| John Playfair - Euclid's Elements - 1842 - 317 pages
...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 - Geometry - 1843 - 68 pages
...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... | |
| Education - 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.... | |
| Church schools - 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... | |
| Scottish school-book assoc - 1845
...are the doubles of equiangular triangles. PROPOSITION LXXI THEOREM. Similar polygons ABODE, FGHIK, **may be divided „ into the same number of similar triangles, having the same ratio** that the polygons have ; and the polygons are to one another as the squares of their corresponding... | |
| Euclid - Geometry - 1845 - 199 pages
...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 sides.** Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
| Euclid, James Thomson - Geometry - 1845 - 352 pages
...easiest methods, however, of performing this and many other problems, the student PROP. XIX. THEOR. — **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar triangles, having the angles B and E equal, and AB : BC : : DE : EF, so that... | |
| Euclides - 1845
...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 homologous sides.** Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
| Joseph Denison - 1846
...ultimately become similar, and consequently the approximating sides homologous, and (6 Euclid 19) because **similar triangles are to one another in the duplicate ratio of their homologous sides;** the evanescent triangles are in the duplicate ratio of the homologous sides; and this seems the proper... | |
| Euclides - 1846
...similar, and similarly situated, to a given rectilineal figure of six sides ; &c. QEF PROP. XIX. THEOB. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar triangles, having the angle at B equal to the angle at E, and let AB be to... | |
| |