 | Colin MacLaurin - Algebra - 1748 - 490 pages
...is lefs than the half of that which preceded it next but one. Now if from any Quantity you take away more than its half, and from the Remainder, more than its half, and proceed in this Manner, you will come at a Remainder lefs rhan any allignable Quantity. It appears... | |
 | Colin MacLaurin - Algebra - 1756 - 538 pages
...is lefs than the half of that which preceded it next but one. Now if from any quantity you take away more than its half, and from the remainder more than its half, and proceed in this manner, you will come at a remainder lefs than any affignable quantity. It appears... | |
 | Robert Simson - Trigonometry - 1762 - 488 pages
...lead of the propofed magnitudes. D Let AB and C be two- unequal magnitudes, of which AB is the Beater. if from AB there be taken more than its half, and from the remainder more than its half, and fo on ; there fhall at length remain a magnitude Ids than C. For C may be multiplied fo as at length... | |
 | Euclid - Geometry - 1765 - 492 pages
...the tenth book* that if there be two propufed unequal magnitudes, and from the greater he taken away more than its half, and from the remainder more than its half, and this be continually done, there will at laft remain fome magnitude that is lefs than the leaft of the... | |
 | Robert Simson - Trigonometry - 1775 - 534 pages
...lefs than the lead of the propofed magnitudes. Let AB and C be two unequal magnitudes, of which AB a the greater. If from AB there be taken more .^ than its half, and from the remainder more than ft its half, and fo on ; there fua'.l at length remain a magnitude lefs than C. For C may be multiplied... | |
 | Euclid - 1781 - 552 pages
...the leaft of the propofcd magnitudes. • D Let AB and C be two unequal magnitudes, of which AB i: the greater. If from AB there be taken more than its half, and from the remainder more than f its half, and fo on; there fball at length remain a magnitude lefs than C. For C may be multiplied... | |
 | Euclid - Euclid's Elements - 1789 - 296 pages
...continually. Since, therefore, the circle ABCD is greater than the fpace s, and from the former there has been taken more than its half, and from the remainder more than its half, &c. there will at length remain fegments which, taken together, fhall be lefs than the excefs of the... | |
 | Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...leaft of the propofed magnitudes. r ° - , . », » .».i,-«i Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken away its half, and from the remainder its half, and fo on ; there fliall at length remain a magnitude... | |
 | Colin MacLaurin - Algebra - 1796 - 554 pages
...is lefs than the half of that which preceded it next but one. Now if from any quantity you take away more than its half, and from the remainder more than its half, and proceed in this manner, you will come at a remainder lefs (Euclid Prop. i. Book 10) than any aflignable... | |
 | Colin Macfarquhar, George Gleig - Encyclopedias and dictionaries - 1797 - 446 pages
...in the proof of prop. I. bookx. which imports, that if, from the greater of two quantities, you take more than its half, and from the remainder more than its half, and fo continually, there will, at length, remain a quantity lefs than cither of thofe propofed. On this... | |
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Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so... 
