 | 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: 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... | |
 | 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... | |
 | 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... | |
 | Henry White - 1864 - Liczba stron: 156
...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...same ratio to one another that the polygons have. 4. Investigate a rule for extracting the cube root of an algebraical expression. 5. Reduce to its lowest... | |
 | Euclides - 1864 - Liczba stron: 448
...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... | |
 | Woolwich roy. military acad - 1864 - Liczba stron: 588
...angle at the vertex is the side of a regular decagon inscribed in the same circle. 11. Assuming that similar polygons may be divided into the same number of similar triangles, show that the polygons have to one another the duplicate ratio of their homologous sides. ABOD is a... | |
 | Simon Somerville Laurie - 1865 - Liczba stron: 432
...other, and the sides about the equal angles proper tionals, the triangles shall be equiangular. 7. Similar polygons may be divided into the same number...similar triangles, having the same ratio to one another which the polygons have ; and that ratio is the duplicate ratio of homologous sides. TRIGONOMETRY,... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
