portable tables and pavilions
- Weights over unequal wheels, and the friction of dragging a beam
- Motion: how a mover's speed governs the spacing of moved weights
- Crossbows, the shoulder's load, and falling hammers
- Percussion, supports, and a loaded beam
- Recipes for varnish, glue and cloth-dyeing, with number rules
Codex Madrid II98 pages
- River survey of the lower Arno valley with distances
- Tally of the books, with measurements and worked figures
- Money reckonings beneath a rocky crag crowned with buildings
- A Wind-Driven Wheel and the Rim That Outruns the Air
- A Winter Proverb and Sums for the Ditch
- Costing the Excavation of the Fortress Ditch
- Map of the Lower Arno Valley: Caprona, Vico, Montecchio
- Cost of Excavating the Fortress Ditch and Foundations
- Rows of Diggers and the Rising Price of the Ditch by Depth
- Dimensions of the Fortress Ditch and the Files of Diggers
- Stepped Trench: Men Needed to Cast Earth Up by Depth
- Costing the removal of a cylindrical mass of rock
- On Perspective: the eye and images on a wall
- Hill profile (Montici, Edna) with column multiplication
- The stamp of the flax-brake: five ways to gain power
- The blow amplified by a rebound motion
- Estimating the earthwork: cutting the hill and moat
- Cost accounts for the fortification
- Masonry of the fortress and moat walls
- Quadrature (volume) of the pyramid
- Cost calculations for a round fortress tower
- Excavation costing for the fortress ditch
- The citadel tower and moat: dimensions and cost
- Excavating the ditch of Monte a Santa Maria in live rock
- Piombino Fortifications: Parapet, Covered Way, and Costs
- The Citadel Tower: Dimensions and Masonry Costs
- The never-emptied barrel, rivers moving the earth, and whirlpools
- A windmill built entirely of cloth, with its costing
- Pyramids Divided into Equal Triangular Solids
- Sapping Trenches That Show the Enemy Fewest Angles
- The Force Needed to Move a Cart
- Continuous and Discontinuous Proportionality
- On Proportion: Its Names, Members, and Three Species
- Commensurable and Incommensurable Quantities
- Simple Inequality: Multiple, Superparticular, Superpartient
- Summary of the Ratio Types, with a Multiplication Table
- 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
- A windmill, a wedge's centre of gravity, and mean proportionals
- Squaring circular portions into triangles
- Squaring circular sectors and figures
- Squaring Triangles and the Volume of Pyramids
- Angles of the Balance and the Diagonal of a Cube
- Dividing the Cube into Pyramids; the Two Mathematical Sciences
- The Pyramid as One-Third of the Cube; the Order of the Sciences
- 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
- Disjunct and conjunct proportionality
- A jest: the thief who turned the tables on the mercer
- Branching tree of proportion and proportionality
- Quadrature of lunes: crescents equal to rectilinear areas
- Common measure of line a c and a doubling number series
- The Ten Kinds of Gun, Their Alloys and Powder Charges
- The science of the cord: how a rope bears weight and where it breaks
- Squaring the circle by 196 sectors
- Volume of a truncated pyramid and squaring the circle
- Squaring the sectors of quadruple circles
- 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
- Squaring Curved Triangles from Circles in Double Ratio
- Curvilinear Triangles Equal to Any Rectilinear Triangle
- 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
- The Cube's Diagonal in Sesquialteral Proportion
- A Jest: The Poor Man Who Claimed Kinship from Adam
- Dividing a Cube into Pyramids and Their Weights
- 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
- Dividing a Semicircle into Curvilinear 'Pyramids'
- Cutting a Third from a Semicircle Between Parallels
- Casting proportions: bronze per pound of earth, wax and wood
Codex Urbinas (Treatise on Painting)17 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 as a Mental Science; Painter, Poet, and Musician
- Painting a Mental Science of Shadow, Light, and Form
- Study by Season, Attitudes, and Measures of the Statue
- A colour unchanged across varying thicknesses of air
- Reckoning air-thickness before distance for colour
- The perspective of colours: brightening in proportion to distance
- Colour-loss proportional to distance; unchanged colour across air
- The Tower's Colour Proved by Proportion; Sunbeams in Clouds
- The measured rule of diminution; bodies enlarged by fog
- Reflected Light Weakens in Proportion to Its Source
- Distance and color of peaks are not in the same ratio
- Book on Painting: Whether Painting Is a Science
- Painting versus Poetry; First Principles of Painting
Codex on the Flight of Birds4 pages
Paris Manuscript A15 pages
- Balances, a Beam's Load, and the Proportions of a Head
- 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
- Percussion studies and a compass proportion puzzle
- Postulates of perspective and the diminishing of distance
- Inscribing a hexagon and pentagon; area of a quarter-corona
- Nested squares and circles in geometric ratio
- Squares and circles that hold four equal copies of themselves
- Measuring a rope's length with proportional triangles
- Definitions of the Blow and the Nature of Motion
- Percussion, colliding balls, and the force of the crossbow
- Rebounding blows, crossbow arrows, and falling weights
- The Strength of Loaded Staffs, Beams, and Twisted Cords
- Levers, Pulleys, and Why a Long Rope Cannot Be Pulled Straight
Paris Manuscript B7 pages
- Finding circle centres, an octagon, and a divided triangle
- Measuring heights and distances with a ground square; fire trebuchet
- Measuring a river's width; barrels rolled down a slope in defence
- On the Nature of Force; Weight of a Beam Between Two Walls
- Components of a geared lever; moulds for gun-shot; calculations
- Variant worm-and-fork gear, with cast-iron screw and gear ratios
- Memoranda: Master Ludovico, Water Conduits and Wing-Load Sums
Paris Manuscript C1 pages
Paris Manuscript E12 pages
- How a Hanging Weight Divides Along a Cord and an Angle
- 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
- Six rules for the quadrature of the circle
- Dividing a line into equal parts by a triangle
- The Angled Cord and the Balance of a Hanging Weight
- Weight of a Beam and the Eight-to-One Balance Arm
- Real and Potential Arms of the Balance
- Finding the Center of a Suspended Body
Paris Manuscript F11 pages
- Balance-arm and the proportion of combined weights
- Propositions on force, mass, space, and time in motion
- The zig-zag motion of the celestial thunderbolt
- The true ounce of water: flow from spouts at different heights
- 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
- Sea raised by the sun, discharge and fall, and river eddies
- Angle of Contingency; Why the Sea Seems Higher than Land
Paris Manuscript G23 pages
- Gearing of a grinding mill
- On Proportion: Doubling Circles and Squares
- The Light of the Moon: Is the Moon Water?
