| Bengal council of educ - 1852 - 348 pages
...triangle, right angled at A, if CD be drawn bisecting the angle C, show that AB : AC :: BC — AC : AD. .3. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 4. Planes to which the same straight line is perpendicular, are parallel to one another. 5. If two... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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 - 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
...triangle, right angled at A, if CD be drawn bisecting the angle C, show that AB : AC :: BC — AC : AD. 8. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 4. Planes to which the same straight line is perpendicular, are parallel to one another. 5. If two... | |
| 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.'... | |
| Euclides - 1855 - 270 pages
...and this has been proved of triangles (VI. 19). Therefore, universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COROLLARY 2, — If to AB and FG, two of the homologous sides of the polygon, a third proportional... | |
| Euclides - 1855 - 230 pages
...In like manner it may be proved, that similar four-sided figures, or figures of any number of sides, **are to one another in the duplicate ratio of their homologous sides,** as has already been proved in the case of triangles. Therefore, universally, similar rectilineal figures... | |
| Cambridge univ, exam. papers - 1856 - 200 pages
...are proportionals. Shew how this proposition may be proved by superposition as in Prop. 4, B. 1. 4. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** What can you infer from this as to the ratio of squares to each other ? 5. Describe a rectilineal figure... | |
| 1857 - 408 pages
...the base, the triangles on each^side of it are similar to the whole triangle and to one another. 2. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 3. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to both... | |
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