Geometry of Indivisibles (Geometria Indivisibilibus Continuorum)

method, we bring it into port, so that all ambiguity of risking danger on the rocks of that infinity is finally removed. I know, however, that at first glance these things may be less approved by those who weigh them lightly, since they have not been investigated through the long-trodden path of Geometry. But those who do not disdain to suppress the swelling breaths of a nauseous stomach at the beginning and reach the final goal of this doctrine, will perhaps no longer feel nausea over it. Therefore, I ask that no one wish to condemn this method before they have surveyed all these things with the pure eye of truth and a sincere affection for it. Here they will notice that the things demonstrated by natural reason constantly agree perfectly original: "ad unguem", literally "to the fingernail," a Roman idiom for high precision with the discoveries of others. Let no one approach this work who is not well-versed in at least the first six Books and the eleventh Book of the Elements This refers to Euclid's Elements, the foundational textbook for geometry.. If the reader is also experienced in the works of Apollonius and Archimedes, they will grasp these things more easily. If not, they can assume the few things that have been taken from them.

He who has seen the Commentary on the Motion of Mars Referring to Johannes Kepler's Astronomia Nova (1609), which transformed astronomy by introducing elliptical orbits. by the aforementioned Kepler will clearly understand through our speculations how easily he could have erred original: "hallucinari", meaning to wander in mind or commit a blunder in the dimension of the plane of the ellipse. This occurred while he thought the measure of all distances of a planet from the Sun, as it revolves along the elliptical line, was equivalent to the measure of the plane of the ellipse. This is somewhat similar to an error into which I myself had fallen at the beginning of the present speculation, thinking that coinciding lines or planes preserve the same proportion as the planes or solids. However, Kepler afterwards detects his own error and strives to correct it in some way. These things having been duly considered, I believe there will be no one who considers this new method worthy of rejection. Instead, they will perhaps later approve it more fully with a white stone original: "albo adiecto calculo," a Roman custom of using a white stone to signify a favorable vote or approval. They will see it as a golden key that unlocks several doors of the highest citadel of Geometry that have been closed until now, so that we may become very rich with the greatest treasures of the most beautiful speculations.

A horizontal row of nine small decorative woodcut ornaments is displayed. Each ornament depicts a stylized cluster of grapes hanging from a vine with two leaves.