Introduction and books 1,2The University Press, 1908 - Mathematics, Greek |
Common terms and phrases
Abū al-Hajjāj angle ABC angle BAC Apollonius appears Arabic Archimedes Aristotle assumed axioms base bisects Campanus centre circle circumference coincide commentary Common Notion congruent conics construction contained curve definition edition Elements enunciation equal equilateral Eucl Euclid Euclid of Megara Euclid's Elements Eudemus Eutocius fact figure Fihrist follows Geminus geometers geometry given straight line gives gnomon greater Heiberg Heron hypothesis ibid interior angles interpolated later Latin lemma less magnitude mathematical means meet namely Pappus parallel parallelogram passage perpendicular plane Plato porism Posidonius postulate problem Proclus produced proposition proved Pythagorean quoted rectangle rectilineal reductio ad absurdum reference regards respectively right angles says Schol scholia scholium segment sides Simplicius Simson six Books solid square suppose surface Suter Tannery Theon Theonine MSS theorem things translation treatise triangle ABC words wrote δὲ καὶ τὰ τὸ τοῦ τῶν
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.
