| Thomas Lund - 1854 - Liczba stron: 362
...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... | |
| 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.'... | |
| Euclides - 1855
...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
...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
...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
...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... | |
| Henry Latham - 1857 - Liczba stron: 59
...triangle. 7. Give Dcf. 5, Book V. of Euclid, and shew whether the areas 3, 4, 7, 8 are proportionals. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Shew how to inscribe a rectangle DEFG in a triangle ABC, so that the angles D, E may be in the straight... | |
| Middle-class education - 1857
...the algebraical expression for the mean proportional between two given quantities ? 19. Prove that **similar triangles are to one another in the duplicate ratio of their homologous sides.** 20. Show that, if an equilateral triangle be inscribed in a circle, the square of its side is equal... | |
| sir Thomas Dyke Acland (11th bart.) - 1858
...the algebraical expression for the mean proportional between two given quantities ? 19. Prove that **similar triangles are to one another in the duplicate ratio of their homologous sides.** 20. Show that, if an equilateral triangle be inscribed in a circle, the square of its side is equal... | |
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