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" Similar triangles 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 ... - Seite 167
von Robert Simson - 1762 - 466 Seiten
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Elementary algebra, with brief notices of its history

Robert Potts - 1879 - 668 Seiten
...triplicate 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', V, ¿ represent the sides of two similar triangles ; Then,...
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Report on Foreign Systems of Naval Education

James Russell Soley - 1880 - 346 Seiten
...meet the 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 at entrance to ...

Sandhurst roy. military coll - 1880 - 68 Seiten
...proportion, and explain the terms triplicate ratio, componendo, and ex sequali. 7. Prove that similar triangles are to one another in the duplicate ratio of their homologous sides. 8. What is meant by the circular measure of an angle ? How many degrees, minutes, and seconds...
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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 426 Seiten
...situated to a given rectilineal figure of six sides ; and so on. y. KF PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, having the angle B equal to the angle E, and let AB be...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1881 - 236 Seiten
...to its 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...
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University local half-hour examination papers

John Robertson (LL.D., of Upton Park sch.) - 1882 - 152 Seiten
...square on 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...
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The Competitor, Bände 1-2

1882 - 480 Seiten
...equiangular pentagon. Euclid Book IV. Prop. 13. 5 (a) What is meant by duplicated ratio 1 (b) Similar triangles are to one another in the duplicate ratio of their homologous sides. (a) "When three magnitudes are proportionals, the first is said to have to the third the duplicate...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 Seiten
...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...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1883 - 428 Seiten
...proportionals ; therefore they are similar to one another. [VI. Definition 1, PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC and DEF be similar triangles, having the angle B equal to the angle E, and let AB be...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 Seiten
...BLMN similar and oppositely situated to the figure BAGH be obtained? PROPOSITION 19. THEOREM. Similar triangles are to one another in the duplicate ratio of their homologous sides. G Let ABC and DEF be similar triangles, having L. B = LE, and LC — LF, so that BC and EF are...
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