 | Āryabhaṭa - 1878 - 100 sider
...them (As. I). Wherefore if two triangles &c. QED PEOP. xxxrv. THEOREM. (E. 6. 1.9). Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, and let the angle ABC be equal to the i^ngle DEF, and let AB... | |
 | Robert Potts - 1879 - 668 sider
...in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. (Eue. VI. 19.) Let а, Ь, с ; a', V, ¿ represent the sides of two similar triangles ; Then, because... | |
 | Robert Potts - 1879 - 672 sider
...in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. Similar triangles are to one another in the duplicate ratio of their homologous sides. (Eue. VI. 19.) Let а, Ь, с ; a', I', c' represent the sides of two similar triangles ; Then, because... | |
 | Isaac Todhunter - 1880 - 426 sider
...to one another in the duplicate ratio of their homologous sides ; and it has already been shewn for triangles ; therefore universally, similar rectilineal...in the duplicate ratio of their homologous sides. COROLLARY 2. If to AB and FG, two of the homologous sides, a third proportional M be taken, [VI. 11.... | |
 | Oxford univ, local exams - 1880 - 396 sider
...middle point of the base to the opposite vertex. z. Euclid VI— XI, and Conic Sections. 10. Similar figures are to one another in the duplicate ratio of their homologous sides. Bisect a given triangle by a straight line drawn parallel to the base. 11. The rectangle contained... | |
 | James Russell Soley - 1880 - 346 sider
...tangents at A, B in D, E; prove that AB is a mean proportional between AD, BE. 12. Similar triangles are to one another in the duplicate ratio of their homologous sides. TRIGONOMETRY. Examiner.— Prof. C. NIVEN. Lieutenants qualifying for gunnery and torpedo officers.... | |
 | Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 sider
...Prove that АO . OD = BO . 0C (the corners А, C being opposite to one another). 11. Similar triangles are to one another in the duplicate ratio of their homologous sides. 1. Prove that am x a" = am + ', m and n being positive integers ; and assuming this formula to hold... | |
 | 1884 - 538 sider
...of similar triangles, having the same ratio to one another that the polygons have, and the polygons are to one another in the duplicate ratio of their homologous sides. . / 16. "From the same point in a given plane, there cannot be two straight lines at right angles to... | |
 | Euclides - 1881 - 236 sider
...different nngles. The proof In thus also more easlly established. PROP. XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, and let the angle ABC be equal to the angle DEF, and let AB be... | |
 | 1882 - 486 sider
...4. Inscribe a regular equilateral and equiangular pentagon in a given circle. 5. Similar triangles are to one another in the duplicate ratio of their homologous sides. 6. Two circles whose centres are A and B, intersect in C and D, shew that AB bisects CD at right angles.... | |
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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
