The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 16
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal ...
... wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is equal to BC . Wherefore from the given point A a straight line AL has been drawn equal ...
Página 17
... wherefore also the point C shall coincide with the point F , because the straight line AC is equal to DF : but the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF , because the point B ...
... wherefore also the point C shall coincide with the point F , because the straight line AC is equal to DF : but the point B coincides with the point E ; wherefore the base BC shall coincide with the base EF , because the point B ...
Página 21
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal to it . Therefore if two b 8. Ax . triangles , & c . Q. E. D. ر PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two ...
... wherefore likewise the angle BAC coincides with the angle EDF , and is equal to it . Therefore if two b 8. Ax . triangles , & c . Q. E. D. ر PROP . IX . PROB . TO bisect a given rectilineal angle , that is , to di- vide it into two ...
Página 33
... wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is impossible ; therefore ... wherefore BC is not unequal to b 16. 1 . EF , that is , it is equal to it ; and AB is equal to DE ; there- fore the ...
... wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is impossible ; therefore ... wherefore BC is not unequal to b 16. 1 . EF , that is , it is equal to it ; and AB is equal to DE ; there- fore the ...
Página 42
... Wherefore triangles , & c . Q. E. D. c . 34. 1 . d 7. Ax . a 31. 1 . b 36. 1 . c 34. 1 . PROP . XXXVIII . THEOR . TRIANGLES upon equal bases , and between the same parallels , are equal to one another . Let the triangles ABC , DEF be ...
... Wherefore triangles , & c . Q. E. D. c . 34. 1 . d 7. Ax . a 31. 1 . b 36. 1 . c 34. 1 . PROP . XXXVIII . THEOR . TRIANGLES upon equal bases , and between the same parallels , are equal to one another . Let the triangles ABC , DEF be ...
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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