Errand lists, definitions of point and line, and measuring motion
Household and study memoranda beside geometry and a clock that divides the hour into 3000 parts
A densely worked opening that mixes Leonardo's household and study memoranda with physics and geometry. Long errand-and-shopping lists name books to bind or borrow (Aristotle's Meteora, Pandolfini's book, Lorenzo de' Medici's grammar, the Benci world-map), materials, tools and people to see. Between them he sets definitions of the instant, point, line and surface, and works out how to divide an hour into 3000 parts with a counterweight clock so as to measure motion, concluding that the ratio of transversal to natural motion equals that of the sides of a right angle cut by its hypotenuse. Right-angle triangles labelled a, b, c and d and columns of figures accompany the reasoning.
On this page
Florentine errands: books, purchases and people
A running memorandum lists a market book, the waters of the Clonica and Tanaglino, berets, a red mirror to see made, Aristotle's Meteora, cases of Lorenzo di Pierfrancesco, binding his own book, nutmeg, gum, a square, brass for the spectacles, and men to visit such as Giovanni Benci and Maestro Piero dal Borgo.
Further errands: tools, clothes and books
A second list gathers a chest, a level, Pandolfini's book, little knives, a ruling pen, dyeing a garment, Lattanzio Tedaldi, boots hose and shoes, lacquer, a boy for the models, Lorenzo de' Medici's grammar, spectacles, multiplications of roots, the Benci world-map and cordovan leather.
Definitions of the instant, point, line and surface
The instant has no time and time is made by the motion of the instant; the point has no part; the line is the transit and motion of the point, points being its ends; the angle is the contact of the extremities of two lines; and a surface is made by the line moved crosswise to its straightness.
An hour divided into 3000 parts by the clock
One hour is to be divided into 3000 parts, and this is done with the clock by lightening or making heavier the counterweight, so its beats can serve as a fine unit of time.
One braccio per beat gives a third of a mile per hour
If the motion a d is made in the time of the descent a b, the two are of equal length and velocity. With the hour set at 3000 beats and a b made one braccio, each time the diametral line strikes at d the mover has gone one braccio per beat, that is a third of a mile per hour; doubling the weight a b does not change this.
Transversal to natural motion as the sides of a right angle to the hypotenuse
a b descends in one time and is one braccio, so the diametral line shows the mover a d moving one braccio per time. The proportion of the transversal motion to the natural motion is that of the sides of the right angle cut by the hypotenuse.