...unequal magnitudes, there be taken SeeN. more than its half, and from the remainder more than its hay, and so on ; there shall at length remain a magnitude...less than the least of the proposed magnitudes. Let AB and C be two unequal magnitudes, of which AB is the greater : if from AB there be taken more than...

...and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more Sec N. than its half, and from the remainder more than its...there shall at length remain a magnitude less than C. For C may be multiplied so as at length to become greater than AB. Let it be so multiplied, and...

...unequal magnitudes there be taken away its half, and from the remainder its half: and so on ; there will at length remain a magnitude less than the least of the proposed magnitudes. II. Equilateral polygons, of the same number of sides, inscribed in circles, are similar, and are to...

...triangular prisms, &c. BOOK XII. LEMMA I.* 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 will at length remain a magnitude less than the least of the proposed magnitudes. Let AB and C be two...

...magnitudes, of which AB is the greater. If from AB there be taken away its half, and from the remainder 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. Let it be so multiplied, and...

...magnitudes, of which AB is the greater. If from AB there be taken away its half, and from the remainder 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. Let DE, therefore, be a multiple...

...some of the propositions of this book. IF from the greater of two unequal magnitudes, there be taken more than its half, and from the remainder more than...magnitude less than the least of the proposed magnitudes.* K H Let AB and C be two unequal magnitudes, of which AB is the greater. If from AB there be taken more...

...which AB is the greater. If from AB there be taken more than its half, and from the remainder more D than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so at length to become greater than AB. Let it be so multiplied, and let...

...manner are to be understood some things in some of the following Propositions. magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there at length remains a magnitude less than the least of the proposed magnitudes. Let then the segments...

...the dividend, more than its half is taken away, and so on ; but if from any quantity there be taken more than its half, and from the remainder more than its half, and so on, there will, at length, remain a quantity less than any that can be asigned (Eue. x. I.) [109. In practice...