 If from the greater of two unequal magnitudes, 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 the least of the proposed magnitudes.  Appendix to Euclid's Elements ... - Page 51by I. Newton - 1825Full view - About this book
 | 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 aTTignable 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
...the firfl Propofition of the tenth Book, arid is neceflaiy to fome of the Propofitions of this Book. IF from the greater of two unequal magnitudes there...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 propofed magnitudes. Let... | |
 | Robert Simson - Trigonometry - 1775 - 534 pages
...fhall be lefs than the excefs of the circle EFGH above the fpace S: Becaufe, by the preceding lemma, if from the greater of two unequal magnitudes there...taken more than its half, and from the remainder more titan its bWI.i and fo on, there fhall at length remain a magnitude let'* dun the leaft of the propofcd... | |
 | Colin MacLaurin - Algebra - 1779 - 610 pages
...lefs than the half of- that which preceded 1 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 - 1781 - 534 pages
...the fir ft Propofition of the tenth Book, and is necefcry to fomc of the Propofitions of this Book. IF from the greater of two unequal magnitudes there...half, and from the remainder more than its half; and fo on. there fhall at length remain a magnitude lefs than the leaft of the propofed magnitudes. Let... | |
 | Euclid - 1781 - 552 pages
...firft propofition of the tenth book, and is neceffary to fome of the propofitions of this book. TF from the greater of two unequal magnitudes, there...half, and from the remainder more than its half; and fo on : There fhall at length remain a magnitude lefs than the leaft of the propofed magnitudes. Let... | |
 | Euclid - Euclid's Elements - 1789 - 296 pages
...through the centre, and terminated both ways by the furface. PROP. I. LEMMA. If from the greater of two magnitudes, there be taken more than its half; and from, the remainder, more than its half; and fo on : there will at length remain a magnitude lefs than the leait of the propafed maguitudes. Let... | |
 | 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... | |
 | Alexander Ingram - Trigonometry - 1799 - 374 pages
...from the fame point, to touch *-**<f^J the circle in the extremities of the arch. PROP. I. THEOR *. IF from the greater of two unequal magnitudes, there...half, and from the remainder more than its half; and fo on : There fliall at length remain a magnitude lefs than the leaft of the propofed magnitudes. Let... | |
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