| Euclides - 1860
...rectilineal figure may be described upon a given straight line, similar to one of six or more sides. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Given that ABC and DEF are similar triangles, having the angle B equal to the angle E, and AB to BC... | |
| EDUCATION SOCIETY'S PRESS, CULLA - 1860
...has to the fourth ? The sides about the equal angles of equiangular triangles are proportionals. 12. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** LOGIC. I.—LOWER STANDARD. What ii the use of words ? Explain First and Second Intention. 2. Give... | |
| Eucleides - 1860
...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
...angles proportionals, they are similar to one another. In the same manner a rectilineal figure of six **sides may be 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... | |
| Euclides - 1865
...proportionals ; wherefore AB3&HG la similar to CDKEF. In the same manner a rectilineal figure of six **sides [may 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... | |
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