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 61751 - 399 pagesFull view - About this book
| 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... | |
| 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... | |
| 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,... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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