| 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.... | |
| 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... | |
| 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 - 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... | |
| 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... | |
| W. PEASE - 1846 - 86 páginas
...another, AC will be the homologous side of a similar polygon, equal to the sum of the given polygons. For **"universally, similar rectilineal figures are to one...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... | |
| Dennis M'Curdy - 1846 - 138 páginas
...(b) p. 32, 1 ; (c) p. 4, 6 ; ( d) p. 22, 5 ; (c) def. 1, 6 and def. 35, 1. 19 Th. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** Given the similar triangles ABC, DEF; having the angles at B, E, equal, and AB to BC as DE to EF: then... | |
| Euclides - 1846 - 292 páginas
...And, in like manner, it may be proved, that similar figures of any number of sides more than three **are to one another in the duplicate ratio of their homologous sides** ; and it has already been proved (9. 19) in the case of triangles. Wherefore, universally, Similar... | |
| Euclides - 1846 - 272 páginas
...AEDCB) may be divided into similar triangles, equal in number, and homologous to all. And the polygons **are to one another in the duplicate ratio of their homologous sides.** PART 1. — Because in the triangles FGI and AED, the angles G and E are G ( equal, and the sides about... | |
| Joseph Denison - 1846 - 106 páginas
...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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