The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 101
... less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , See N. when any equimultiples whatsoever of the first and.
... less can be multiplied so as to exceed the other . V. The first of four magnitudes is said to have the same ratio to the second , which the third has to the fourth , See N. when any equimultiples whatsoever of the first and.
Page 102
... fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth : or , if the multiple of the first be equal to that of the second , the multiple of the third is ...
... fourth ; if the multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth : or , if the multiple of the first be equal to that of the second , the multiple of the third is ...
Page 103
... fourth , and so on unto the last magnitude . For example , if A , B , C , D be four magnitudes of the same kind ... fourth ; or that the first is to the third as the second to the fourth : as is shewn in the 16th Prop . BOOK V ...
... fourth , and so on unto the last magnitude . For example , if A , B , C , D be four magnitudes of the same kind ... fourth ; or that the first is to the third as the second to the fourth : as is shewn in the 16th Prop . BOOK V ...
Page 104
... fourth to the third . Prop . B. Book 5 . XV . Componendo , by composition ; when there are four proportionals , and it is inferred that the first together with the second , is to the second , as the third together with the fourth , is ...
... fourth to the third . Prop . B. Book 5 . XV . Componendo , by composition ; when there are four proportionals , and it is inferred that the first together with the second , is to the second , as the third together with the fourth , is ...
Page 105
... fourth of the first rank , so is the third from the last to the last but two of the second rank ; and so on in a cross order and the inference is as in the 18th de- finition . It is demonstrated in the 23rd Prop . of Book 5 . : AXIOMS ...
... fourth of the first rank , so is the third from the last to the last but two of the second rank ; and so on in a cross order and the inference is as in the 18th de- finition . It is demonstrated in the 23rd Prop . of Book 5 . : AXIOMS ...
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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