Girolamo Saccheri's Euclides Vindicatus

Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: EUCLID FREED OF EVERY FLECK A GEOMETRIC ENDEAVOR IN WHICH ARE ESTABLISHED THE FOUNDATION PRINCIPLES OF UNIVERSAL GEOMETRY GIROLAMO SACCHERI OF THE SOCIETY OF JESUS norusoR Of Mathematics In The University Of Favia. A WORK DEDICATED TO THE NOBLE SENATE OF MILAN BY THE AUTHOR MILAN, 1733 PAOLO ANTONIO...
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Purchase of this book includes free trial access to www.million-books.com where you can read more than a million books for free. This is an OCR edition with typos. Excerpt from book: EUCLID FREED OF EVERY FLECK A GEOMETRIC ENDEAVOR IN WHICH ARE ESTABLISHED THE FOUNDATION PRINCIPLES OF UNIVERSAL GEOMETRY GIROLAMO SACCHERI OF THE SOCIETY OF JESUS norusoR Of Mathematics In The University Of Favia. A WORK DEDICATED TO THE NOBLE SENATE OF MILAN BY THE AUTHOR MILAN, 1733 PAOLO ANTONIO MONTANO SUPEXIOKUM PERMTSSU PROGEMIUM AD LECTOREM. Quanta sit Elementorum Euclidis praestantia, ac dig- nitas, nemo omnium, qui Mathematicas disciplinas no- verint, ignorare potest. Lectissimos hanc in rem testes adhibeo Archimedem, Apollonium, Theodosium, aliosque pene innumeros, ad haec usque nostra tempora rerum Mathematicarum Scriptores, qui non aliter haec Euclidis Elementa usurpant, nisi ut principia jam diu stabilita, ac penitus inconcussa. Verum tanta haec nominis celebri- tas vetare non potuit, quin multi ex Antiquis pariter, ac Recentioribus, iique Magni Geometrae naevos quosdarn a se deprehensos censuerint in his ipsis pulcherrimis, nec unquam satis laudatis Elementis. Tres autem hujus- modi naevos designant, quos statim subnecto. Primus respicit definitionem parallelarum, et sub ea Axioma, quod apud Clavium est decimumtertium Libri primi, ubi Euclides sic pronunciat: Si in duas rectas lineas, in eodem plano existentes recta incidens linea duos ad easdem partes internos angulos minores duobus rectis cum eisdem efficiat, duae illae rectae lineae ad eas partes in infinitum protractae inter se mutuo incident. Porro nemo est, qui dubitet de veritate expositi Pronunciati; sed in eo unice Euclidem accusant, quod nomine Axio- matis usus fuerit, quasi nempe ex solis terminis rite per- spectis sibi ipsi faceret fidem. Inde autem non pauci (retenta caeteroquin Euclidaea parallelarum definitione)PREFACE TO THE READER. Of all who have lea...