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angle abc angle acb angle bad base bisected centre chord circle abcd circumference clid construction contains 30 cord Corollary demonstrated describe a square describe the circle describe the square diagonal diameter diameter ac divided double the square draw duplicate ratio equal angles equal sides equal to half equilateral triangle Euclid fore four given circle given circle abd given circle efgh given line given square abcd hexagon homologous sides hypothenuse join Let abcd manner multiple nine one-third PROBLEM produce Proposition quadruple the square radii radius ac remaining angle represent right line right-angle scribed sextuple side ab side bc square described square efgh square gikl square of ac subtend Supplement triangle abc trigon abc triple the square trisected wherefore the angle wherefore the square whole
Pagina 62 - Similar triangles are to one another in the duplicate ratio of their homologous sides.
Pagina 41 - PROP. XV. THEOR. Magnitudes have the same ratio to one another which their equimultiples have. Let AB be the same multiple of C, that DE is of F: C shall be to F, as AB to DE.
Pagina 63 - Ratios that are the same to the same ratio, are the same to one another.
Pagina 39 - F is of B, and that magnitudes have the same ratio to one another which their equimultiples have; (v.
Pagina 13 - PQ the given straight line, and A the given point in it. It Is required to describe a circle to touch ihe 0 DEB, and also to touch PQ at A.
Pagina 56 - In any triangle the square on a side opposite to an acute angle is less than the sum of the squares on the sides which contain the acute angle ; (e}. In an obtuse-angled triangle the square on the side subtending the obtuse angle is greater than the sum of the squares on the sides containing...
Pagina 57 - PROPOSITION 20. In a circle the angle at the centre is double of the angle at the circumference, when the angles have the same circumference as base.
Pagina 63 - CE equal to the ratio of the square of AB to the square of AD.