 | Anthony Nesbit - 1847 - 492 sider
...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 sider
...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 sider
...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 sider
...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 - 390 sider
...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 - 394 sider
...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 - 942 sider
...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 - 912 sider
...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 - 626 sider
...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 - 400 sider
...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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... rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
