| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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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