By Thomas L. Heath, Euclid
This unabridged republication of the unique enlarged variation comprises the full English textual content of all thirteen books of the Elements, plus a severe equipment that analyzes each one definition, postulate, and proposition in nice element. It covers textual and linguistic issues; mathematical analyses of Euclid’s principles; classical, medieval, Renaissance, glossy commentators; refutations, helps, extrapolations, reinterpretations, and old notes, all given with wide quotes.
“The textbook that shall quite change Euclid has no longer but been written and doubtless by no means will be.” — Encyclopaedia Britannica.
Volume 1. 151-page creation: existence and different works of Euclid; Greek and Islamic commentators; surviving mss., scholia, translations; bases of Euclid’s concept. Books I and II of the Elements, immediately strains, angles, intersection of traces, triangles, parallelograms, etc.
Volume 2. Books III-IX: Circles, tangents, segments, figures defined round and inside of circles, rations, proportions, magnitudes, polygons, major numbers, items, airplane and good numbers, sequence of rations, etc.
Volume three. Books X to XIII: planes, sturdy angles, etc.; approach to exhaustion in related polygons inside circles, pyramids, cones, cylinders, spheres, and so forth. Appendix: Books XIV, XV, occasionally ascribed to Euclid.
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Additional info for The thirteen books of Euclid's Elements, Vol 1 Books 1-2
46, 47. 1 2 PROCLUS AND HIS SOURCES CR. " Further, the pupils whom he was addressing were beginners in mathematics; for in one place he says that he omits" for the present" to speak of the discoveries of those who employed the curves of Nicomedes and Hippias for trisecting an angle, and of those who used the Archimedean spiral for dividing an angle in any given ratio, because these things would be too difficult for beginners (ovU(J€ClJP~TOU" TOIS €lua'Yol1-€l/o~,,)3. , or to exhort them, as he often does, to work out other particular cases for themselves, for practice ('YuJLl/aura" [l/€Ka )6.
Van Pesch further supposes that it was in Heron's commentary that the proof by Menelaus of I. 25 and the proof by Philo of I. 8 were given. 1 Cf. I ... • 2 De Proclifontibus, Lugduni-Batavorum, 1900. 289, 18 Xl-y.. o~j, ns I)n OUK tgn INTRODUCTION 24 ECHo III The last reference to Heron made by an-N airizi occurs in the note on VIII. 27, so that the commentary of the former must at least have reached that point. II. Porphyry. D. Whether he really wrote a systematic commentary on the Elemmts is uncertain.
32 to the effect that the converse (that a figure with its interior angles together equal to two right angles is a triangle) is not true unless we confine ourselves to rectilineal figures. This statement is supported by reference to a figure formed by four semicircles whose diameters form a square, and one of which is turned inwards while the others are turned outwards. The figure forms two angles « equal to" right angles in the sense described by Pappus on Post. 4, while the other curvilineal angles are not considered to be angles at all, and are left out in summing the internal angles.
The thirteen books of Euclid's Elements, Vol 1 Books 1-2 by Thomas L. Heath, Euclid