The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 130
... taken two and two of each rank , and it is in- ferred , that the first is to the last of the first rank of magnitudes , as the first is to the last of the others : Of this there are the two fol- ' lowing kinds , which arise from the ...
... taken two and two of each rank , and it is in- ferred , that the first is to the last of the first rank of magnitudes , as the first is to the last of the others : Of this there are the two fol- ' lowing kinds , which arise from the ...
Page 133
... taken equimultiples ; these shall be equimultiples , the one of the se- cond , and the other of the fourth . Let A the first be the same multiple of B the second , that C the third is of D the fourth ; and of A , C let equimultiples EF ...
... taken equimultiples ; these shall be equimultiples , the one of the se- cond , and the other of the fourth . Let A the first be the same multiple of B the second , that C the third is of D the fourth ; and of A , C let equimultiples EF ...
Page 134
... which the equimultiple of the third has to that of the fourth . ' Let A the first have to B the second the same ratio which the third C has to the fourth D ; and of A and C let there be taken any equimultiples 134 EUCLID'S ELEMENTS .
... which the equimultiple of the third has to that of the fourth . ' Let A the first have to B the second the same ratio which the third C has to the fourth D ; and of A and C let there be taken any equimultiples 134 EUCLID'S ELEMENTS .
Page 135
... taken any equimultiples whatever E , F ; and of B and D any equimultiples whatever G , H ' : then E shall have the same ratio to G , which F has to H. Take of E and F any equi- multiples whatever K , L , and of G , H any equimultiples ...
... taken any equimultiples whatever E , F ; and of B and D any equimultiples whatever G , H ' : then E shall have the same ratio to G , which F has to H. Take of E and F any equi- multiples whatever K , L , and of G , H any equimultiples ...
Page 136
... taken , viz . K and L ; and of B and D certain equimultiples G , H ; therefore , if K be greater than G , L is ... taken from the first is of a magnitude taken from the other ; the remainder shall be the same multiple of the remainder ...
... taken , viz . K and L ; and of B and D certain equimultiples G , H ; therefore , if K be greater than G , L is ... taken from the first is of a magnitude taken from the other ; the remainder shall be the same multiple of the remainder ...
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