| Euclides, James Hamblin Smith - 1872 - 372 páginas
...described, on a given line, similar to a given fig. QEF PROPOSITION XIX. THEOREM. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** Let ABC, DEF be similar AS, having L s at A, B, C= s.sa.tD,E,F respectively, so that BC and EF are... | |
| Euclides - 1874 - 342 páginas
...duplicate ratio of their homologous sides ; and it has already been proved in triangles (VI. 19) ; **therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides.** COT. 2. And if to AB, FG, two of the homologous sides, a third proportional M be taken (VI. 11), 1.... | |
| George E. Webster - 1874 - 136 páginas
...equal, then the greatest area is possessed by the figure which has the largest number of sides. (7) **Similar rectilineal figures are to one another in the duplicate* ratio of their homologous^ sides.** (8) If three straight lines oe proportionals, as the first quantity is to the third quantity, so is... | |
| Euclides - 1874 - 234 páginas
...homologous sides. Cor. 2. — In like manner it may be proved that any similar figures of four sides **are to one another in the duplicate ratio of their homologous sides,** and the same has been proved of triangles (VI. 14); therefore, universally, similar rectilineal figures... | |
| Francis Cuthbertson - 1874 - 396 páginas
...ratio of AB to AH. Hence, proceeding as in Proposition VIII., it may be proved that Similar polygons **are to one another in the duplicate ratio of their homologous sides.** PROPOSITION (r). If four straight lines are proportional, the duplicate ratio of the first two is the... | |
| Braithwaite Arnett - 1874 - 130 páginas
...shall be parallel to the remaining side of the triangle. 10. Define duplicate ratio. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** 11. Define a plane. State when a straight line is perpendicular to a plane, and when two planes are... | |
| 1874
...duplicate ratio, and illustrate its meaning as you would to a class. (b.) Prove that similar triangles **are to one another in the duplicate ratio of their homologous sides.** 2. Describe a circle which will pass through a given point, and touch a given circle in a given point.... | |
| Robert Potts - 1876 - 446 páginas
...duplicate ratio of their homologous sides : and it has already been proved in triangles: (vi. 19.) **therefore, universally, similar rectilineal figures...in the duplicate ratio of their homologous sides.** COB. 2. And if to AB, FG, two of the homologous sides, a third proportional M\K taken, (vi. 11.) AB... | |
| Euclides - 1876 - 238 páginas
...homologous sides, as has already been proved in the case of triangles. Therefore, universally, sjmilar **rectilineal figures are to one another 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... | |
| Association for the improvement of geometrical teaching - 1876 - 66 páginas
...ratio compounded of the ratios of their bases and of their altitudes. THEOR. 15. Similar triangles **are to one another in the duplicate ratio of their homologous sides.** THEOR. 16. The areas of similar rectilineal figures are to one another in the duplicate ratio of their... | |
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