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It is difficult to argue with the fact that Euclid stands as one of the founding figures of mathematics. The ability of the ancient Greeks to perform complex mathematical calculations using only logic ... Read full review
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an-Nairizi angle ABC angle BAC angles equal Apollonius Arabic Archimedes Aristotle assumed axiom base BC bisects Book Campanus centre circle circumference coincide commentary Common Notion congruent construction curve definition diameter distance drawn edition Elements enunciation equilateral triangle Eucl Euclid Euclid's Elements Eudemus Eutocius figure Fihrist follows Geminus geometry given straight line gives gnomon greater Greek Heiberg Heron hypothesis ibid interior angles interpolated intersection joined lemma length less Let ABC magnitude means meet method observes Pappus parallel parallelogram passage perpendicular plane Plato porism Posidonius postulate problem Proclus produced proof proposition proved Pythagoras Pythagorean quadrilateral quoted rectangle contained reductio ad absurdum reference remaining angle respectively Riemann hypothesis right angles right-angled triangle says Schol scholia segment Simplicius solid square suppose surface Suter Theon theorem things three angles translation triangle ABC words
Page 402 - 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 307 - If two triangles have two sides of the one equal to two sides of the...
Page 202 - 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 218 - In any triangle, the sum of the three angles is equal to two right angles, or 180°.
Page 176 - 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 181 - 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 315 - 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 190 - 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.