| 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:... | |
| Euclides - 1848
...describe a 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
...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
...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
...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
...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
...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 - 147 sider
...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.... | |
| Royal Military Academy, Woolwich - 1853
...and it has already been proved in triangles ; therefore, universal!}', similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** the duplicate ratio of that which AB has to FG ; therefore, as AB is to M, so is the figure upon AB... | |
| Thomas Lund - 1854 - 192 sider
...which tA = ta, d> b * Sometimes called 'homologous sides'. •f Euclid's enunciation of this is : ' **Similar triangles are to one another in the duplicate ratio of their homologous** aides'. iB= tb, fC- ic; then AB, ab being ant/ two corresponding, or homologous, sides, the triangle... | |
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