The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 132
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first toge- ther with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . Let ...
... fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first toge- ther with the fifth be the same multiple of the second , that the third together with the sixth is of the fourth . Let ...
Page 133
... fourth : then shall AG , the first together with the fifth , be the same multiple of C the se- fond , that DH , the third toge- ther with the sixth , is of F the fourth . B A D E 1 CHF Because AB is the same multiple of C that DE is of ...
... fourth : then shall AG , the first together with the fifth , be the same multiple of C the se- fond , that DH , the third toge- ther with the sixth , is of F the fourth . B A D E 1 CHF Because AB is the same multiple of C that DE is of ...
Page 134
... fourth D , and that the fifth KF is the same multiple of the second B , which the sixth LH is of the fourth D ; EF the first , together with the fifth , is the same multiple * of the second B , which GH the third , together with the ...
... fourth D , and that the fifth KF is the same multiple of the second B , which the sixth LH is of the fourth D ; EF the first , together with the fifth , is the same multiple * of the second B , which GH the third , together with the ...
Page 135
... fourth , then also any equimultiples whatever of the first and third shall have the same ratio to the second and fourth and in like manner , the first and the third shall have the same ratio to any equi- multiples whatever of the second ...
... fourth , then also any equimultiples whatever of the first and third shall have the same ratio to the second and fourth and in like manner , the first and the third shall have the same ratio to any equi- multiples whatever of the second ...
Page 138
... fourth ; then , if the first be greater than the second , the third is also greater than the fourth ; ana if equal , equal ; if less , less . Take any equimultiples of each of them , as the doubles of each : then , by def . 5th of this ...
... fourth ; then , if the first be greater than the second , the third is also greater than the fourth ; ana if equal , equal ; if less , less . Take any equimultiples of each of them , as the doubles of each : then , by def . 5th of this ...
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