The Elements of Geometry: Or, The First Six Books, with the Eleventh and Twelfth, of Euclid |
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Σελίδα 102
Therefore , whatsoever multiple A B is of E , the same multiple is A B and C D together , of E and together . The same demonstration holds in any number of magnitudes which is here applied to two . Therefore , if any number of ...
Therefore , whatsoever multiple A B is of E , the same multiple is A B and C D together , of E and together . The same demonstration holds in any number of magnitudes which is here applied to two . Therefore , if any number of ...
Σελίδα 105
Because AG is the same multiple of E , that CH is of F ( Hyp . ) ; and G B is equal to E , and CK to F. Therefore A B is the same multiple of E , that K H is of F. But AB ( Hyp . ) is the same multiple of E , that CD is of F. Therefore ...
Because AG is the same multiple of E , that CH is of F ( Hyp . ) ; and G B is equal to E , and CK to F. Therefore A B is the same multiple of E , that K H is of F. But AB ( Hyp . ) is the same multiple of E , that CD is of F. Therefore ...
Σελίδα 114
If KO , the multiple of B E , be greater than K H , which is also a multiple of BE . Therefore , NP , the multiple of DF , is also greater than NM , the multiple of the same DF ; if K O be equal to KH , N P is equal to NM ; and if less ...
If KO , the multiple of B E , be greater than K H , which is also a multiple of BE . Therefore , NP , the multiple of DF , is also greater than NM , the multiple of the same DF ; if K O be equal to KH , N P is equal to NM ; and if less ...
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A B C ABCD altitude applied base bisected Book Cassell's centre circle circumference cloth coincide common cone Const contained Corollary cylinder definition demonstration described diagonal diameter divided double draw Edition equal equal angles equiangular equimultiples Exercise extremities fore four fourth given straight line greater half Illustrated inscribed interior join less magnitudes manner meet multiple parallel parallelogram parallelopiped pass perpendicular plane polygon prism PROBLEM produced PROP proportionals proposition proved pyramid ratio reason rectangle rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle sphere square straight lines A B taken THEOREM third touch triangle triangle ABC twice vertex Vols Wherefore whole