| 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
...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... | |
| Robert Potts - 1879
...triplícala ratios in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** (Eue. VI. 19.) Let а, Ь, с ; a', I', c' represent the sides of two similar triangles ; Then, because... | |
| Robert Potts - 1879
...triplicate ratios in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** (Eue. VI. 19.) Let а, Ь, с ; a', V, ¿ represent the sides of two similar triangles ; Then, because... | |
| Euclides, James Hamblin Smith - 1879
...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,... | |
| James Russell Soley - 1880 - 335 páginas
...BC, AC meet the tangents at A, B in D, E; prove that AB is a mean proportional between AD, BE. 12. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** TRIGONOMETRY. Examiner.— Prof. C. NIVEN. Lieutenants qualifying for gunnery and torpedo officers.... | |
| Woolwich roy. military acad, Walter Ferrier Austin - 1880
...inscribe a triangle equiangular to a given triangle. Show how to inscribe a circle in a given rhombus. 9. **Similar triangles are to one another in the duplicate ratio of their homologous** sidos. The sides of a regular hexagon ABCDEF are produced both ways, forming with each other six points... | |
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