...or \b. The third Remainder, in the fame Manner muft be lefs than ^c, which is itfelf lefs than 4** Thus thefe Remainders decreafe fo that every one is...in this Manner, you will come at a Remainder lefs rhan any allignable Quantity. It appears therefore that it the Remainders c, J, &c. never end, they...

...fome of the Propofitions of this Book. 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 propofed magnitudes. D Let...

...of 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...

...fome of the propofitions of this book. TF 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 lhall at length remain a magnitude lefs than the lead of the propofed magnitudes. Let...

...fa: thus thefe remainders ctecreafe fo, that every one is lefs than the half of- that which preceded1 it next but one. Now if from any quantity you take...remainder lefs than any affignable quantity. It appears there» fore that if the remainders V, </, &c. never end» they will become lefs than any affignable...

...feme of the propofitions of this book. TF 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 leaft of the propofcd magnitudes. •...

...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...

...manner rf muft be lefs than \ b, for d is lefs than f, and confequently lefe than-jrf + iBf> Or i£. The third remainder, in the fame manner, muft be lefs...in this manner, you will come at a remainder lefs (Euclid Prop. i. Book 10) than any aflignable quantity. It appears therefore that if the remainders...

...one. Now if from any quantity you take away more than its half, and from the remainder more than ks half, and proceed in this manner, you will come at a remainder lefs (Euclid Prop. i. Book 10) than any affignable quantity. It appears therefore that if the remainders...

...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...