Excerpt from Euclidis Elementorum Libri Priores Sex, Item Undecimus Et Duodecimus, Ex Versione Latina Federici Commandini: Sublatis Iis Quibus Olim Libri Hi a Theone, Aliisve, Vitiati Sunt, Et Quibusdam Euclidis Demonstrationibus Restitutis Bus planis multitudine et magnitudine aequalibus continentur; efi vero Prepofitio haec Theorema, non Definitio, quoniam acqualitas fi gurarum quammcunquc demonfiranda efi, non vero afiumenda. Quam; vis igitur vera fuifiet, demonfirari debuit haec Propofitio; non autem femper vera efi extra cafum in quo figurarum anguli folidi non pluri bus tribus angulis planis continentur, in aliis enim cafibus, duac figurae folidae pof'funt contineri planis fimilibus, multitudine et magnitudine ae qualibus, et tamen inter fe inaequales effe, ut in Notis, bifee Elemen tis annexis, perfpicue ofiendetur. Fimiliter, in Demonfiratione Prepo fitionis 26tac Libri I 1 mi, afiumitur duos angulos folidos inter fe ae quales effe, fi angulis planis multitudine et magnitudine aequalibus con tineantur fed neque hoc femper verum efi extra cafum in quo anguli folidi non pluribus tribus angulis planis continentur, cujus tamen ca fus nulla, quamvrs omnino fit necefiaria, in Elementis Demonfiratio hac tenus habetur. Ex Definitione autem 1 o ma pendentpropofitioncs 2 5ta et 28 Libri 1 I mi, et ex Propofitione 2 5ta vel 2 6 pendent ocio aliac, viz. Propp. 27m, 3 1 ma, 3 2 da, 3 3 'i, 34 3 6 37m, 40ma Libri ejufdem; et 1 2 ma Libri I 2 mi pendet ex 8 ejufdem, eademque Corollarium 1 7mae, et Prop. 1 8 Libri 1 2 mi pen dent ex Definiti0ne Libri 1 1 mi quae minime proba efi, quo niam pofiimt effe figurae folidae contentae planis fimilibus, multitudine aequalibus, quae tamen minime funi fimiles. Omnes igitur hac Propofitio nes infirrno haéienus innitebantur fundam ento. Alia etiam funt, non pau ca, quae minime videntur Euclidis effe, et quae fatis ofiendunt Elcmenta ejus a Geometriae imperitis non leviter effe corrupta; et quidem quam vis haec non aeque craflà fim: ac praedié'ta errata, funt tamen necef. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.