| Euclides - 1846 - 272 pages
...AEDCB) may be divided into similar triangles, equal in number, and homologous to all. And the polygons **are to one another in the duplicate ratio of their homologous sides.** PART 1. — Because in the triangles FGI and AED, the angles G and E are G ( equal, and the sides about... | |
| Anthony Nesbit - Plane trigonometry - 1847 - 492 pages
...both ; then the triangle ABC is to the triangle ADE, as the square of BC to the square of D E. That is **similar triangles are to one another in the duplicate ratio of their homologous sides.** (Euc. VI. 19. Simp. IV. 24. Em. II. 18.) THEOREM XIV. In any triangle ABC, double the square of a line... | |
| Samuel Hunter Christie - 1847 - 172 pages
...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, W. Hammond - 1848 - 390 pages
...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 the... | |
| Bengal council of educ - 1848 - 394 pages
...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 - 52 pages
...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 - 606 pages
...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... | |
| Her MAjesty' Inspectors of schools - 1850 - 912 pages
...of the second. 5. Solve Kiic. IV. 6. To inscribe a square in a given circle. 7. Prove Kuc. VI. 19. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 8. Solve Kuc. VI. 30. To divide a given finite itraight line in extreme and mean ratio. 9. In the construction... | |
| Education - 1851 - 626 pages
...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.... | |
| Charles Astor Bristed - 1852 - 470 pages
...Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their **sides. 2. Draw a straight line perpendicular to a plane from a given point** above it. a. Show how to find the number of positive integral solutions of ax + by = c, where a, b... | |
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