| Joseph Denison - 1841 - 210 páginas
...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 - 320 páginas
...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 - 1842 - 332 páginas
...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 - 1843 - 80 páginas
...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... | |
| 1844
...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... | |
| 1844 - 688 páginas
...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 - 544 páginas
...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 - 1845 - 380 páginas
...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 - 1845 - 218 páginas
...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... | |
| John Playfair - 1846 - 332 páginas
...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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