| 1876
...to one another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their... | |
| Robert Potts - 1876 - 403 pagina’s
...equal to one angle of the other, have their sides about the equal angles reciprocally proportional. 4. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 5. In any right angled triangle, any rectilineal figure described on the side subtending the right... | |
| James Hamblin Smith - 1876
...described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. Similar triangles an **to one another in the duplicate ratio of their homologous sides. Let ABC,** DBF be similar A s, having / s at A, B, C= L s at D, E, F respectively, so that BC and EF are homologous... | |
| Dublin city, univ - 1876
...the other segment. If the whole line be 10 feet long, find the lengths of the segments. 2. Prove that **similar triangles are to one another in the duplicate ratio of their** sides. Divide a triangle into three equal parts by right lines drawn parallel to its base. 3. Divide... | |
| Samuel H. Winter - 1877 - 413 pagina’s
...have the same base, are to one another as their altitudes. 7. Define duplicate ratio, and prove that **similar triangles are to one another in the duplicate ratio of their homologous sides.** On the side AB of a triangle ABC, AD is taken equal to one third of AB ; and on AC, AE is taken equal... | |
| D. Tierney - 1877
...HE, HF. Then EHF is the triangle required, for it is isosceles and equal to EFG, that is, to ABC. 10. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 11. Given a point O in the line AB, find two other points 0, J?, such that a line OP given in direction... | |
| James Maurice Wilson - 1878
...triangle DEF in the duplicate ratio of BC to EF. THEOREM 16. The areas of similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides. Let** ABCDE, PQ_RST\3z similar polygons. JD S Divide each of them into the same number of similar triangles... | |
| Āryabhaṭa - 1878
...and this has been proced of triangles (P. 34). 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 Is taken... | |
| Isaac Sharpless - 1879 - 266 pagina’s
...resulting polygons similar. Proposition 19. Theorem.—Similar triangles are to one another as the squares **of their homologous sides. Let ABC, DEF be similar...having the angle B equal to the angle E, and let AB** : BC :: DE : EF, so that BC and EF are homologous sides; then ABC : DEF ::BC* : EF\ Because ABC, DEF... | |
| Euclides, James Hamblin Smith - 1879 - 349 pagina’s
...the same way a fig. of six or more sides may be described, on a given line, similar to a given fig. **PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their** houwlogous sides. H Let ABC, DEF be similar A s, haying L s at A, B, C= L s at D, E, F respectively,... | |
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