Search Loci: Convergence:
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. . . . The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test; there is no permanent place in the world for ugly mathematics.
G. H. Hardy
Christopher Clavius's edition of Euclid's Elements
This is the title page of Christopher Clavius’ ( 1538--1612) Elements published in Rome in 1574. Note that Clavius indicates his volume contains 15 books of Euclid. Many medieval authors erroneously attributed two extra books to Euclid's Elements. Book XIV extends Euclid discussion in book XIII on the comparison of the regular solids inscribed in a sphere. This work is now believed to have been composed by Hypsicles of Alexandria (ca.190 BCE—ca 120 BCE). Book XV also deals with the properties of regular solids and is believed to have been compiled by Isidore of Miletus (fl.ca. 532), who was the architect responsible for the Cathedral of Holy Wisdom in Constantinople, later to become the Hagia Sophia.
Below are Euclid’s propositions I-46 and I-47 as given in Clavius’ Elements. Proposition 47 is the Pythagorean Theorem.