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Library/Codex Madrid I/f 89v-f 90r

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Codex Madrid I — f 89v-f 90r

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Biblioteca Nacional de España, Madrid

(Dall'alto al basso:)

Colpo.

Quel cubo d'equali angoli e llati, si transformerà in più perfecto circulo, che dda equal colpo sarà più dilatato.

Tucta la grosseza del cubo che sspericamente il suo cientro circunda, è quella che, mediante il colpo, con equal circulation dal suo cientro si dilata, onde che i recti angoli e llati, che da ttal multiplication sosspinti sono in nella figura che dentro a llor s'acresscie fien consumati282.

Il cientro indivisibile esser non può se ssperico imaginato non fia. E ss'elli è ssperico, spericamente dal suo contacto283è circundato. E così succiessivamente l'uno sperico dall'altro è vesstito, insin che ll'ultimo ne' più vicini stremi de' corpi è consummato. Onde se lla magior somma del corpo spericamente il suo cientro circunda, quando esso sarà dal colpo premuto, ogni parte d'esso fia d'equal circulatione284 dal cientro dilatata. E lle linie de' moti fatti da' fugienti stremi saranno tucte d'equal lungheza e circularmente al cientro riguardevoli. E lle parti de' lati che ffieno più propinque a esso cientro285, si partiranno fra angoli più equali e ssi faranno dalla linia d'essi lati più remoti. Essendo le parti dal lor cientro equalmente pel colpo remosse, fanno a llor atione obbedienti le diritte stremità de' corpi, onde di recte linie in curve si convertano. Li angoli adunque, che fuori dello sperico286 rimangano, pel circulare acresscimento che con loro287 si congiugnie, si vano aprendo e ssi fanno grossi, e 'nsieme con tutto il corpo in un circulo si convertano.

(From top to bottom:)

Blow.

That cube of equal angles and sides will transform into a more perfect circle the more it is dilated by an equal blow.

The whole thickness of the cube that spherically surrounds its centre is that which, by means of the blow, dilates with equal circulation from its centre, whence the right angles and sides, which are thrust by such multiplication into the figure that grows within them, will be consumed.

The centre cannot be indivisible unless it be imagined as spherical. And if it is spherical, it is spherically surrounded by its own contact. And thus successively one sphere is clothed by another, until the last is consumed in the nearest extremities of the bodies. Whence, if the greater sum of the body spherically surrounds its centre, when it is pressed by the blow, every part of it will be dilated with equal circulation from the centre. And the lines of the motions made by the fleeing extremities will all be of equal length and directed circularly toward the centre. And the parts of the sides nearest to that centre will separate at more equal angles and will move farther from the line of those sides. The parts being equally removed from their centre by the blow, the straight extremities of the bodies obey their action, whence they are converted from straight lines into curves. The angles, therefore, that remain outside the sphere, through the circular growth that joins with them, go on opening and become thick, and together with the whole body are converted into a circle.

How a struck cube dilates into a circle

The theory of the blow: matter spreads equally from the centre, turning a square body round

Physics & Mechanics Geometry

This densely written page sets out Leonardo's theory of impact: a cube of equal sides and angles, when struck by a blow, dilates equally in all directions from its centre and so tends toward a 'more perfect circle.' He imagines the centre as a sphere clothed by successive spheres, so that when the body is compressed every part moves outward along lines of equal length directed toward the centre, and the straight edges are converted into curves. The corners left outside the sphere open out and thicken until the whole body is turned into a circle. A small circle-with-cross figure at the top right accompanies the argument.

On this page

A blow dilates the cube equally from its centre

The whole thickness of the cube that spherically surrounds its centre is what, under the blow, dilates with equal circulation from that centre. Every part is moved outward by equal amounts, so that the body swells uniformly and its right angles and sides are consumed as the growing round figure absorbs them.

Straight edges converted into curves

Leonardo pictures the centre as spherical, clothed by one sphere after another. When the body is pressed, the lines of motion from its fleeing extremities are all of equal length and point circularly toward the centre; the straight sides obey and are converted from straight lines into curves, until the whole becomes a circle.

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