| THOMAS GASKIN, M.A., - 1847
...angle $ = 45. See fig. 121 . 19= See Appendix, Art. 31. ST JOHN'S COLLEGE. DEC. 1843. (No. XIV.) 1. **SIMILAR triangles are to one another in the duplicate ratio of their homologous sides,** 2. Draw a straight line perpendicular to a plane from a given point without it. 3. Shew that the equation... | |
| Samuel Hunter Christie - 1847
...of the ratios of their bases and altitudes : the bases being similar rectilineal figures (Def. 13) **are to one another in the duplicate ratio of their homologous sides** (VI. 20); and the solids being similar, their altitudes are in the simple ratio of the homologous sides:... | |
| J. Goodall - 1848
...from the opposite angle. (The first case only of this proposition need be demonstrated.) Section 2. 1. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 2. If one angle of a triangle be equal to the sum of the other two, the greatest side is double of... | |
| Bengal council of educ - 1848
...Morning Paper. 1. Find a mean proportional between two given straight lines. In this case shew how **similar triangles are to one another in the duplicate ratio of their homologous sides.** 2. The parallelograms about the diameter of any parallelogram are similar to the whole and to one another.... | |
| Euclides - 1848
...rectilineal figure similar, and similarly situated, to a given rectilineal figure. PROP. XIX. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** COR. From this it is manifest, that if three straight lines be proportionals, as the first is to the... | |
| Great Britain. Committee on Education - 1848
...from the opposite angle. (The first case only of this proposition need be demonstrated.) Section 2. 1. **Similar triangles are to one another in the duplicate ratio of their** homologuous sides. 2. If one angle of a triangle be equal to the sum of the other two, the gteatest... | |
| Great Britain. Committee on Education - 1850
...remainder is the same multiple of the second that the first magnitude is of the second. 7. Prove Euc. **VI. 19. Similar triangles are to one another in the...sides. 8. Solve Kuc. VI. 30. To divide a given finite** straight line in extreme and mean, ratio. 9. In the construction of Euc. II. II, it is usually taken... | |
| William Cowper - 1851
...Morning Paper. 1. Find a mean proportional between two given straight lines. In this case shew how **similar triangles are to one another in the duplicate ratio of their homologous sides.** 2. The parallelograms about the diameter of any parallelogram are similar to the whole and to one another.... | |
| Euclides - 1853 - Liczba stron: 147
...sides, and it has already been proved in triangles. Therefore, universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COR. 2. And if to ab, fg, two of .the homologous sides, a third proportional m be taken, ab has (v.... | |
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