 | Joseph Denison - Mechanics - 1841 - 210 pages
...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... | |
 | Euclides - 1842 - 316 pages
...Wherefore similar polygons, &c. QED COR. 1. In like manner it may be proved that similar figures of four, or of any number of sides, are one to another in the...in the duplicate ratio of their homologous sides. NB Squares are similar figures, and therefore they are to one another in the duplicate ratio of their... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...to another in the duplicate ratio of their homologous sides, and the same has already been proved of triangles : therefore, universally, similar rectilineal...2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (def. 11. 5.) to M the duplicate ratio of that which AB has to... | |
 | William Pease - Geometry - 1843 - 80 pages
...a 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
...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
...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.... | |
 | Euclides - 1845 - 546 pages
...duplicate ratio of their homologous sides : and it has already been proved in triangles: (vi. 19.) therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides. COH. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, (vi. 11.) AB... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...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... | |
 | Euclid - Geometry - 1845 - 218 pages
...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, John Playfair - Euclid's Elements - 1846 - 334 pages
...to another in the duplicate ratio of their homologous sides, and the same has already been proved of triangles : therefore, universally, similar rectilineal...2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has (def. 11. 5.) to M the duplicate ratio of that which AB has to... | |
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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
