The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 102
... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first is said to have to the fourth the triplicate ratio of that ...
... proportionals , the first is said to have to the third the duplicate ratio of that which it has to the second . XI . When four magnitudes are continual proportionals , the first is said to have to the fourth the triplicate ratio of that ...
Page 103
... proportionals , so that they continue ' still to be proportionals . ' XIII . Permutando , or alternando , by permutation or alter- See N. nately . This word is used when there are four pro- portionals , and it is inferred that the first ...
... proportionals , so that they continue ' still to be proportionals . ' XIII . Permutando , or alternando , by permutation or alter- See N. nately . This word is used when there are four pro- portionals , and it is inferred that the first ...
Page 104
... proportionals , and it is inferred that the first together with the second , is to the second , as the third together with the fourth , is to the fourth . 18th Prop . Book 5 . XVI . Dividendo , by division ; when there are four propor ...
... proportionals , and it is inferred that the first together with the second , is to the second , as the third together with the fourth , is to the fourth . 18th Prop . Book 5 . XVI . Dividendo , by division ; when there are four propor ...
Page 111
... proportionals , they are propor- See N. tionals also when taken inversely . Let A'be to B , as C is to D : then also inversely B shall be to A , as D to C. * 5 Def . 5 . Take of B and D any equimultiples whatever E and F ; and of A and ...
... proportionals , they are propor- See N. tionals also when taken inversely . Let A'be to B , as C is to D : then also inversely B shall be to A , as D to C. * 5 Def . 5 . Take of B and D any equimultiples whatever E and F ; and of A and ...
Page 117
... proportionals , as one of the antecedents is to its consequent , so shall all the antecedents taken together be to all the consequents . Let any number of magnitudes A , B , C , D , E , F , be proportionals ; that is , as A is to B , so ...
... proportionals , as one of the antecedents is to its consequent , so shall all the antecedents taken together be to all the consequents . Let any number of magnitudes A , B , C , D , E , F , be proportionals ; 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,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr 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 logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn 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