| Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...In like manner it may be shewn that similar four-sided figures, or figures of any number of sides, **are to one another in the duplicate ratio of their homologous sides** ; and it has already been shewn for triangles ; therefore universally, similar rectilineal figures... | |
| Euclides - 1881
...point D to its different nngles. The proof In thus also more easlly established. PROP. XIX. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides. Let ABC** and DEF be similar triangles, and let the angle ABC be equal to the angle DEF, and let AB be to BC,... | |
| Education, Higher - 1884
...of similar triangles, having the same ratio to one another that the polygons have, and the polygons **are to one another in the duplicate ratio of their homologous sides.** . / 16. "From the same point in a given plane, there cannot be two straight lines at right angles to... | |
| 1882
...than a right angle. 4. Inscribe a regular equilateral and equiangular pentagon in a given circle. 5. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** 6. Two circles whose centres are A and B, intersect in C and D, shew that AB bisects CD at right angles.... | |
| John Robertson (LL.D., of Upton Park sch.) - Examinations - 1882
...to the square on the line which meets the circle, the line which meets the circle shall touch it. 7. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** TnEEE-nouE PAPEE. 1. Quote the passages in Genesis which relate to a SAVIOUE, as nearly as you can... | |
| Mathematical association - 1883
...to one another the ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 400 pages
...; and it has already been shewn for triangles ; therefore universally, similar rectilineal figures **are to one another in the duplicate ratio of their homologous sides.** COROLLARY 2. If to AB and FG, two of the homologous sides, a third proportional M be taken, [VI. 11.... | |
| Euclides - 1884
...figure BLMN similar and oppositely situated to the figure BAGH be obtained? PROPOSITION 19. THEOREM. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** G Let ABC and DEF be similar triangles, having L. B = LE, and LC — LF, so that BC and EF are homologous... | |
| Dalhousie University - 1884
...= 0, between 1 and 2. GEOMETRY AND MENSURATION.— SECOND YEAR. APRIL 15iH.— 10 AM TO 1 p. M. I. **Similar triangles are to one another in the duplicate ratio of their homologous sides.** Prove this : and represent the ratio of the two triangles by means of two straight lines whereof one... | |
| John Harris - Geometry - 1884 - 144 pages
...area of) the eq. triangle DAB of four to nine. It demonstrates therefore (by inspection) the theorem ; **Similar triangles are to one another in the duplicate ratio of their** respondent sides. (Euclid, IV. 19.) It also demonstrates that if from an eq. triangle a lesser eq.... | |
| |