 | 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.... | |
 | 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... | |
 | 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... | |
 | 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.... | |
 | Euclides - 1853 - 176 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 - 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... | |
 | Euclides - 1855 - 230 sider
...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 - 270 sider
...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 - 1050 sider
...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 - 864 sider
...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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Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
