 First then I will set out the very first theorem which became known to me by means of mechanics, namely that Any segment of a section of a right-angled cone (ie a parabola) is four-thirds of the triangle which has the same base and equal height, and after...  The Works of Archimedes - Page 246by Archimedes - 1897 - 326 pagesFull view - About this book
 | Archimedes - Geometry - 1912 - 568 pages
...given sphere to cut off a segment by a plane so that the segment may have a given ratio to the cone which has the same base as the segment and equal height. Let AA' be the diameter of a great circle of the sphere. It is required to draw a plane at right angles... | |
 | Archimedes - Geometry - 1912 - 60 pages
...known to me by means of mechanics, namely that Any segment of a section of a right-angled cone (ie a parabola) is four-thirds of the triangle which has the same base and equal height, and after this I will give each of the other theorems investigated by the same method.... | |
 | Sir Thomas Little Heath - Geometry - 1920 - 74 pages
...known to me by means of mechanics, namely, that Any segment of a section of a right-angled cone [ie a parabola} is four-thirds of the triangle which has the same base and equal height ; and after this I will give each of the other theorems investigated by the same method.... | |
 | Reinhard Laubenbacher, David Pengelley - Mathematics - 2000 - 292 pages
...it is here shown that every segment bounded by a straight line and a section of a right-angled cone [a parabola] is four-thirds of the triangle which has the same base and equal height with the segment, and for the demonstration of this property the following lemma is... | |
 | Saul Stahl - Mathematics - 1999 - 288 pages
...it is here shown that every segment bounded by a straight line and a section of a right.angled cone [a parabola] is four.thirds of the triangle which has the same base and equal height with the segment, and for the demonstration of this property the following lemma is... | |
 | Geometry - 1912 - 56 pages
...known to me by means of mechanics, namely that Any segment of a section of a right-angled cone (ie a parabola) is four-thirds of the triangle which has the same base and equal height, and after this I will give each of the other theorems investigated by the same method.... | |
 | Arhimēdēs - 2004 - 522 pages
...the proofs, showing that any segment bounded by a straight line and a section of a right-angled cone [a parabola] is four-thirds of the triangle which has the same base with the segment and equal height. Since then certain theorems not hitherto demonstrated (a.ve\eyKro1v)... | |
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