 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 - Strona 61751 - Liczba stron: 399Pełny widok - Informacje o książce
 | Colin Maclaurin - 1742 - Liczba stron: 482
...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 - Liczba stron: 506
...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 - Liczba stron: 296
...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 - Liczba stron: 476
...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 - Liczba stron: 222
...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 - Liczba stron: 798
...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 - Liczba stron: 542
...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 - Liczba stron: 216
...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 - Liczba stron: 304
...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 - Liczba stron: 370
...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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