| Joseph Denison - 1841 - Liczba stron: 184
...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... | |
| Joseph Denison - 1841 - Liczba stron: 184
...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... | |
| Euclides - 1841 - Liczba stron: 351
...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
...proportionals, they are similar to one another ; and in the same manner a rectilineal figure of six or more **sides 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... | |
| John Playfair - 1842 - Liczba stron: 317
...proportionals, they are similar to one another ; and in the same manner a rectilineal figure of six, or more, **sides may be described upon a given straight line similar to one given, and so on.** PROP. XIX. THEOR. Similar triangles are to one another in the duplicate ratio of the homologous sides.... | |
| William Pease - 1843 - Liczba stron: 68
...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... | |
| 1844
...that their common chord will be bisected at right angles by a straight line joining their centres. 4. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 5. About the centre of a given circle describe another circle, equal in area to half the former. TRIGONOMETRY... | |
| 1844
...and u the distance of A" from K. FRIDAY, Jan. 5. 9. ..ll£ SENIOR MODERATOR AND JUNIOR EXAMINER. 1. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 2. Every solid angle is contained by plane angles which are together less than four right angles. 3.... | |
| Euclid - 1845 - Liczba stron: 199
...proportionals, they are similar to one another : and in the same manner a rectilineal figure of six or more **sides may be described upon a given straight line...similar to one given, and so on. Which was to be done.** PROPOSITION XIX. THEOR. — Similar triangles are to one another in the duplicate ratio of their homologous... | |
| Euclides - 1845
...angles proportionals, they are similar to one another. In the same manner a rectilineal figure of six **sides may be described upon a given straight line similar to one given, and so on.** QEF PROPOSITION XIX. THEOREM. Similar triangles are to one another in the duplicate ratio of their... | |
| |