| Anthony Nesbit - 1847 - 426 páginas
...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 of... | |
| Samuel Hunter Christie - 1847 - 172 páginas
...of the ratios of their bases and altitudes : the bases being similar rectilineal figures (Def. 13) **are to one another in the duplicate ratio of their homologous sides** (VI. 20); and the solids being similar, their altitudes are in the simple ratio of the homologous sides:... | |
| Thomas Gaskin - 1847 - 301 páginas
...you recollect. How did Legendre escape the difficulty by an analytical process. 2. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 3. If a straight line be at right angles to a plane, every plane which passes through it is at right... | |
| Euclides - 1848 - 52 páginas
...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 to the third,... | |
| J. Goodall, W. Hammond - 1848 - 388 páginas
...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 of... | |
| Bengal council of educ - 1848 - 396 páginas
...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 one another.... | |
| Great Britain. Committee on Education - 1850 - 914 páginas
...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. In the... | |
| Her MAjesty' Inspectors of schools - 1850
...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 the construction... | |
| 1851
...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 one another.... | |
| Royal Military Academy, Woolwich - 1853
...ratio of their homologous sides, and it has already been proved in triangles ; therefore, universal!}', **similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.** the duplicate ratio of that which AB has to FG ; therefore, as AB is to M, so is the figure upon AB... | |
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