 | 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.... | |
 | 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... | |
 | 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.... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...proportionals, they are similar to one another : and in the same manner a rectilineal figure of six or more sides may be 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... | |
 | 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 - 520 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... | |
 | Education - 1855 - 864 pages
...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 - 1050 pages
...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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SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
