| James Russell Soley - 1880 - 346 páginas
...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.... | |
| Euclides - 1881 - 236 páginas
...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... | |
| 1884 - 532 páginas
...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... | |
| John Robertson (LL.D., of Upton Park sch.) - 1882 - 148 páginas
...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... | |
| 1882 - 476 páginas
...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.... | |
| Euclid, Isaac Todhunter - 1883 - 426 páginas
...to one another in the duplicate ratio of their homologous sides ; and it has already been shewn for **triangles ; therefore universally, similar rectilineal...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.... | |
| Mathematical association - 1883 - 86 páginas
...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... | |
| John Harris - 1884 - 188 páginas
...the square on A c, including the diagonal A e of the square on A b. Then because similar trianglcs **are to one another in the duplicate ratio of their homologous sides** (Euclid VI. 19) and the triangles A eb and Afc are similar, the " '' triangle A eb has the ratio to... | |
| Dalhousie University - 1884 - 184 páginas
...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... | |
| Euclides - 1884 - 434 páginas
...that these triangles have each to each the same ratio which the polygons have ; and that the polygons **are to one another in the duplicate ratio of their homologous sides.** Join BE, EC, GL, LH. Because the polygon ABCDE is similar to the polygon FGHKL, .-. LA = LF, and BA... | |
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