 | Euclides - 1861 - 464 pages
...Maps, and Geometrical Drawings of every kind. PROP. 19. — THEOR. (Very important.) Similar triangles are to one another in the duplicate ratio of their homologous sides ; ie, as the squares of their like sides. CON. 11, VI. DEM. Def. 12, V.— 16, V. If four Ms of of... | |
 | Euclides - 1863 - 122 pages
...and this has been proved of triangles (VI. 19); therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Cor. 2.-—If to AB and FG, two of the homologous sides of the polygon, a third proportional M bo taken... | |
 | Education - 1863 - 406 pages
...the triangle ABC. I should mention 2 to draw ox parallel to BG. Now we know that similar triangles are to one another in the duplicate ratio of their homologous sides . • . BGC : oxC::BGa : ox', or 47.04 : 42::11.2" : 112 the square root of which is 10.583+=ox, or... | |
 | Architecture - 1863 - 300 pages
...how a rule of three sum may be solved geometrically. 9. Proposition 19. Theorem. Similar triangles are to one another in the duplicate ratio of their homologous sides. J 0. If the superficial content of a triangle which has a base of 40 feet is 800 feet, what is the... | |
 | Euclides - 1864 - 448 pages
...has already been proved in triangles : (VI. 19.) therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, (vI. 11.) 280... | |
 | Robert Potts - 1865 - 528 pages
...has already been proved in triangles : (vi. 19.) therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. CoR. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, (vi. 11.) AB... | |
 | Thomas Baker (Civil engineer) - 1865 - 278 pages
...ABC is to the triangle AED as the square of AB is to I lie. square of AE : that is, similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of their homologous,... | |
 | Thomas Baker (C.E.) - 1865 - 174 pages
...greatest angle : theorem, 17 ; any two angles being Rven, the, becomes known : theorem, ' ; similar, are to one another in the duplicate ratio of their homologous sides: theorem, 17. Triangular prism, definition of, 52. Triangular fields, method of surveying with chain... | |
 | McGill University - 1865 - 332 pages
...that it agrees with Euclid's. 9. Find a third proportional to two given lines. 10. Similar triangles are to one another in the duplicate ratio of their homologous sides. 11. If 3 men can mow 7 acres of grass in 5 days of 9 hours each, in how many days of 8 hours each will... | |
 | Euclides - 1865 - 402 pages
...has already been proved in triangles; (vi. 19.) therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. Cor. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken ; (vi. 11.)... | |
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... figures are to one another in the duplicate ratio of their homologous sides. 
