| Bengal council of educ - 1848
...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.... | |
| 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... | |
| Great Britain. Committee on Education - 1850
...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... | |
| 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.... | |
| Euclides - 1853 - 147 sider
...Wherefore similar polygons, &c. QED Сок. 1. In like manner, it may be proved, that similar four-sided **figures, or of any number of sides, are one to another...And if to ab, fg, two of .the homologous sides, a** third proportional m be taken, ab has (v. def. 10) to m the duplicate ratio of that which ab has to... | |
| 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... | |
| Euclides - 1855
...another in the duplicate ratio of their homologous sides, as has already been proved in the case of **triangles. Therefore, universally, similar rectilineal...in the duplicate ratio of their homologous sides.** COROLLARY 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken, AB has... | |
| Euclides - 1855
...in the duplicate ratio of their homologous sides ; and this has been proved of triangles (VI. 19). **Therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides.** COROLLARY 2, — If to AB and FG, two of the homologous sides of the polygon, a third proportional... | |
| Robert Potts - 1855
...point, either without or in the circumference, which shall touch a given circle. 16. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 18. ABC is a triangle having each of the angles at JB, C double of that at A, CD is drawn bisecting... | |
| 1855
...A, if CD be drawn bisecting the angle C, show that AB : AC :: BC — AC : AD. 8. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 4. Planes to which the same straight line is perpendicular, are parallel to one another. 5. If two... | |
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