| Euclides - 1874
...deducing the truth of I. 37, since VI. 6 does not depend on I. 37. PKOP. XIII.— THEOREM. (Euc. VI. 19.) **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC and OPQ be similar triangles, having the angle B equal to the angle P, and AB to BC as OP to... | |
| Braithwaite Arnett - 1874
...proportionally, this line shall be parallel to the remaining side of the triangle. 10. Define duplicate ratio. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 11. Define a plane. State when a straight line is perpendicular to a plane, and when two planes are... | |
| Francis Cuthbertson - Euclid's Elements - 1874 - 349 pages
...proportionals are said to be homologous to one another; so also are the consequents. PROPOSITION (q). **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let the similar triangles ABC, AHK be placed so as to have the sides AB, AC along the homologous sides... | |
| 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.... | |
| Euclides - 1874
...described upon a given straight line similar to one given, and so on. QEF PROPOSITION 19.— Theorem. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF lie similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
| 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,... | |
| 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... | |
| James Hamblin Smith - Geometry - 1876
...the figure A is similar to the figure B. VI. Def. 1. y. ED PROPOSITION XXI. THEOREM. (Eucl. vi. 20.) **Similar polygons may be divided into the same number...similar triangles, having the same ratio to one another,** which the polygons have ; and the polygons are to one another in the duplicate ratio of their 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... | |
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