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added alphabet Apollonius appear applied Arabic Archimedes arithmetical astronomical attributed base begins calculation called Cantor centre century Chasles chord circle cited commentary common cone conic contains curve definitions described diameter Diophantus divided division doubt draw drawn early Egyptian Elements equal equations Euclid Eutocius evidence fact figure follows four fractions geometry given gives greater Greek hand Heiberg Heron instance interesting introduced invented kind known later less magnitude mathematics means measure mentioned method numbers observations original Pappus parallel perhaps plane Plato porism position practice probably problem Proclus produced proof Prop proportion propositions proved Ptolemy quoted ratio rectangle reference remains right angles rule says seems segment side signs similar solution sphere square straight line suggested supposed symbolism taken theorem theory translation treated treatise triangle whole writer written
Page 199 - 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 292 - 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 298 - He finds as a general law that a ray, passing from a rarer to a denser medium, is refracted towards the perpendicular : if...
Page 194 - Give him threepence, since he must make gain out of what he learns.
Page 56 - 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 145 - 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 53 - 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 176 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.