Transforming rectangles: widening and shortening

Widening a parallelogram's front and finding its shortening

The front of parallelogram a c b d is widened from a to g, then its shortening is sought. Extending line g f straight until it joins corner b and meets line c f at point f gives the required width in g c and the length in d f.

Length gained as width is uniformly narrowed

A series of paired problems asks for the length a quadrilateral acquires when its width is diminished, and conversely the width regained when it is shortened. Leonardo repeats the reciprocal statement several times, treating the reshaping as an exchange of proportional quantities.

A note on raising ten pounds

A small figure at the right is marked with the numbers 100 and 99 and the remark that here ten pounds is raised. It sits apart from the geometric transformations that occupy the rest of the sheet.

Cancellato nel margine superiore:

Figura colle lettere:

Figura di rettangolo raccortato:

Doppia figura di rettangolo raccortato e alzato:

Due figure analoghe:escerà per lunghezza?

Figura di parallelogrammo:

Parallelogrammo:

A destra, figura con:

Figura biffata, con:

Analoga figura, con:

Cancelled in the upper margin:

Figure with letters:

Figure of a shortened rectangle:

Double figure of a rectangle shortened and heightened:

Two analogous figures:

Figure of a parallelogram:

Parallelogram:

On the right, figure with:

Struck-out figure, with:

Analogous figure, with:

Transforming rectangles: widening and shortening

On this page

Widening a parallelogram's front and finding its shortening

Length gained as width is uniformly narrowed

A note on raising ten pounds