Geometry of Indivisibles (Geometria Indivisibilibus Continuorum)

...which he called the chief and the capital city, ought to be held in high regard by students of the finest arts. For this reason, that great leader of the Academy The philosopher Plato, who founded the Academy in Athens. kept those ignorant of geometry away from the doors of the school. When Plato was asked about the Delphic Problem Also known as the problem of doubling the cube. According to legend, the oracle at Delos told the Athenians they must double the size of Apollo's cubic altar to stop a plague., he immediately responded that the Greeks were being accused by Apollo of neglecting Geometry.

Moreover, he criticized Eudoxus, Archytas, and Menechmus because they attempted to solve that problem using mechanical instruments. He said that by doing this, the virtue of Geometry was lost and corrupted, since it is sought for the sake of knowledge alone. Finally, he decorated geometry with so many praises that he asserted God himself always practices Geometry This refers to the famous phrase often attributed to Plato: "God always geometrizes.".

Among geometric subjects, I believe these are of a more difficult nature to contemplate. This is especially true because the path I have chosen has not yet, as far as I know, been worn by any previous footprint. For here, if I am not mistaken, you will find a new Geometry that has emerged by a reasoning unheard of until now. It weaves the complex web The Latin text uses the word Arachne, the mythical spider-weaver, to describe the intricate structure of geometric objects. of Continua using indivisibles Indivisibles are the building blocks of Cavalieri's method. He imagined a plane as made of infinitely many lines and a solid as made of infinitely many planes. as if they were threads. Therefore, although this work is modest, it is a new invention. It should be no less valuable to you in Mathematics than in other [matters]...