The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 21.
Σελίδα 89
V. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and ...
V. The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and ...
Σελίδα 90
a third , and of the ratio which the third has to the fourth , and so on unto the last magnitude . For example , if a , b , c , d be four magnitudes of the same kind , the first is said to have to the last d the ratio compounded of the ...
a third , and of the ratio which the third has to the fourth , and so on unto the last magnitude . For example , if a , b , c , d be four magnitudes of the same kind , the first is said to have to the last d the ratio compounded of the ...
Σελίδα 91
... one of the second rank ; and as the third is to the fourth of the first rank , so is the third from the last to the last but two of the second rank , and so on in a cross order : and the · inference is as in the 18th definition .
... one of the second rank ; and as the third is to the fourth of the first rank , so is the third from the last to the last but two of the second rank , and so on in a cross order : and the · inference is as in the 18th definition .
Σελίδα 92
If the first magnitude be the same multiple of the second that the third is of the fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same ...
If the first magnitude be the same multiple of the second that the third is of the fourth , and the fifth the same multiple of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same ...
Σελίδα 93
5 ) of the second b , which gh the third together with the sixth , is of the fourth d . If , therefore , the first , & c . Q. É . D. pas PROPOSITION IV . - THEOREM . If the first of four magnitudes has the same ratio to the second which ...
5 ) of the second b , which gh the third together with the sixth , is of the fourth d . If , therefore , the first , & c . Q. É . D. pas PROPOSITION IV . - THEOREM . If the first of four magnitudes has the same ratio to the second which ...
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a b c angle a b c angle bac base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square square of a c straight line a b Take taken third touches the circle triangle triangle a b c wherefore whole