 | Charles Austin Hobbs - 1899 - 266 σελίδες
...triangle similarly situated in , Proposition 142. Theorem. 176. Two polygons are similar when they are composed of the same number of triangles, similar each to each, and similarly placed. Since the homologous A are either homologous A of similar A, or else the sums of such A, the -polygons... | |
 | George Albert Wentworth - 1899 - 500 σελίδες
...triangles CED and CAB are similar. PROPOSITION XXV. THEOREM. 365. If two polygons are similar, they are composed of the same number of triangles, similar each to each, and similarly placed. BC B' C Let the polygons ABCDE and A'B'C'D'E' be similar. From two homologous vertices, as E and E',... | |
 | William James Milne - 1899 - 398 σελίδες
...they have their homologous angles equal and their homologous sides proportional. § 299 6. If each is composed of the same number of triangles similar each to each and similarly placed. § 301i SUPPLEMENTARY EXERCISES Ex. 433. Construct a triangle whose sides are 6, 8, and 10 ; then construct... | |
 | William James Milne - 1899 - 258 σελίδες
...they have their homologous angles equal and their homologous sides proportional. § 299 6. If each is composed of the same number of triangles similar each to each and similarly placed. § 309 SUPPLEMENTARY EXERCISES Ex. 433. Construct a triangle whose sides are 6, 8, and 10 ; then construct... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1899 - 412 σελίδες
....: AlBi + Bid + ..... :A2B2 + B2C2 + ..... = r. (Why?) 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For O and 0" coincide, and the figures can be placed having 0 within each. The triangles AiOBi, A2OB2... | |
 | Harvard University - 1899 - 39 σελίδες
...sides of the angle. THEOREM VI. 10 Conversely, if two polygons are similar, they can be decomposed into the same number of triangles, similar each to each and similarly placed. THEOREM VII. The perimeters of two similar polygons are in the same ratio as any two corresponding... | |
 | Wooster Woodruff Beman, David Eugene Smith - 1899 - 272 σελίδες
...= r. .-. AiBi + B1C1 + :A 2 B 2 + B 2 C 2 + =r. (Why?) 4. Two similar polygons can be divided into the same number of triangles similar each to each, and similarly placed. For 0 and O" coincide, and the figures can be placed having 0 within each. The triangles AiOBi, A^OB... | |
 | Arthur Schultze, Frank Louis Sevenoak - 1902 - 394 σελίδες
...A ADE and A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. E' D' ED Hyp. In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', A CDE ~ A C'D'E'.... | |
 | Arthur Schultze - 1901 - 260 σελίδες
...A ADE and A'D'E' are similar. QED PROPOSITION XXVII. THEOREM 304. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and similarly placed. ED Hyp, In the polygons ABCDE and A'B'C'D'E', A ABE ~ A A'B'E', A BCE ~ A B'C'E', D A CDE ~ A C'D'E'.... | |
 | Alan Sanders - 1901 - 260 σελίδες
...circles. Draw the two common chords. PROPOSITION XXV. THEOREM 542. Two polygons are similar if they are composed of the same number of triangles, similar each to each, and .similarly placed. Let the A ABC, ADC, DEC, and EFC be similar respectively to the A GHI, GJl, JLI, and LMI, and be similarly... | |
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If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar. 
