The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 146
... 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 ...
Page 150
... proportionals , viz . as A to B , so C to D : they shall also be proportionals when taken alternately ; that is , A shall be to C , as B to D. Take of A and B any equimultiples whatever E and F ; and of C and D take any equimulti- ples ...
... proportionals , viz . as A to B , so C to D : they shall also be proportionals when taken alternately ; that is , A shall be to C , as B to D. Take of A and B any equimultiples whatever E and F ; and of C and D take any equimulti- ples ...
Page 151
... proportionals , they shall also be proportionals when taken separately : that is , if two magnitudes together have to one of them the same ratio which two others have to one of these , the remaining one of the first two shall have to ...
... proportionals , they shall also be proportionals when taken separately : that is , if two magnitudes together have to one of them the same ratio which two others have to one of these , the remaining one of the first two shall have to ...
Page 152
... proportionals , they 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 to- gether shall be to the second , as the third ana fourth together to ...
... proportionals , they 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 to- gether shall be to the second , as the third ana fourth together to ...
Page 155
... proportionals , they are also proportionals by conversion ; that is , the first is to its excess 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 proportionals by conversion ; that is , the first is to its excess 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 ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole