| Geometry - 1751 - 399 pages
...what Art they could make a Tranfition from the one to the other. They found that fimilar Triangles **are to each other in the duplicate Ratio of their homologous Sides** •, and by refolving fimilar Polygons into fimilar fimilar Triangles, the fame Propofuion was extended... | |
| Colin MacLaurin - Calculus - 1801 - 510 pages
...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... | |
| University of Cambridge - 1802 - 298 pages
...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,... | |
| Cambridge (England) - 1804 - 476 pages
...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 - 179 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 - Mathematics - 1825 - 798 pages
...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... | |
| Euclides - 1826 - 226 pages
...triangle any part required, by a right line drawn parallel to a given right line. PROPOSITION XX. THEOREM. **Similar polygons may be divided into similar triangles, equal in number, and** homologous to the whole, and the polygons have to one another a duplicate ratio of that which their... | |
| Euclid - 1826 - 236 pages
...triangle any part required, by a right line drawn parallel to a given right line. PROPOSITION XX. THEOREM. **Similar polygons may be divided into similar triangles, equal in number, and** homologous to the whole, anf the polygons have to one another a duplicate ratio of that which their... | |
| Isaac Newton - Curves, Plane - 1826 - 208 pages
...what art they could make a transition from the one to the other. 2. 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 proportion was extended to these... | |
| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 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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