The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Results 6-10 of 66
Page 120
... proportionals , st they shall also be proportionals when taken alternately 28 Let A , B , C , D be four magnitudes of the same kind , which are proportionals , viz . as A to B , so C to Da they shall also be proportionals when taken ...
... proportionals , st they shall also be proportionals when taken alternately 28 Let A , B , C , D be four magnitudes of the same kind , which are proportionals , viz . as A to B , so C to Da they shall also be proportionals when taken ...
Page 121
... proportionals , they see N. shall also be proportionals when taken jointly : that is , if the first be to the second , as the third to the fourth , the first and second together shall be to the second , as the third and fourth together ...
... proportionals , they see N. shall also be proportionals when taken jointly : that is , if the first be to the second , as the third to the fourth , the first and second together shall be to the second , as the third and fourth together ...
Page 122
... proportionals when taken jointly ; that is , as AB to BE , so shall CD be to DF . Take of AB , BE , CD , DF any equimultiples what- ever GH , HK , LM , MN ; and again , of BE , DF , take any equimultiples whatever KO , NP : and because ...
... proportionals when taken jointly ; that is , as AB to BE , so shall CD be to DF . Take of AB , BE , CD , DF any equimultiples what- ever GH , HK , LM , MN ; and again , of BE , DF , take any equimultiples whatever KO , NP : and because ...
Page 123
... proportionals , they are also proportionals * , when taken separately ; therefore , * 17 . 5 . as BE is to EA , so is DF to FC ; and alternately , as 101 † 11. 5 . & * 17.5 . * BOOK V. PROP . XIX . 123.
... proportionals , they are also proportionals * , when taken separately ; therefore , * 17 . 5 . as BE is to EA , so is DF to FC ; and alternately , as 101 † 11. 5 . & * 17.5 . * BOOK V. PROP . XIX . 123.
Page 124
... proportionals , they are also pro- portionals by conversion : that is , the first is to its ex- cess above the second , as the third to its excess above the fourth . Let AB be to BE , as CD to DF : then BA shall be to AE , as DC to CF ...
... proportionals , they are also pro- portionals by conversion : that is , the first is to its ex- cess above the second , as the third to its excess above the fourth . Let AB be to BE , as CD to DF : then BA shall be to AE , as DC to CF ...
Other editions - View all
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