| Robert Potts - 1879 - 668 Seiten
...triplicate ratios in Geometry correspond to the ratios of the squares and cubes in Algebra : — 1. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. (Eue. VI. 19.) Let а, Ь, с ; a', V, ¿ represent the sides of two similar triangles ; Then,... | |
| James Russell Soley - 1880 - 346 Seiten
...meet the tangents at A, B in D, E; prove that AB is a mean proportional between AD, BE. 12. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. TRIGONOMETRY. Examiner.— Prof. C. NIVEN. Lieutenants qualifying for gunnery and torpedo officers.... | |
| Sandhurst roy. military coll - 1880 - 68 Seiten
...proportion, and explain the terms triplicate ratio, componendo, and ex sequali. 7. Prove that similar **triangles are to one another in the duplicate ratio of their homologous** sides. 8. What is meant by the circular measure of an angle ? How many degrees, minutes, and seconds... | |
| Isaac Todhunter - 1880 - 426 Seiten
...situated to a given rectilineal figure of six sides ; and so on. y. KF PROPOSITION 19. THEOREM. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. Let ABC and DEF be similar triangles, having the angle B equal to the angle E, and let AB be... | |
| Euclides - 1881 - 236 Seiten
...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... | |
| John Robertson (LL.D., of Upton Park sch.) - 1882 - 152 Seiten
...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... | |
| 1882 - 480 Seiten
...equiangular pentagon. Euclid Book IV. Prop. 13. 5 (a) What is meant by duplicated ratio 1 (b) Similar **triangles are to one another in the duplicate ratio of their homologous** sides. (a) "When three magnitudes are proportionals, the first is said to have to the third the duplicate... | |
| Mathematical association - 1883 - 86 Seiten
...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... | |
| Euclid, Isaac Todhunter - 1883 - 428 Seiten
...proportionals ; therefore they are similar to one another. [VI. Definition 1, PROPOSITION 19. THEOREM. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. Let ABC and DEF be similar triangles, having the angle B equal to the angle E, and let AB be... | |
| Euclides - 1884 - 434 Seiten
...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... | |
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