- Perspective: apparent size and distance from the eye
- Doubling of Concentric Circles and Squares
- Divisions of Solids: Pyramids Within Cubes
- Subdividing a great disc into 57,600 squares, and its gilding cost
- Parity Rules, and Squares Equal to Lunes
- Geometry: Dividing a Circle's Circumference into Equal Parts
- 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
- The lever double its counter-lever
- Squaring Lunes: Circle Sectors, an Inscribed Square and Equal Areas
- On the Cubature of the Sphere
- Resolving the Spherical Body into Pyramids
- Squaring the circle: lunes and doubled circles
- Drawplate armature, edge-power ratios, and an angle-sighting device
- Roller machine with pyramidal beams for shaping plates
- The power of the cut: subdividing a four-braccia square
- On the Nature of Heat: Power Concentrated on a Smaller Base
- Mechanical measurements, a ruler, breathing, and mathematics
Paris Manuscript H15 pages
- Hydraulic wheel and eddies below a fall of water
- On painting: the shifting highlight; a millstone's power
- Reckoning the cost of digging a canal in ducats
- How a suspended weight divides between two supports
- Numbers in red chalk and a gloss on ancient military ranks
- Plan of an oven with its measurements in ounces
- Oven drawing with lettered dimensions, a profile head and spelling drills
- Full plan of the oven with all dimensions in ounces
- Peg-lifters driven by scroll wheels
- Ordinary and proportional compasses
- Two gear-pairs with retaining teeth for alternating motion
- Proportions of an Ionic Capital
- River-bed studies, jotted aphorisms and numbers
- Back-eddies that lay down earth, with sums and a cart part
- Rod suspended on two cords, plank tiers, and figures
Paris Manuscript I51 pages
- 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)
- 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
- Geometry of angles inscribed in circular segments
- Circle theorems: chords, secants, tangents and Pythagoras
- Tangent and secant of a circle; the Pythagorean theorem
- Heating the duchess's bath water, and a seated man
- Geometry: circles, squares, Pythagoras and cubes
- Bouncing as reflected motion; a wheel divided into sectors
- Two rods: the lifting power of the longer rod
- Multiplication sums and an indeterminate figure
- Rapid sketch of a mountainous landscape
- Latin glossary with land-measure reckonings in pertiche
- Latin glossary with a land-cost calculation
- Latin glossary and conversion of the trabocco measure
- Latin adverbs of place, with an addition sum
- Land measure: 96 trabocchi make a pertica
- Table of land measures: braccia, trabocco, tavola, pertica
- On the proportion of motions, powers and resistances
- Ricochet of a Stone and a Water Vortex
- The Jet from a Draining Barrel
- Proportion Study of a Dog's Muzzle
- The Rule of Three Applied to a Bombard's Ball
- Against Infinite Speed from an Ever-Smaller Ball
- Weight or percussion: which drives a projectile farther
- Equal weights, equal motion; unequal weights ranked by distance
- Problem: how deep a falling weight sinks into the ground
- Antifriction roller system with multiplied leverage
- Survey Continued: Bridge, Gate and Church Measures
- Questions on Motion; Proportional Ratios
- The question of the bouncing ball
- The range of a bombard and its trajectory
- Aiming a bombard by a graduated range scale
- The voice of the echo across distance
- Ballistics of Bombards: Ball Weight, Powder and Range
- Triangular-Mouthed Bombard and Graded Thrown Weights
- Fractions by the Rule of Three, with 'alius' Declined
- Lunes of a square in a circle, with a profile head
Paris Manuscript K86 pages
- Parallelogram within a parallelogram; three joined parallelograms
- Polygons and triangles compared by side and area
- Circular segments in continuous proportion
- Two pentagons and three measured triangles
- Triangles and a segment: a proof of proportionality
- Faint study of proportionally divided line segments
- Line segments divided in continued proportion
- Circle-arcs, segments and joined rectangles
- 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 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
- First conclusion on multiple proportions
- Converse and disjunctive proportion
- Proportion in all things, not only in number
- Euclid, Book V: the definitions of part and multiple
- Equal triangles and the squares upon their bases
- Refuting Zenophon: Equal Subtraction Alters a Ratio
- How Zenophon Proposed a Falsehood
- A force of 12 lifts 11 - and infinitely more, but never 12
- Proportional number pairs in pencil: 8-4-2 and 12-6-3
- Converse argument: swapping antecedents and consequents
- Cubic multiplication and a doubling series
- Multiplying double and triple ratios
- Heading: the eighth definition
- Likeness of proportion
- 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
- A Partitioned Rectangle and Circular Rings
- The roots of numbers marked along a line
- 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
- Dividing a Semicircle into Proportional Parts
- The Rule of Subtracting Four to Divide a Semicircle
- Of What Number Is Four the Three-Quarters?
