 | Braithwaite Arnett - 1874 - 130 páginas
...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... | |
 | 1874 - 682 páginas
...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 - 208 páginas
...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 - 1874 - 400 páginas
...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 - 136 páginas
...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... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 páginas
...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 - 1876 - 446 páginas
...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 - 1876 - 382 páginas
...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 - 268 páginas
...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... | |
 | Association for the improvement of geometrical teaching - 1876 - 66 páginas
...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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SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
