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 122
... magnitudes be of all the other : For the same demonstration ' holds in any number of magnitudes , which was here applied to ' two . ' Q. E. D. PROP . II . THEOR . If the first magnitude be the same multiple of the se- cond that the ...
... magnitudes be of all the other : For the same demonstration ' holds in any number of magnitudes , which was here applied to ' two . ' Q. E. D. PROP . II . THEOR . If the first magnitude be the same multiple of the se- cond that the ...
Side 123
... magnitudes in EF equal to A ; as are in GH equal to C : let EF be di- K vided into the magnitudes F EK , KF , each equal to A , and GH into GL , LH , each equal to C : the number therefore of the magnitudes EK , KF , shall be equal to ...
... magnitudes in EF equal to A ; as are in GH equal to C : let EF be di- K vided into the magnitudes F EK , KF , each equal to A , and GH into GL , LH , each equal to C : the number therefore of the magnitudes EK , KF , shall be equal to ...
Side 125
... 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- ple of CD , that AE taken from ...
... 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- ple of CD , that AE taken from ...
Side 126
... magnitude , & c . Q. E. D. PROP . VI . THEOR . IF two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to these others , or equimulti- ples of them ...
... magnitude , & c . Q. E. D. PROP . VI . THEOR . IF two magnitudes be equimultiples of two others , and if equimultiples of these be taken from the first two , the remainders are either equal to these others , or equimulti- ples of them ...
Side 127
... magnitudes be proportionals , they are propor- tionals also when taken inversely . * If the magnitude A be to B , as C is to D , then also inversely B is to A , as D to C. G Take of B and D any equimultiples whatever E and F ; and of A ...
... magnitudes be proportionals , they are propor- tionals also when taken inversely . * If the magnitude A be to B , as C is to D , then also inversely B is to A , as D to C. G Take of B and D any equimultiples whatever E and F ; and of A ...
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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