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Paris Manuscript F — 173

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Bibliothèque de l'Institut de France, Paris

Due sistemi di sfere elementari a contatto:

Dato che fussi il contatto di due corpi terresti co' sua elementi, che figura piglierebbono essi elementi ne' loro contatti?

Dato un grave sperico nel contatto dell'elemento del foco coll'altro elemento del foco, che pesi tanto in verso l'un de' centri di tali elementi, quanto in verso il centro delli altri elementi, questo grave discenderà per obliquo, e poserassi sopra il contatto de' due corpi terresti, come most[r]a la figura, e 'l suo moto fia obbliquo.

Diagramma d'un grave fra i centri di due mondi, con:

c - d e - a g b - f

Dato li centri di due mondi sanza elementi, forte remoti l'un dall'altro, e dato un grave uniforme, del quale il centro de la gravità sia equalmente distante alli due detti centri, di poi sia lasciato cadere tal grave, qual sarà il suo moto?

Andrà lungo tempo movendosi con moto, del quale ogni parte della sua lunghezza sarà sempre equalemente distante a ciascun d'essi centri, e in ultimo si fermerà equalmente distante a ciascun de' due detti centri, nel più propinquo loco che abbia la linia del suo moto. E così tal grave non s'accosterà a nessuno centro de' 2 mondi1.

Two systems of elemental spheres in contact:

Given that there were the contact of two terrestrial bodies with their elements, what figure would these elements take at their contacts?

Given a spherical weight at the contact of the element of fire with the other element of fire, which weighs as much toward the one of the centers of such elements as toward the center of the other elements, this weight will descend obliquely, and will come to rest upon the contact of the two terrestrial bodies, as the figure shows, and its motion will be oblique.

Diagram of a weight between the centers of two worlds, with:

c - d e - a g b - f

Given the centers of two worlds without elements, greatly remote one from the other, and given a uniform weight whose center of gravity is equally distant from the two said centers, and then let this weight be dropped: what will its motion be?

It will go on moving for a long time with a motion in which every part of its length will always be equally distant from each of those centers, and in the end it will stop equally distant from each of the two said centers, in the nearest place that the line of its motion has. And thus this weight will approach no center of the 2 worlds.

A Weight Poised Between the Centers of Two Worlds

How the elements meet where two earths touch, and where a weight falls between two centers

Physics & Mechanics Astronomy

Leonardo poses two thought experiments about gravity toward more than one center. In the first, two terrestrial bodies with their elemental spheres touch, and a weight placed at the contact of their spheres of fire, pulled equally toward each center, descends obliquely and comes to rest on the point where the two earths touch. In the second, a uniform weight starting equidistant from the centers of two remote worlds falls along a path that keeps it always equally distant from both, halting midway without ever reaching either center; the margin diagrams label the centers and the weight.

On this page

A weight at the meeting of two elemental spheres descends obliquely

Leonardo asks what figure the elements would take where two terrestrial bodies and their spheres touch. A spherical weight placed where the two spheres of fire meet, weighing equally toward each center, descends along an oblique line and rests upon the contact of the two earths, its motion oblique.

A weight equidistant from two world-centers halts midway (c, d e, a g b, f)

Given the centers of two worlds far apart and a uniform weight whose center of gravity is equally distant from both, Leonardo asks how it will fall. It moves for a long time along a path each part of which stays equally distant from both centers, finally stopping midway at the nearest such place, approaching neither center.

Reader's Edition — described with AI from the e-Leo transcription.