 | 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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... rectilineal figures are to one another in the duplicate ratio of their homologous sides. 
