 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 pàgines
...truth of I. 37, since VI. 6 does not depend on I. 37. PKOP. XIII.— THEOREM. (Euc. VI. 19.) Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and OPQ be similar triangles, having the angle B equal to the angle P, and AB to BC... | |
 | Richard Wormell - 1876 - 268 pàgines
...circumscribed circles, or their proportionals the radii of the inscribed circles. THEOREM LXXXV. (¿.) Similar triangles are to one another in the duplicate ratio of their homologous sides. Let А В С, DEF be similar triangles having Z. B = ¿EandAB:DE = BC:EFso that В С and E^F... | |
 | Association for the improvement of geometrical teaching - 1876 - 66 pàgines
...another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles are to one another in the duplicate ratio of their homologous sides. THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio... | |
 | Robert Potts - 1876 - 446 pàgines
...taking equimultiples according to the definition, that 2, 3, 9, 13, are not proportionals. , 4. Similar triangles are to one another in the duplicate ratio of their homologous sides. 5. To find a mean proportional between two given straight lines. 6. Through C, the vertex of... | |
 | D. Tierney - 1877 - 126 pàgines
...Then EHF is the triangle required, for it is isosceles and equal to EFG, that is, to ABC. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. Given a point O in the line AB, find two other points 0, J?, such that a line OP given in... | |
 | Samuel H. Winter - 1877 - 452 pàgines
...same base, are to one another as their altitudes. 7. Define duplicate ratio, and prove that similar triangles are to one another in the duplicate ratio of their homologous sides. On the side AB of a triangle ABC, AD is taken equal to one third of AB ; and on AC, AE is taken... | |
 | James Maurice Wilson - 1878 - 450 pàgines
...another in the ratio compounded of the ratios of their bases and of their altitudes. THEOREM 15. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC, DEF be similar triangles having the angles at A, B, C respectively equal to the angles... | |
 | Āryabhaṭa - 1878 - 100 pàgines
...equal to 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... | |
 | Isaac Sharpless - 1879 - 282 pàgines
...Theorem.—Similar triangles are to one another as the squares of their homologous sides. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB : BC :: DE : EF, so that BC and EF are homologous sides; then ABC : DEF ::BC* : EF\ Because ABC, DEF... | |
 | Robert Potts - 1879 - 672 pàgines
...triplícala ratios 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,... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
