Introduction and books 1,2The University Press, 1908 - Mathematics, Greek |
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Page 2
... says namely that he was of the school of Plato and in close touch with that philosophy ' . But this was only an attempt of a New Platonist to connect Euclid with his philosophy , as is clear from the next words in the same sentence ...
... says namely that he was of the school of Plato and in close touch with that philosophy ' . But this was only an attempt of a New Platonist to connect Euclid with his philosophy , as is clear from the next words in the same sentence ...
Page 3
... says that Euclid had not completely worked out the synthesis of the " three- and four - line locus , " which in fact was not possible without some theorems first discovered by himself . Pappus says on this1 : " Now Euclid- regarding ...
... says that Euclid had not completely worked out the synthesis of the " three- and four - line locus , " which in fact was not possible without some theorems first discovered by himself . Pappus says on this1 : " Now Euclid- regarding ...
Page 4
... says in the Aiadoxai . " In view of the poverty of Greek tradition on the subject even as early as the time of Proclus ( 410-485 A.D. ) , we must necessarily take cum grano the apparently circumstantial accounts of Euclid given by ...
... says in the Aiadoxai . " In view of the poverty of Greek tradition on the subject even as early as the time of Proclus ( 410-485 A.D. ) , we must necessarily take cum grano the apparently circumstantial accounts of Euclid given by ...
Page 5
... says that Euclid cut out two of 15 books of elements then existing and published the rest under his own name . According to Qādizade the king heard that there was a celebrated geometer named Euclid at Tyre : Naşir- addin says that he ...
... says that Euclid cut out two of 15 books of elements then existing and published the rest under his own name . According to Qādizade the king heard that there was a celebrated geometer named Euclid at Tyre : Naşir- addin says that he ...
Page 6
... say , geometry , so that Uclides is equivalent to the key of geometry ! Lastly the alternative version , given in brackets above , which says that Euclid made the Elements out of commentaries which he wrote on two books of Apollonius on ...
... say , geometry , so that Uclides is equivalent to the key of geometry ! Lastly the alternative version , given in brackets above , which says that Euclid made the Elements out of commentaries which he wrote on two books of Apollonius on ...
Common terms and phrases
angle ABC angle ACB angle BAC angles equal Apastamba Apollonius Arabic Archimedes Aristotle assumed axiom base BC bisects Book Campanus centre circle circumference coincide commentary Common Notion congruent construction contained definition diameter drawn edition Elements enunciation equal angles equal sides equal to AC Eucl Euclid Euclid's Elements Eudemus Eutocius exterior angle figure Fihrist follows Geminus geometry given straight line gives gnomon greater Greek Heiberg Heron hypothesis ibid interpolated isosceles triangle joined lemma length less Let ABC magnitude means meet method observed Pappus parallel parallelogram passage perpendicular plane Plato porism Posidonius postulate problem Proclus produced proposition proved Pythagoras Pythagorean Pythagorean theorem quoted rectangle reductio ad absurdum reference remaining angles respectively right angles right-angled triangle says Schol scholia segment semicircle Simplicius Simson square suppose surface Theon Theonine MSS theorem things translation triangle ABC words καὶ τὸ
Popular passages
Page 322 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 204 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 259 - If two triangles have two sides of the one equal to two sides of the...
Page 188 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Page 204 - In any triangle, the sum of the three angles is equal to two right angles, or 180°.
Page 162 - A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line.
Page 167 - When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.
Page 257 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 176 - Parallel straight lines are straight lines which, being in the same plane and being produced indefinitely in both directions, do not meet one another in either direction.
Page 235 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of' the base, equal to one another, and likewise those which are terminated in the other extremity.