The Method of Archimedes, Recently Discovered By Heiberg; a Supplement to the Works of Archimedes, 1897
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In our eReader you can find the full English version of the book. Read The Method of Archimedes, Recently Discovered By Heiberg; a Supplement to the Works of Archimedes, 1897 Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book The Method of Archimedes, Recently Discovered By Heiberg; a Supplement to the Works of Archimedes, 1897
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To quickly assess the difficulty of the text, read a short excerpt:
MS) : (circle, rad. OS) = (circle in cylinder) : (circle in paraboloid).
Therefore the circle in the cylinder, in the place where it is, will be in equilibrium, about A, with the circle in the paraboloid, if the latter is placed with its centre of gravity at H.
Similarly for the two corresponding circular sections made by a plane perpendicular to AD and passing through any other straight line in the parallelogram which is parallel to BC.
Therefore, as usual, if we take all the circles making up... the whole cylinder and the whole segment and treat them in the same way, we find that the cylinder, in the place where it is, is in equilibrium about A with the segment placed with its centre of gravity at H.
If Κ is the middle point oi AD, Κ is the centre of gravity of the cylinder ; therefore HA : ^Z'= (cylinder) : (segment).
Therefore cylinder = 2 (segment).
And cylinder = 3 (cone ^5C); [Eucl. xii. 10] therefore segment = f (cone ABC).
Proposition 5.
The centre of gravity of a segment of a right-angled conoid {i.e.
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To quickly assess the difficulty of the text, read a short excerpt:
MS) : (circle, rad. OS) = (circle in cylinder) : (circle in paraboloid).
Therefore the circle in the cylinder, in the place where it is, will be in equilibrium, about A, with the circle in the paraboloid, if the latter is placed with its centre of gravity at H.
Similarly for the two corresponding circular sections made by a plane perpendicular to AD and passing through any other straight line in the parallelogram which is parallel to BC.
Therefore, as usual, if we take all the circles making up... the whole cylinder and the whole segment and treat them in the same way, we find that the cylinder, in the place where it is, is in equilibrium about A with the segment placed with its centre of gravity at H.
If Κ is the middle point oi AD, Κ is the centre of gravity of the cylinder ; therefore HA : ^Z'= (cylinder) : (segment).
Therefore cylinder = 2 (segment).
And cylinder = 3 (cone ^5C); [Eucl. xii. 10] therefore segment = f (cone ABC).
Proposition 5.
The centre of gravity of a segment of a right-angled conoid {i.e.
What to read after The Method of Archimedes, Recently Discovered By Heiberg; a Supplement to the Works of Archimedes, 1897?
You can find similar books in the "Read Also" column, or choose other free books by Archimedes to read onlineMoreLess
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