| 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... | |
| 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... | |
| Henry Latham - 1857 - 59 pages
...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... | |
| 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... | |
| Sandhurst roy. military coll - 1859 - 1869 pages
...Extract the square root of 321489. Voluntary Portion. 1. To describe a circle about a given square. 2. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 3. One of the two digits of a number is double the other, and if 27 be added to the number the digits... | |
| Thomas Lund - Geometry - 1859 - 362 pages
...= / a, JP -# a, tt/ DX * Sometimes called 'homologous sides'. 'f- Euclid's enunciation of this is: **'Similar triangles are to one another in the duplicate ratio of their homologous sides'.** X zB=z&, zC=zc; then AB, ab being any two corresponding, or homologous, sides, the triangle ABC shall... | |
| Robert Potts - Geometry, Plane - 1860 - 361 pages
...angles proportionals, they are similar to one another. In the same manner a rectilineal figure of six **sides may be described upon a given straight line similar to one given, and so on.** QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their... | |
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