| Robert Potts - Geometry, Plane - 1860 - 361 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, D.EFbe similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
| Euclides - 1860 - 288 pages
...the first to a similar, and similarly described triangle upon the second. PROPOSITION XX. THEOREM. **Similar polygons may be divided into the same number of similar triangles,** having the same ratio to one another that the polygons have ; and the polygons have to one another... | |
| Eucleides - 1860 - 396 pages
...homologous sides are parallel. PROPOSITION XIX. THEOREM. — If triangles (ABC, DEF) are similar, they **are to one another in the duplicate ratio of their homologous sides** (BC, EF). CONSMHTCTION. Take BG a third proportional to BC, EF (a), so that BC is to EF, as EF f* to... | |
| Euclides - 1861
...— to Plans, 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... | |
| War office - 1861 - 12 pages
...less than a semicircle is greater than a right angle. 10 DIRECT COMMISSIONS. VOLUNTAKY PORTION. 1. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 2. Describe a rectilineal figure which shall be similar to one given rectilineal figure and equal to... | |
| Education - 1863
...^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... | |
| Architecture - 1863
...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... | |
| Euclides - 1863
...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... | |
| Henry White - 1864
...it is the segment. 3. Give Euclid's definition of proportion and of similar figures, and show that **similar polygons may be divided into the same number of similar triangles** having the same ratio to one another that the polygons have. 4. Investigate a rule for extracting the... | |
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