The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 120
... ratio are called propor- tionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying ... triplicate ratio of that which it has to the second , and so on , quadruplicate , & c . increasing the denomination ...
... ratio are called propor- tionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying ... triplicate ratio of that which it has to the second , and so on , quadruplicate , & c . increasing the denomination ...
Página 236
... triplicate ratio of their homologous sides . Let AB , CD be similar solid parallelopipeds , and the side AE homologous to the side CF : the solid AB has to the solid CD , the triplicate ratio of that which AE has to CF. Produce AE , GE ...
... triplicate ratio of their homologous sides . Let AB , CD be similar solid parallelopipeds , and the side AE homologous to the side CF : the solid AB has to the solid CD , the triplicate ratio of that which AE has to CF. Produce AE , GE ...
Página 237
... ratio of that which it has to the second : therefore the solid AB has to the solid KO the triplicate ratio of that which AB has to EX : but as AB is to EX , so is the parallelogram AG to the parallelogram GK , and the straight line AE ...
... ratio of that which it has to the second : therefore the solid AB has to the solid KO the triplicate ratio of that which AB has to EX : but as AB is to EX , so is the parallelogram AG to the parallelogram GK , and the straight line AE ...
Página 266
... triplicate ratio of that of their homologous sides . Let the pyramids having the triangles ABC , DEF for their bases , and the points G , H for their vertices , be similar , and similarly situated ; the pyramid ABCG has to the pyramid ...
... triplicate ratio of that of their homologous sides . Let the pyramids having the triangles ABC , DEF for their bases , and the points G , H for their vertices , be similar , and similarly situated ; the pyramid ABCG has to the pyramid ...
Página 267
... triplicate e e 33. 11 . ratio of that which their homologous sides have : therefore the solid BGML has to the solid EHPO the triplicate ratio of that which the side BC has to the homologous side EF : but as the solid BGML is to the ...
... triplicate e e 33. 11 . ratio of that which their homologous sides have : therefore the solid BGML has to the solid EHPO the triplicate ratio of that which the side BC has to the homologous side EF : but as the solid BGML is to the ...
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Términos y frases comunes
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore