 | 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 - 316 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 - 456 pages
...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 - 382 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 - 546 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... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
