Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books 1 - 7 of 7 on BA'B' = the cone H'BB'. COR. The segment BAB' is to a cone with the same base and....  
" 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 62
by Archimedes - 1897 - 326 pages
Full view - About this book

A short account of the history of mathematics

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,...
Full view - About this book

Bulletin of the American Mathematical Society

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...
Full view - About this book

The Education Outlook, Volume 51

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 "...
Full view - About this book

Mathematical Thought from Ancient to Modern Times:

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...
Limited preview - About this book

A Manual of Greek Mathematics

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,...
Limited preview - About this book

Euclid's Book on Divisions of Figures: With a Restoration Based on Woepcke's ...

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...
Limited preview - About this book

The Works of Archimedes

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'...
Limited preview - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download PDF