| Architecture - 1863 - 300 pages
...scale of equal parts 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... | |
| Education - 1863 - 406 pages
...^5-^— 9=42 or £ 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... | |
| 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... | |
| Euclides - 1864 - 448 pages
...described upon a given straight line similar to one given, and so on. QE r. PROPOSITION XIX. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
| Robert Potts - 1865 - 528 pages
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION XIX. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB bo to BC, as... | |
| Thomas Baker (Civil engineer) - 1865 - 278 pages
...then, the triangle 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,... | |
| Euclides - 1865 - 402 pages
...be described upon a given straight line similar to one given, and so on. QEF PROP. XIX.— THEOBEM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** (References— Prop. v. 11, 16, def. 12; vi. 1, 11, 15.) Let ABC, DEF be similar triangles, having... | |
| McGill University - 1865 - 332 pages
...proportion, and show 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... | |
| 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... | |
| James Robert Christie - Mathematics - 1866 - 428 pages
...together with the segmenta of the former will be equal to the square of the radius of the circle. i 3. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 4. If two straight lines be at right angles to the same plane, they shall be parallel to one another.... | |
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