| 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 - 598 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
...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
...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.... | |
| Royal Military Academy, Woolwich - Mathematics - 1853
...described upon a given straight line similar to one given, and so on. Which was to be done. PRG-POSITION **XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
| Euclides - Geometry - 1853 - 176 pages
...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.... | |
| Thomas Lund - Geometry - 1854 - 192 pages
...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... | |
| William Somerville Orr - Science - 1854
...upon the first to a similar and sinularly situated triangle upon the second. PEOPOSITION XX.-THEOREM. **Similar polygons may be divided into the same number of similar triangles,** which are to one another as the polygons themselves : and the polygons are to one another as the squares... | |
| Education - 1855
...centre of gravity of the hemisphere from its vertex being = $ rad. FOURTH CLASS. EUCLID AND ALGEBRA. 1. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 2. If two parallel planes be cut by another plane their common sections with it are parallel. 3. If... | |
| Robert Potts - 1855
...and inscribed circles of a triangle, the square of the distance between the centres = J? - 2Br. 2. **Similar triangles are to one another in the duplicate ratio of their homologous** side*. 4. Divide -01 by -0002 and -00001 by -03; find also a irth proportional to -999, 33-3 and -03.'... | |
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