 | Colin MacLaurin - 1748 - 490 sider
...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 - 1756 - 538 sider
...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 - 1762 - 488 sider
...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...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 to berome greater... | |
 | Euclid - 1765 - 492 sider
...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 - 1775 - 534 sider
...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 sider
...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... | |
 | Colin MacLaurin - 1796 - 554 sider
...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 - 1797 - 446 sider
...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 foundation... | |
 | Alexander Ingram - 1799 - 374 sider
...leall of the propofed magnitudes. 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...the remainder more than its half, and fo on ; there fhall at length remain a magnitude lefs than C. For C may be multiplied fo, as at length to become... | |
 | Robert Simson - 1804 - 530 sider
...EFGH above the fpace S. becaufe, by the preceding Lemma, if from the greater of two unequal magnitudes 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 lefs than the lead of the propofecl magnitudes. Let then the fegments... | |
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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 as at length to become greater than AB. 
