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Books Books 1 - 10 of 31 on Y3 inscribed regular figures of sixteen sides, &r. the preceding process gives the....  
" Y3 inscribed regular figures of sixteen sides, &r. the preceding process gives the proof that circles are to one another as the squares on their diameters. "
The Works of Archimedes - Page xlviii
by Archimedes - 1897 - 326 pages
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The Penny Cyclopaedia of the Society for the Difussion of Useful ..., Volume 11

1838
...octagons, X3 and Y3 inscribed regular figures of sixteen sides, &r. the preceding process gives the proof that circles are to one another as the squares on their diameters. Book xiii., the last of those written by Euclid, applies some results of the tenth book to the sides...
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The Penny Cyclopædia of the Society for the Diffusion of ..., Volumes 11-12

Encyclopedias and dictionaries - 1838
...X3 and Y3 inscribed regular figures of sixteen sides, &<•. the preceding process gives the proof that circles are to one another as the squares on their diameters. Book xiii., the last of those written by Euclid, applies some results of the tenth book to the sides...
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The Penny Cyclopædia of the Society for the Diffusion of Useful ..., Volume 11

Encyclopedias and dictionaries - 1838
...octagons, X3 and Y3 inscribed regular figures of sixteen sides, &c. the preceding process gives the proof that circles are to one another as the squares on their diameters. Book xiii., the last of those written by Euclid, applies some results of the tenth book to the sides...
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Bibliotheca Indica, Volume 270

India - 1848
...6th magnitude. But Euclid has demonstrated in the last proposition of the 12th Book of the Elements, that circles are to one another as the squares on their diameters, that is, if the ratio of one diameter to another be one-half or less, there will be three times the...
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The English Cyclopaedia: Division. Geography. 4v. and Suppl

Charles Knight - Encyclopedias and dictionaries - 1867
...xn and Y., inscribed regular figures of sixteen sides, &c. : the preceding process gives the proof that circles are to one another as the squares on their diameters. Book xiii., the last of those written by Euclid, applies some results of the tenth book to the sides...
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Arts and Sciences: Or, Fourth Division of "The English Encyclopedia"

Charles Knight - Encyclopedias and dictionaries - 1867
...properties which are analogous to those of triangles, &c., in the first and sixth books. It also shows that circles are to one another as the squares on their diameters, and spheres as the cubes on their diameters, in which, for the first time in Euclid, the celebrated...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides - Geometry - 1872 - 349 pages
...ratio of AD to DE is double of the ratio of AF to F B. xn. 1. Give an outline of Euclid's demonstration that circles are to one another as the squares on their diameters. 1867. VI. A. Each acute angle of a right.angled triangle and its corresponding exterior angle are bisected...
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Books 10-13 and appendix

Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - Mathematics, Greek - 1908
...Preface), who says in another place (Quadrature of the Parabola, Preface) that the first of the two, and the theorem that circles are to one another as the squares on their diameters, were proved by means of a certain lemma which he states as follows : "Of unequal lines, unequal surfaces,...
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Archimedes

Sir Thomas Little Heath - Geometry - 1920 - 58 pages
...nevertheless contained the germ of the method of exhaustion. Hippocrates, as we have seen, is said to have proved the theorem that circles are to one another as the squares on their diameters, and it is difficult to see how he could have done this except by some form, or anticipation, of the...
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