| Joseph Denison - 1840 - 84 pagina’s
...square of b$ is to the homologous side de ; or as the square of ac is to the homologous side ae. Because **similar triangles are to one another in the duplicate ratio of their homologous sides** (6 Euclid, 19), the triangle ate is to the triangle abe in the duplicate ratio of the side ab to the... | |
| London City Mission - 1840
...argument nor testimony would suit the determination of such a case. If I want to determine whether **similar triangles are to one another in the duplicate ratio of their homologous sides;** the proper evidence will be to examine, by the powers of the mind, into the proofs which are alleged,... | |
| Euclides - 1840
...rectilineal figure similar to a given rectilineal figure, and similarly situated. PROP. XIX. THEOR. **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 of similar triangles, each similar... | |
| Euclides - 1840
...but ABC : CAG : : AB : AG (vi. Prop. i) ; and therefore ABC : DEF : : AB : AG, that is to say, the **triangles are to one another in the duplicate ratio of their homologous sides** AB, DE (v. Def. ii). COR. — Hence it is manifest that if three straight lines be proportional, as... | |
| Joseph Denison - 1841 - 184 pagina’s
...lines are to each other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) **similar triangles are to one another in the duplicate ratio of their homologous sides,** therefore, (5 Euclid, 11.) the similar triangles are to one another as the squares of their homologous... | |
| Joseph Denison - 1841 - 184 pagina’s
...lines are to each other in the duplicate ratio of the lines themselves, and because (by 6 Euclid, 19.) **similar triangles are to one another in the duplicate ratio of their homologous sides,** therefore, (5 Euclid, 11.) the simi-lar triangles are to one another as the squares of their homologous... | |
| Euclides - 1841 - 351 pagina’s
...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 * 11. 6. sides, a third* proportional M be taken, AB... | |
| Euclides - 1842
...may be described upon a given straight line similar to one given, and so on. QEF PROP. XIX. THEOR. **SIMILAR triangles are to one another in the duplicate ratio of their homologous sides.** ABC has to the triangle DEF the duplicate ratio of that which вc has to EF. Take BG a third proportional... | |
| John Playfair - 1842 - 317 pagina’s
...the same has already been proved of 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 (def.... | |
| William Pease - 1843 - 68 pagina’s
...similar polygon, equal to the sum of the given polygons. For, " universally, similar'rectilineal figures **are to one another in the duplicate ratio of their homologous sides."** Duplicate ratio is the ratio of the square of one quantity to the square of another. EXAMPLES. 1. Make... | |
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