 Similar polygons may be divided into the same number Of similar triangles, having the same ratio to one another that the polygons have; and the polygons are to one another in the duplicate ratio of their homologous sides.  Education in Scotland - Page 223by Great Britain. Scottish Education Dept - 1896Full view - About this book
 | Robert Simson - Trigonometry - 1806 - 546 pages
...similar, and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number of similar triangles,...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...the second. For, BC : BG : : triangle ABC : triangle DEF. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number of similar triangles,...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
 | John Mason Good - 1813 - 714 pages
...another in the duplicate ratio of their homologous sides. Prop. XX. Theor. Similar polygons may be divided into the same number of similar triangles,...another that the polygons have ; and the polygons hare to one another the duplicate ratio of that which their homo, logons sides have. Prop. XXI. Theor.... | |
 | Euclides - 1814 - 560 pages
...similar and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number of similar triangles, having the same ratio to one another that thepolygons have; and the polygons have to one another the duplicate ratio of that which their homologous... | |
 | 1814 - 760 pages
...have met it before. The demonstration of the 19tb Prop, of Euclid's 6th book, ie " Similar triangles are to one another in the duplicate ratio of their homologous sides," requires the previous or the syn hro nous establishment of Props, vi. 11, v. 16, v. 11, vi. 15., and... | |
 | Euclides - 1816 - 588 pages
...similar and similarly described triangle upon the second, PROP. XX. THEOR. SIMILAR polygons may he divided into the same number of similar triangles,...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
 | John Playfair - 1819 - 354 pages
...similar, and similarly described triangle upon the second, PROP. XX. THEOR. Similar polygons may be divided into the same number of similar triangles,...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
 | Euclides - 1821 - 294 pages
...proportionality of the sides about 'the «£^.s composing them. 52 PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of their homologous sides. Assume on the greater base from either extremity a third proportional to that base and the homologous... | |
 | Anthony Nesbit - Surveying - 1824 - 476 pages
...triangle ABC is to the triangle ADE, as the square of BC to the square of DE. That is, similar triangles are to one another in the duplicate ratio of their homologous sides. (Euc. VI. 19. Simp. IV. 24. Em. II. BC THEOREM XIV. In any triangle ABC, double the square of a line... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...sides, and it has already been proved in triangles Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has ( 10.... | |
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