| Euclides - 1846 - 292 Seiten
...similarly situated, to a given rectilineal figure of six sides ; &c. QEF PROP. XIX. THEOB. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. Let ABC, DEF be similar triangles, having the angle at B equal to the angle at E, and let AB... | |
| Dennis M'Curdy - 1846 - 166 Seiten
...p. 23, 1 ; (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... | |
| Joseph Denison - 1846 - 106 Seiten
...become 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... | |
| Anthony Nesbit - 1847 - 492 Seiten
...proposed Quantity of Land, by a Line parallel to any one of its Sides. RULE. — The areas of similar **triangles are to one another in the duplicate ratio of their homologous** sides : hence, as the area of the triangle ABC is to the square of the side AC, or BC, so is the area... | |
| Thomas Gaskin - 1847 - 301 Seiten
...according to Euclid's definition, that the magnitudes 4, 5, 7 , 9 are not proportional. 3. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. How does it appear from Euclid that the duplicate ratio of two magnitudes is the same as that... | |
| Euclid - 1848 - 52 Seiten
...figure similar, and similarly situated, to a given rectilineal figure. PROP. XIX. THEOREM. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. COR. From this it is manifest, that if three straight lines be proportionals, as the first is... | |
| J. Goodall, W. Hammond - 1848 - 388 Seiten
...opposite angle. (The first case only of this proposition need be demonstrated.) Section 2. 1. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. 2. If one angle of a triangle be equal to the sum of the other two, the greatest side is double... | |
| Bengal council of educ - 1848 - 394 Seiten
...Paper. 1. Find a mean proportional between two given straight lines. In this case shew how similar **triangles are to one another in the duplicate ratio of their homologous** sides. 2. The parallelograms about the diameter of any parallelogram are similar to the whole and to... | |
| Her MAjesty' Inspectors of schools - 1850 - 912 Seiten
...second. 5. Solve Kiic. IV. 6. To inscribe a square in a given circle. 7. Prove Kuc. VI. 19. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. 8. Solve Kuc. VI. 30. To divide a given finite itraight line in extreme and mean ratio. 9. In... | |
| Great Britain. Committee on Education - 1850 - 942 Seiten
...same multiple of the second that the first magnitude is of the second. 7. Prove Euc. VI. 19. Similar **triangles are to one another in the duplicate ratio of their homologous** sides. 8. Solve Kuc. VI. 30. To divide a given finite straight line in extreme and mean, ratio. 9.... | |
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