 | 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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... polygons are to each other in the duplicate ratio of their homologous sides. 
