 | Manchester univ - 1872 - 380 pagina’s
...stand. cal angle and the segments into which the line bisecting it divides the base. 4. Similar polygons are to one another in the duplicate ratio of their homologous sides. 5. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle is equal to the... | |
 | L J V. Gerard - 1874 - 428 pagina’s
...have an equal angle formed by proportional sides, are similar to each other. Let ABC and DEF be two triangles having the angle B equal to the angle E, and let AB be to DE as BC is to E F. If AB be equal to DE, the side BC is equal to EF [Gen. Def. 28] : therefore the... | |
 | 1874 - 682 pagina’s
...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.... | |
 | Braithwaite Arnett - 1874 - 130 pagina’s
...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... | |
 | Thomas Baker (C.E.) - 1874 - 208 pagina’s
...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,... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 236 pagina’s
...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... | |
 | Francis Cuthbertson - 1874 - 400 pagina’s
...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 pagina’s
...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 - 342 pagina’s
...has already been proved in triangles (VI. 19) ; therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COT. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken (VI. 11), 1.... | |
 | Euclides, James Hamblin SMITH - 1876 - 382 pagina’s
...same way a fig. of six or more sides may be described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. Similar triangles are to...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... | |
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SIMILAR triangles are to one another in the duplicate ratio of their homologous sides. 
