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 118
... proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second , as the third to the fourth . ' VII . When of the equimultiples of four magnitudes ( taken as in the fifth ...
... proportionals . N. B. When four magnitudes are proportionals , it is usually expressed by saying , the first is to the second , as the third to the fourth . ' VII . When of the equimultiples of four magnitudes ( taken as in the fifth ...
Side 119
... proportionals . ' XIII . Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is in- ferred , that the first has the same ratio to the third , which the second has ...
... proportionals . ' XIII . Permutando , or alternando , by permutation , or alternately ; this word is used when there are four proportionals , and it is in- ferred , that the first has the same ratio to the third , which the second has ...
Side 120
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first rank of magnitudes , as the first is to the last of the others : " Of this there are the two following kinds , which ...
... proportionals when taken two and two of each rank , and it is inferred , that the first is to the last of the first rank of magnitudes , as the first is to the last of the others : " Of this there are the two following kinds , which ...
Side 127
... 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 and C any ...
... 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 and C any ...
Side 134
... proportionals as one of the antecedents is to its consequent , so shall all the an- tecedents taken together be to all the consequents . Let any number of magnitudes A , B , C , D , E , F be propor tionals ; that is , as A is to B , so ...
... proportionals as one of the antecedents is to its consequent , so shall all the an- tecedents taken together be to all the consequents . Let any number of magnitudes A , B , C , D , E , F be propor tionals ; that is , as A is to B , so ...
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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