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" Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Side 180
av Robert Simson - 1806 - 518 sider
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Elementary algebra, with brief notices of its history

Robert Potts - 1879
...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
...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 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....
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Examination papers, and division lists, &c. [afterw.] General certificate of ...

Oxford univ, local exams - 1880
...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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Report on Foreign Systems of Naval Education

James Russell Soley - 1880 - 335 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....
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Military examinations. Mathematical examination papers, set for entrance to ...

Woolwich roy. military acad, Walter Ferrier Austin - 1880
...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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The Cambridge Examiner, Volum 4

1884
...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...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881
...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...
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The Competitor, Volumer 1-2

1882
...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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University local half-hour examination papers

John Robertson (LL.D., of Upton Park sch.) - 1882
...the line which meets the circle, the line which meets the circle shall touch it. 7. Similar triangles are to one another in the duplicate ratio of their homologous sides. TnEEE-nouE PAPEE. 1. Quote the passages in Genesis which relate to a SAVIOUE, as nearly as you can...
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