 | Euclides - 1846 - 292 pages
...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 - Geometry - 1846 - 166 pages
...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 pages
...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 - Plane trigonometry - 1847 - 492 pages
...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 - Geometry, Analytic - 1847 - 301 pages
...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... | |
 | Euclides - 1848 - 52 pages
...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 - 390 pages
...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 pages
...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 pages
...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 pages
...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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Similar triangles are to one another in the duplicate ratio of their homologous sides. 
