 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 - Σελίδα 126των Henry White - 1864Πλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | John Playfair - 1806 - 320 σελίδες
...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 - 1806 - 546 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 1825 - 1046 σελίδες
...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 - 1826 - 326 σελίδες
...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 - 1827 - 546 σελίδες
...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 - 1829 - 210 σελίδες
...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... | |
| |
