A glossary of geometry for the science of weights
Point, line, angle, triangle, base and perpendicular defined and drawn beside the angular balance
Folio 78v is an illustrated glossary of the geometric terms Leonardo needs for his statics: point, straight and curved line, pyramid and base, right (orthogonal) triangle, perpendicular, equidistant (parallel) and oblique lines, acute, obtuse, right, curved, convex and gibbous angles, chord and arc, diameter, circumference, surface and cube. A long passage defines greater and lesser angles by how their sides meet the equidistant or the perpendicular line, notes that within the quarter-circle the acute angles are infinite, and redefines 'base' as any line drawn between the two ends of an angle's sides. Interspersed figures of an angular balance, lever and counter-lever, and lines of gravity and levity of a weight tie the vocabulary to the mechanics of equilibrium.
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Greater and lesser angles; equidistant and oblique lines defined
The greater angle has its ends near the extremities of the equidistant line, the lesser angle near the perpendicular; between them lie innumerable angles, half greater than the right (obtuse) and half lesser (acute). Equidistant lines, produced to infinity, never meet; oblique lines set in contrary obliquity soon meet and diverge infinitely at the opposite ends.
Angles and oblique lines within the quarter-circle
All angles are found in the semicircle and arise at its centre; all acute angles are found within the quarter-circle, and within it lie all the oblique lines. Because continuous quantity is divisible to infinity, the acute (and, with the other quarter, the obtuse) angles are infinite in number.
The angular balance
Angular balance: as regards the attached weights this behaves as if it were straight along m n, but not as regards the weights of its own arms. The bent balance is thus treated as an equivalent straight beam for the loads it carries.
Lines of gravity, levity and motion of a weight
A quadrant figure names the line of the levity of the weight, the line of the gravity of the weight, the line of the first motion and the motion of the weight, together with a 'mathematical line'. These directional lines give the geometric scaffolding for analysing how a weight moves through a swing.