- Triangle of Curved Sides: Counting Similar Triangles
- Two vessels draining water in changing proportion
Paris Manuscript L24 pages
- Opening leaf: decorated 'L' initial with notes and a calculation
- Multiplication notes: 7 times 7 makes 49
- Measured survey line with marginal distance notes
- Perimeter survey with a column-total of 5698
- Multiplying fractions: a worked check of 3/4 x 2/3
- Calculations with fractions
- Fraction sums, and a note on drawing hills
- Arithmetic working: columns of figures and fractions
- Rule of three: finding a number from its fractional part
- Recovering a whole from a fractional part of it
- Merchant problems solved by the rule of three
- Organising an Earth-Moving Operation
- Why doubling a figure needs more than doubled power
- Against Vitruvius on small models
- Why a bird flies faster than the wind that drives it
- Survey of the fortress at the port of Cesena
- Height of a fortress turret measured from the water
- Why Romagna's four-wheeled carts move badly
- Finding the cube root of 81 by a rectangle rule
- On the loss of the voice through distance
- Voices, arithmetic operations and a group of flowers
- Scheme for Excavating a Ditch
- Land-Measure Units and a Water-in-Sunlight Experiment
- Memoranda: the Archimedes of Padua, an itinerary, and sums
Paris Manuscript M55 pages
- Continuous and Discrete Quantity Compared
- Commensurable Sides and Square Numbers
- Square Numbers and Continued Proportion
- Commensurable Quantities and Their Common Measure
- Segments Marked with Numbers and Letters
- Continuous and discontinuous proportion; dividing a line
- Squares, roots and surds; a triangle with extended sides
- The nine common notions (Euclidean axioms)
- Squaring segments and forming rectangles from products
- Geometry is infinite; the arithmetic of discontinuous quantity
- Geometry of rectangles and squares with computed areas
- Squares on a triangle's sides and an 'irrational' height
- Rational and irrational lengths from a semicircle
- The Triangle Inequality: When Two Sides Fall Short
- Roots, Medial Lines and the Number 108
- Commensurable Surfaces and Medial Lines
- Proportional rectangles with root magnitudes
- Irrational roots, triangle angles and polygons split into triangles
- Rectangle divisions, a triangle in a semicircle, paired numbers
- A weight distributed 4 to 1 between two cords of a balance
- Oblique motion still grows in arithmetical proportion (prism figure)
- Air Resistance Subtracted from a Falling Weight's Motion
- Pyramidal Proof That Motion Grows in Arithmetic Proportion
- Doubling the Time Doubles a Body's Descent and Speed
- Degrees of Time, Motion and Velocity in Free Descent
- Falling Bodies and the Paradox of a Pouring River
- Definition and Diagram: Two Bodies Falling in Succession
- Degrees of Motion in a Falling Body
- A Falling Body Gains Speed at Every Degree of Motion
- A Balance with One Arm Inclined Downward
- Percussion of Two Equal Falling Bodies
- Percussion Growing with the Distance Fallen
- Range of a Culverin and How to Measure It
- How a Run-up Affects the Length of a Jump
- Equal increments in the fall of heavy bodies
- The pyramidal law of accelerating fall
- How much faster the larger weight descends
- A sling and the changing power of its launch trajectories
- Two experiments on freely falling balls
- On motion: smaller weights are thrown farther
- On the power of the crossbow
- Parallel figures compared, and the law of motion
- The impossible cut: a test of judgment about weights
- Balance staffs: arms cut and re-hung as counterweights
- Force and distance in the crossbow's discharge
- Two crossbows compared: which shoots farther?
- The Crossbow's Diminishing Force and a Subdivided Triangle
- Why a heavy hammer drives a nail in one blow
- On the power of percussion
- 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"
- Continuous Proportions: Summing 1, 2, 4, 8, 16, 32, 64
- Measuring a Crossbow's Force by an Equivalent Weight
- Worn End Leaf with Arithmetic Jottings and a Flourish