 | Euclides - 1860 - Liczba stron: 288
...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 - Liczba stron: 612
...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 - Liczba stron: 396
...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 - Liczba stron: 464
...— 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 - Liczba stron: 714
...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... | |
 | 1863 - Liczba stron: 406
...^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... | |
 | 1863 - Liczba stron: 300
...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 - Liczba stron: 122
...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 - Liczba stron: 448
...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 - Liczba stron: 402
...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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SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
