The Thirteen Books of Euclid's Elements, Tr. from the Text of Heiberg, Volume 1The University Press, 1926 - Mathematics, Greek |
From inside the book
Results 1-5 of 99
Page 11
Euclid Sir Thomas Little Heath. and proved only the fact that that which is sought really exists , but did not ... prove this he assumes the following construction . E being any straight line greater than c , he says : let KG be parallel ...
Euclid Sir Thomas Little Heath. and proved only the fact that that which is sought really exists , but did not ... prove this he assumes the following construction . E being any straight line greater than c , he says : let KG be parallel ...
Page 13
... prove ) that the angles at the base of isosceles triangles are equal is a matter of theoretic argument , and it is with ... proved , that certain points lie on straight lines given in position , with the class indicated by II . above ...
... prove ) that the angles at the base of isosceles triangles are equal is a matter of theoretic argument , and it is with ... proved , that certain points lie on straight lines given in position , with the class indicated by II . above ...
Page 27
... proved by me without using the parallels of the commentators " . " By " the commentators " Pappus is doubtless meant ... prove the parallel - postulate . It starts from a definition of parallels which agrees with Geminus ' view of them ...
... proved by me without using the parallels of the commentators " . " By " the commentators " Pappus is doubtless meant ... prove the parallel - postulate . It starts from a definition of parallels which agrees with Geminus ' view of them ...
Page 28
... proved and warned the unwary against hastily concluding that two straight lines approaching one another must necessarily meet ( cf. a curve and its asymptote ) , gives no hint that Geminus did try to prove the postulate . It may well be ...
... proved and warned the unwary against hastily concluding that two straight lines approaching one another must necessarily meet ( cf. a curve and its asymptote ) , gives no hint that Geminus did try to prove the postulate . It may well be ...
Page 33
... proved by Euclid , selecting the more subtle of the comments made on them by the ancient writers , and cutting down their interminable diffuse- ness ... " : not a word about anything of his own . At the same time , he seems to imply ...
... proved by Euclid , selecting the more subtle of the comments made on them by the ancient writers , and cutting down their interminable diffuse- ness ... " : not a word about anything of his own . At the same time , he seems to imply ...
Other editions - View all
Common terms and phrases
angle ABC angle ACB angle BAC angles equal Apollonius Arabic Archimedes Aristotle assumed axiom bisected Book Campanus centre circle circumference commentary Common Notion congruent construction definition diameter drawn edition Elements enunciation equilateral triangle Eucl Euclid Euclid's Elements Eudemus Eutocius Fihrist follows Geminus geometry given straight line gives gnomon greater Greek Heiberg Heron hypothesis ibid interior angles interpolated isosceles joined lemma less Let ABC magnitude means meet namely Pappus parallel parallelogram passage perpendicular plane Plato porism Posidonius postulate problem Proclus produced proposition proved Ptolemy Pythagoras Pythagorean quoted rectangle rectangle contained reductio ad absurdum reference remaining angle respectively right angles right-angled triangle says Schol scholia scholium segment sides Simplicius solid square on AC suppose surface Suter Theon Theonine MSS theorem things three angles translation triangle ABC twice the rectangle words καὶ τὸ τῶν