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Ahmes Alexandria algebraical Almagest alphabet Apollonius Arabic Archimedes Archytas Aristotle arithmetical astronomical attributed Bisect Bretschneider calculation called Cantor centre of gravity century Chasles chord circle circumference cited commentary cone conic sections contains cube curve cylinder Delambre described diameter Diophantus Dioptra drawn Egyptian ellipse equal equations Eratosthenes Euclid Eudemian summary Eudemus Eudoxus Eutocius evidence extant fact figure follows fractions Friedlein Geminus given ratio gives Greek geometry Hankel Heiberg Heron Hipparchus Hippocrates Hultsch hyperbola Hypsicles Iamblichus inscribed invented irepl isosceles later latus rectum lemmas magnitude Math mathematicians mathematics means mentioned method Nesselmann Nicomachus numbers Pappus parabola parallel perpendicular plane Plato Plutarch polygon porism problem Proclus produced proof Prop proportion propositions Ptolemy Pythagoras Pythagorean quoted rectangle right angles says segment shews side similar solution sphere square number straight line Suidas symbolism Thales Theon theorem theory Torelli translation treatise triangle vertex writer
Page 201 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Page 294 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the sum of the two rectangles contained by its opposite sides.
Page 300 - He finds as a general law that a ray, passing from a rarer to a denser medium, is refracted towards the perpendicular : if...
Page 196 - Give him threepence, since he must make gain out of what he learns.
Page 58 - IJandnotwith any special problem. course, that most astronomers mean by 'the universe' the sphere of which the centre is the centre of the earth and the radius is a line drawn from the centre of the earth to the centre of the sun.
Page 147 - At a given point in a given straight line, to make a rectilineal angle equal to a given rectilineal angle. Let AB be the given straight line, and A the given point in, it, and DCE the given rectilineal angle ; it is required to make...
Page 55 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 178 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.