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" ... polygons are to each other in the duplicate ratio of their homologous sides. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 32
by Euclides - 1833
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The Mathematician

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...
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A Treatise on Fluxions: In Two Volumes, Volume 1

Colin MacLaurin - Calculus - 1801 - 412 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...
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Register

University of Cambridge - 1802
...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 ...

Cambridge (England) - 1804 - 130 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,...
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The First Six Books with Notes

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...
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Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1825
...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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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...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...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 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...
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The First Three Sections of Newton's Principia: With Copious Notes and ...

Isaac Newton - Curves, Plane - 1826 - 183 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...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 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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