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" They found, that similar triangles are to each other in the duplicate ratio of their homologous sides; and, by resolving similar polygons into similar triangles, the same proposition was extended to these polygons also. "
The Mathematician - Page 6
1751 - 399 pages
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A treatise of fluxions, Volume 1

Colin Maclaurin - 1742 - 482 pages
...beft guard againft exceptions and cavils, and vary lefe from the old foundations of geometry. A 2 They They found, that fimilar triangles are to each other in the duplicate ratio ot their homologous fides; and, by refblving fimilar polygons into fimilar triangles, the fame propofition...
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A Treatise on Fluxions: In Two Volumes, Volume 1

Colin MacLaurin - 1801 - 506 pages
...cavils, and vary less from the old foun- " dations of geometry. A 2 They • They found, that similar triangles are to each other in the duplicate ratio of their homologous sides ; and, by resolving similar polygons into similar triangles, the same proposition was extended to these polygons...
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Calendar

University of Cambridge - 1802 - 296 pages
...MISCELLANEOUS QUESTIONS. Trisect a right angle. Find the diameter and diagonal of a cube whose side Similar triangles are to each other in the duplicate ratio of their homologous sides. — Prove it. JProve the truth of the Arithmetical rules for the addition, tubtraction, multiplication,...
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New Cambridge Guide; Or, A Description of the University, Town, and County ...

1804 - 476 pages
...MISCELIANEOUS QUESTIONS. Trisect a right angle. Find the diameter and diagonal of a cube whose side = 7Similar triangles are to each other in the duplicate ratio of their homologous sides. — Prove it. Prove the truth of the Arithmetical rules for the addition, subtraction, multiplication,...
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The First Six Books with Notes

Euclid - 1822 - 222 pages
...FGIKLare equiangular, they are similar (5). PROP. XIX. THEOR. Fig. 25. Similar triangles (ABC, F1L) are to each other in the duplicate ratio of their homologous sides, Take a third proportional KC to the homologous . (3) Constr. Since AC is to CB as FL to LI (l), permutando...
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Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - 1825 - 798 pages
...proportionals, the greatest and least of them together are greater than the other two together. 8. Similar triangles are to each other in the duplicate ratio of their homologous sides. 9. In any parallelogram, the sum of the squares of the diagonals is equal to the sum of the squares...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 542 pages
...figure equal to it in area, is given. PROPOSITION XIX. THEOREM. (625) Similar triangles (ABC, FIL) are to each other in the duplicate ratio of their homologous sides. Take a third proportional KC to the homologous sides AC and FL, and join B K. B Since AC 'is to CB...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 216 pages
...divided into similar triangles, equal in number and proportional to the polygons : and the polygons are to each other in the duplicate ratio of their homologous sides. Part 1. For the angles G and E are equal, and the (i) Hypoth. sides about them proportional (1), therefore...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833 - 304 pages
...divided into similar triangles ; equal in number and proportional to the polygons ; and the polygons are to each other in the duplicate ratio of their homologous sides. PART 1. Divide the polygons into AS by lines drawn from the vertices of corresponding L s. The A s...
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A treatise on practical geometry, mensuration, conic sections, gauging, and ...

Ireland commissioners of nat. educ - 1834 - 370 pages
...being to each other as the squares of their homologous sides, (19. VI.) we Cor. As similar polygons are to each other in the duplicate ratio of their homologous sides, (20. VI.) it follows that the square of the side of any polygon, multiplied by the area of a similar...
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