 | Robert Simson - Trigonometry - 1762 - 488 pages
...fame ratio to each of the magnitudes A and B ; A is equal to B. for if they are not, one of them is greater than the other ; let A be the greater, therefore, as was fhewn in Prop. 8th, there is fome multiple F of C, and fome equimultiples E and D of B and A fuch,... | |
 | Robert Simson - Trigonometry - 1804 - 530 pages
...fame ratio to each of the magnitudes A and B ; A is J equal to B. for if they are not, one of them is greater than the other ; let A be the greater, therefore, as was fhewn in Prop. 8th,, there is fdme multiple F of C, and fome equimultiples E and D of B and A fuch,... | |
 | Robert Simson - Trigonometry - 1806 - 546 pages
...ratio to each of the magnitudes A and B ; A is equal to B : for, if they arc not, one of them is B greater than the other ; let A be the greater; therefore, as was shown in Prop. 8th, there is some multiple F of C, and some equimultiples E and D, of B and A such, that F is... | |
 | Charles Hutton - Mathematics - 1811 - 406 pages
...two parallel lines AB, CD ; then will the angle AEF be / equal to the alternate angle EFD. -^ £*- $ For if they are not equal, one of them /.-••'' must be greater than the othig- ; let it be £ , fa « EFD for instance which is the greater, if / possible; ;1i:.l conceive... | |
 | Charles Hutton - Mathematics - 1816 - 610 pages
...parallel lines AB, CD ; then will the angle AEF be . -g / ^ equal to the alternate angle EFD. ~i — ~ For if they are not equal, one of them / ^ must be greater than the other ; let it be /•' EFD for instance which is the greater, if C j^ possible ; and conceive the line FB to be... | |
 | Euclides - 1816 - 588 pages
...ratio to each of the magnitudes A and B; A is equal to B : For, if they are not, one of them ' * is greater than the other ; let A be the greater; therefore, as was shown in Prop. 8th, there is some multiple F of C, and some equimultiples E and D, of B and A such, that F is... | |
 | Charles Hutton - Mathematics - 1822 - 616 pages
...the two parallel lines AB, CD ; then will the angle AEF be equal to the alternate angle EFD. For jf they are not equal, one of them must be greater than the other ; let it be EFD for instance which i? the greater C 71? D if possible ; and conceive the line FB to ' be... | |
 | Edward Riddle - Nautical astronomy - 1824 - 572 pages
...two parallel lines А В and С Т), the alternate angles BEF and С FE will be equal to each other. For if they are not equal, one of them must be \ greater than the other. Suppose BEF to be the л^г greater, and let DEF, a part of BEF, be equal to V '•-•.. С F E. Then... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...one of them is greater than the other ; let A be the greater; therefore, as vva« shown in Prop. 8th, there is some multiple F of C, and some equimultiples E and D, of В and A such, that F is greater than E, and not greater than D; but because С is to B, as О is to... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...are equal. Next, let C have the same ratio to each of the magnitudes A and B : A shall be equal to B. For, if they are not equal, one of them must be greater then the other : let A be the greater : therefore, as was shewn in Prop. 8th, there is some multiple... | |
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A and B are not unequal ; that is, they are equal. Next, let C have the same ratio to each of the magnitudes A and B ; then A shall be equal to B. 
