 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 have to one another the duplicate ratio of that which their homologous sides have.  Guide to the Civil service - Page 126by Henry White - 1864Full view - About this book
 | John Playfair - Mathematics - 1806 - 320 pages
...described triangle upon the second. For, BC : BG : : triangle ABC : triangle DEF. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number...the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...triangle upon the first to a similar, and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number...the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.... | |
 | John Mason Good - 1813 - 714 pages
...Similar triangles are to one another in the duplicate ratio of their homologous sides. Prop. XX. Theor. Similar polygons may be divided into the same number...the same ratio to one another that the polygons have ; and the polygons hare to one another the duplicate ratio of that which their homo, logons sides have.... | |
 | Euclides - 1814 - 560 pages
...triangle upon the first to a similar and similarly described triangle upon the second. PROP. XX. THEOR. SIMILAR polygons may be divided into the same number...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... | |
 | 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,...the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.... | |
 | John Playfair - 1819 - 354 pages
...triangle upon the first to a similar, and similarly described triangle upon the second, PROP. XX. THEOR. Similar polygons may be divided into the same number...the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...upon the first to a 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 tame ratio to one another that the polygon« have ; and the polygons have to one another the duplicate... | |
 | Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...fir«t. to a similar, and similarly deseribed triangle upon the seeond. PROP. XX. THEOR. Similar polygon* may be divided into the same number of similar triangles,...the same ratio to one another that the polygons have ; and the polygons have to one another the duplieate ratio of that whieh their homologous sides have.... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...triangle upon the first to a similar and similarly described triangle upon the second. PROP. XX. THEOR. Similar polygons may be divided into the same number...the same ratio to one another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have.... | |
 | John Playfair - Geometry - 1829 - 210 pages
...triangle DEF : : AB . AB : DE . DE. Therefore, similar triangles &c. QED ED. PROPOSITION XX. THEOREM. 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 have to one another the duplicate ratio of that which their... | |
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