 | 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... | |
 | 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... | |
 | 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.... | |
 | 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... | |
 | Scottish school-book assoc - 1845 - 444 pages
...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... | |
 | 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... | |
 | Joseph Denison - 1846 - 106 pages
...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... | |
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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
