Works
Works
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In our eReader you can find the full English version of the book. Read Works 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 Works
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Hence both points of contact lie on one plane through the axis, and the proposition is reduced to a plane one.
Proposition 17- If two parallel planes touch any of the spheroidal figures, and another plane be drawn parallel to the tangent planes and passing through the centre, the line drawn through any point of the circumference of the residting section parallel to the chord of contact of the tangent planes will fall outside the spheroid.
This is proved at once by reduction to a plane propositi...on.
Archimedes adds that it is evident that, if the plane parallel to the tangent planes does not pass through the centre, a straight line drawn in the manner described will fall without the spheroid in the direction of the smaller segment but within it in the other direction.
Proposition 18.
Any spheroidal figure which is cut by a plane through the centre is divided, both as regards its surface and its volume, into two equal parts by that plane.
To prove this, Archimedes takes another equal and similar spheroid, divides it similarly by a plane through the centre, and then uses the method of application.
What to read after Works?
You can find similar books in the "Read Also" column, or choose other free books by Archimedes to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Hence both points of contact lie on one plane through the axis, and the proposition is reduced to a plane one.
Proposition 17- If two parallel planes touch any of the spheroidal figures, and another plane be drawn parallel to the tangent planes and passing through the centre, the line drawn through any point of the circumference of the residting section parallel to the chord of contact of the tangent planes will fall outside the spheroid.
This is proved at once by reduction to a plane propositi...on.
Archimedes adds that it is evident that, if the plane parallel to the tangent planes does not pass through the centre, a straight line drawn in the manner described will fall without the spheroid in the direction of the smaller segment but within it in the other direction.
Proposition 18.
Any spheroidal figure which is cut by a plane through the centre is divided, both as regards its surface and its volume, into two equal parts by that plane.
To prove this, Archimedes takes another equal and similar spheroid, divides it similarly by a plane through the centre, and then uses the method of application.
What to read after Works?
You can find similar books in the "Read Also" column, or choose other free books by Archimedes to read onlineMoreLess
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