BA'B' = the cone H'BB'. COR. The segment BAB' is to a cone with the same base and equal height in the ratio of OA' -+ A'M to A'M. Proposition 3. (Problem.) To cut a given sphere by a plane so that the surfaces of the segments may have to one another a... The Works of Archimedes - Page 62by Archimedes - 1897 - 326 pagesFull view - About this book
| Walter William Rouse Ball - Mathematics - 1901 - 527 pages
...be greater than 3fc. This proposition was required to complete his solution of the problem to divide **a given sphere by a plane so that the volumes of the segments** should be in a given ratio. One very simple cubic equation occurs in the Arithmetic of Diopbantus,... | |
| Mathematics - 1918
...solution of the following problem of Archimedes reduces to that of the trisection of an angle: "To cut a **sphere by a plane so that the volumes of the segments are to one another in a given ratio."** At this point it would have been interesting to have added a reference to Brocard's pamphlet, Memoire... | |
| Education - 1897
...segments of spheres with equal curved surfaces, the hemisphere has the greatest volume, and proposes th«? **problem : " To cut a given sphere by a plane so that...the segments are to one another in a given ratio,"** a problem leading to a cubic equation of which Dionysiusgave an elegant solution, (ii.) A book on "... | |
| Morris Kline - Mathematics - 1990 - 428 pages
...are significant because they contain new geometrical algebra. For example, he gives : Proposition 4. **To cut a given sphere by a plane so that the volumes...the segments are to one another in a given ratio.** This problem amounts algebraically to the solution of the cubic equation (a- x):c = b*:x* and Archimedes... | |
| Sir Thomas Little Heath - Mathematics - 1931 - 552 pages
...reduces the problem of On the Sphere and Cylinder, II. 4, ' To cut a sphere by a plane in such a way **that the volumes of the segments are to one another in a given ratio'** ; the solution is given by Eutocius. This Dionysodorus may have been Dionysodorus of Amisene in Pontus,... | |
| Raymond Clare Archibald - Euclid's Elements - 2012 - 106 pages
...parallel to the base, of a Pyramid (xx) and of a Cone (xx1). For proof of Proposition xxm : To cut a **sphere by a plane so that the volumes of the segments are to one another in a given ratio,** Heron refers to Proposition 4, Book II of "On the Sphere and Cylinder" of Archimedes ; the third proposition... | |
| Archimedes, Sir Thomas Little Heath - 1900 - 326 pages
...is to a cone with the same base and equal height in the ratio of OA' -+ A'M to A'M. Proposition 3. **(Problem.) To cut a given sphere by a plane so that the** surfaces of the segments may have to one another a given ratio. Suppose the problem solved. Let AA'... | |
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