| Joseph Denison - Mechanics - 1841 - 210 pages
...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 - 1842 - 320 pages
...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 sides.** ABC has to the triangle DEF the duplicate ratio of that which вc has to EF. Take BG a third proportional... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...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. Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and... | |
| William Pease - Geometry - 1843 - 80 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 - 688 pages
...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... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...parallel ruler. For thi easiest methods, however, of performing this and many other problems, the student **PROP. XIX. THEOR. — Similar triangles are to one...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... | |
| Euclid - Geometry - 1845 - 218 pages
...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 sides.** Let ABC, DEF be similar triangles, having the angle B equal to the angle E, and let AB be to BC, as... | |
| Euclides - 1845 - 544 pages
...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... | |
| John Playfair - Euclid's Elements - 1846 - 332 pages
...wherefore also the triangle ABC has to the triangle DEF the duplicate ratio of that which BC has to EF. **PROP. XX. THEOR. 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... | |
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