 Similar polygons may be divided into the same number Of similar triangles, having the same ratio to one another that the polygons have; and the polygons are to one another in the duplicate ratio of their homologous sides.  Education in Scotland - Page 223by Great Britain. Scottish Education Dept - 1896Full view - About this book
 | J. Goodall, W. Hammond - 1848 - 390 pages
...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 pages
...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 pages
...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 pages
...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... | |
 | Education - 1851 - 626 pages
...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 - Mathematics - 1853 - 400 pages
...similar and similarly described triangle upon the second. PROPOSITION XX. THEOR. Similar polygons may be divided into the same number of similar triangles,...another that the polygons have ; and the polygons have to one another the duplicate ratio of that which their homologous sides have. Let ABCDE, FGHKL... | |
 | Euclides - Geometry - 1853 - 176 pages
...sides, and it has already been proved in triangles. Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides. COR. 2. And if to ab, fg, two of .the homologous sides, a third proportional m be taken, ab has (v.... | |
 | Euclides - 1855 - 230 pages
...which their homologous sides have, f Their perimeters are as their \ homologous sides. They may be .divided into the same number of similar triangles,...same ratio to one another that the polygons have. JThey are similar to one another. I second. As ;the first is to the third, so is any rectilineal figure... | |
 | Robert Potts - 1855 - 1050 pages
...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... | |
 | Euclides - 1855 - 270 pages
...and this has been proved of triangles (VI. 19). Therefore, universally, similar rectilineal figures are to one another 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... | |
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