 | Euclides - 1846 - 272 sider
...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... | |
 | Thomas Gaskin - 1847 - 301 sider
...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... | |
 | Anthony Nesbit - 1847 - 492 sider
...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 sider
...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:... | |
 | Euclides - 1848 - 52 sider
...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... | |
 | Bengal council of educ - 1848 - 394 sider
...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.... | |
 | J. Goodall, W. Hammond - 1848 - 390 sider
...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... | |
 | Great Britain. Committee on Education - 1848 - 606 sider
...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 sider
...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... | |
 | 1851 - 626 sider
...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.... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
