| 1874
...Explain the term duplicate ratio, and illustrate its meaning as you would to a class. (b.) Prove that **similar triangles are to one another in the duplicate ratio of their homologous sides.** 2. Describe a circle which will pass through a given point, and touch a given circle in a given point.... | |
| Thomas Baker (C.E.) - 1874
...then, the triangle ABC is to the triangle AED as the square of A. B is to the square of AE : that is, **similar triangles are to one another in the duplicate ratio of their homologous sides.** (Euc. VI. 19.) THEOREM VIII. All similar figures are to one another as the squares of their homologous,... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...ratio of AB to AH. Hence, proceeding as in Proposition VIII., it may be proved that Similar polygons **are to one another in the duplicate ratio of their homologous sides.** PROPOSITION (r). If four straight lines are proportional, the duplicate ratio of the first two is the... | |
| George E. Webster - 1874
...area is possessed by the figure which has the largest number of sides. (7) Similar rectilineal figures **are to one another in the duplicate* ratio of their homologous^ sides.** (8) If three straight lines oe proportionals, as the first quantity is to the third quantity, so is... | |
| Euclides - 1874
...homologous sides. Cor. 2. — In like manner it may be proved that any similar figures of four sides **are to one another in the duplicate ratio of their homologous sides,** and the same has been proved of triangles (VI. 14); therefore, universally, similar rectilineal figures... | |
| Robert Potts - Geometry, Plane - 1876 - 403 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 trianyla are to one another in the duplicate ratio of their homologous... | |
| Euclides, James Hamblin Smith - Geometry - 1876 - 349 pages
...more sides may be described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides. Let** ABC,DEF be similar AS, having / s at A, B, C= L s at D, E, F respectively, so that BC and EF are homologous... | |
| Richard Wormell - 1876
...circumscribed circles, or their proportionals the radii of the inscribed circles. THEOREM LXXXV. (¿.) **Similar triangles are to one another in the duplicate ratio of their homologous sides. Let** А В С, DEF be similar triangles having Z. B = ¿EandAB:DE = BC:EFso that В С and E^F are homologous... | |
| 1876
...to one another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their... | |
| James Hamblin Smith - Geometry - 1876
...described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. Similar triangles an **to one another in the duplicate ratio of their homologous sides. Let ABC,** DBF be similar A s, having / s at A, B, C= L s at D, E, F respectively, so that BC and EF are homologous... | |
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