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" ... rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid - Página 131
por Euclid - 1838 - 416 páginas
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Modern geometry [ed.] with an appendix by W.B. Jack

Richard Wormell - 1876 - 264 páginas
...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 are homologous...
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Mathematical Exercises ...: Examples in Pure Mathematics, Statics, Dynamics ...

Samuel H. Winter - 1877 - 448 páginas
...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 equal...
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Solutions to the mathematical examination papers set for admission to the ...

D. Tierney - 1877 - 122 páginas
...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 direction...
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Elementary geometry

James Maurice Wilson - 1878 - 448 páginas
...the triangle ABC is to the triangle DEF in the duplicate ratio of BC to EF. THEOREM 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Let ABCDE, PQ_RST\3z similar polygons. JD S Divide each of them into the same number of similar triangles...
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The elements of plane geometry, from the Sansk. text of Ayra Bhatta, ed. by ...

Āryabhaṭa - 1878 - 96 páginas
...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...
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Elementary algebra, with brief notices of its history

Robert Potts - 1879 - 676 páginas
...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...
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Elementary algebra: with brief notices of its history

Robert Potts - 1879 - 668 páginas
...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...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 páginas
...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....
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Examination papers, and division lists, &c. [afterw.] General certificate of ...

Oxford univ, local exams - 1880 - 390 páginas
...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...
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880 - 190 páginas
...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...
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