The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner CorrectedT. Desilver and R. Desilver, 1825 - 516 sider |
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Side 124
... multiple of A , that F is of C ; and of E and F have been taken equi- multiples K , L ; therefore K is the same multiple of A , that L is of C ( 3. 5. ) ; for the same reason , M is the same multiple of B , that N is of D and because ...
... multiple of A , that F is of C ; and of E and F have been taken equi- multiples K , L ; therefore K is the same multiple of A , that L is of C ( 3. 5. ) ; for the same reason , M is the same multiple of B , that N is of D and because ...
Side 125
... multiple of another , which a magnitude taken from the first is of a magnitude taken from the other ; the remainder shall be the same multiple of the remainder , that the whole is of the whole . Let the magnitude AB be the same multi ...
... multiple of another , which a magnitude taken from the first is of a magnitude taken from the other ; the remainder shall be the same multiple of the remainder , that the whole is of the whole . Let the magnitude AB be the same multi ...
Side 126
... multiple of FD , that AB is of CD . There- fore , if any magnitude , & c . Q. E. D. PROP . VI . THEOR . IF two ... multiple of E , that CH is of F , and that GB is equal to E , and CK to F ; therefore AB is the same multiple of E , that ...
... multiple of FD , that AB is of CD . There- fore , if any magnitude , & c . Q. E. D. PROP . VI . THEOR . IF two ... multiple of E , that CH is of F , and that GB is equal to E , and CK to F ; therefore AB is the same multiple of E , that ...
Side 127
... multiple of F , that GB is of E. If therefore two magnitudes , & c . Q. E. D. PROP . A. THEOR . If the first of four ... multiples ; and that G is less than E , His H C also ( 5. def . 5. ) less than F ; that is , F is greater than H ...
... multiple of F , that GB is of E. If therefore two magnitudes , & c . Q. E. D. PROP . A. THEOR . If the first of four ... multiples ; and that G is less than E , His H C also ( 5. def . 5. ) less than F ; that is , F is greater than H ...
Side 128
... multiples whatever G and H ; then , because A is the same multiple of B that C is of D ; and that E is the same multiple of A , that F is of C ; E is the same multiple of B that F is of D ( 3. 5. ) ; therefore E and F are the same multiples ...
... multiples whatever G and H ; then , because A is the same multiple of B that C is of D ; and that E is the same multiple of A , that F is of C ; E is the same multiple of B that F is of D ( 3. 5. ) ; therefore E and F are the same multiples ...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid Ingen forhåndsvisning tilgjengelig - 2018 |
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali 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 Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore