The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
From inside the book
Page 126
... multiple of a less , when the greater is measured by the less , that is , when the greater contains the ' less a certain number of times exactly . ' 6 III . " Ratio is a mutual relation of two magnitudes " of the same kind to one ...
... multiple of a less , when the greater is measured by the less , that is , when the greater contains the ' less a certain number of times exactly . ' 6 III . " Ratio is a mutual relation of two magnitudes " of the same kind to one ...
Page 127
... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth : or , if the multiple of the first be equal to that of the second , the multiple of the third is also equal to that ...
... multiple of the first be less than that of the second , the multiple of the third is also less than that of the fourth : or , if the multiple of the first be equal to that of the second , the multiple of the third is also equal to that ...
Page 131
... multiple of a greater magnitude is greater than the same multiple of a less . IV . That magnitude , of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROP . I. THEOR . If any ...
... multiple of a greater magnitude is greater than the same multiple of a less . IV . That magnitude , of which a multiple is greater than the same multiple of another , is greater than that other magnitude . PROP . I. THEOR . If any ...
Page 132
... multiple of E that CD is of F , as many magnitudes as there are in AB equal to E , so many are there in CD equal to ... multiple AB is of E , the same multiple is AB and CD together of E and F together . Therefore , if any magnitudes ...
... multiple of E that CD is of F , as many magnitudes as there are in AB equal to E , so many are there in CD equal to ... multiple AB is of E , the same multiple is AB and CD together of E and F together . Therefore , if any magnitudes ...
Page 133
... multiple of the second C , that DH , the third and sixth toge- ther , is of the fourth F. If there- fore , the first be the same multiple , & c . Q. E. D. B D E K HCLF COR . - From this it is plain , that if any number of magnitudes AB ...
... multiple of the second C , that DH , the third and sixth toge- ther , is of the fourth F. If there- fore , the first be the same multiple , & c . Q. E. D. B D E K HCLF COR . - From this it is plain , that if any number of magnitudes AB ...
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