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The Common Sense of the Exact Sciences (Paperback)
Loot Price: R884
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The Common Sense of the Exact Sciences (Paperback)
Series: Cambridge Library Collection - Physical Sciences
Expected to ship within 12 - 17 working days
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This historic book may have numerous typos and missing text.
Purchasers can download a free scanned copy of the original book
(without typos) from the publisher. Not indexed. Not illustrated.
1891 Excerpt: ...position of the face B E G F, it is easy to see
that the two wedgeshaped figures Bee'b'oc and Pgg'p'ad are exactly
equal; this follows from the equality of their corresponding faces.
Hence the volume of the sheared figure must be equal to the volume
of the right six-face. Now let us suppose in addition that the face
B' E' G' P' is again moved in its own plane into the position B" E"
G" F," So that B' and E' move along B' E' and p' G' respectively.
Then the slant wedge-shaped figures B'b"f"p'ao and E'e"g"p'dc will
again be equal, and the volume of the six-face B" E" G" P" A D C O
obtained by this second shear will be equal to the volume of the
figure obtained by the first shear, and therefore to the volume of
the right six-face. But by n, ns of two shears we can move the face
B E G P to any position in its plane, B" E" G" P," in which its
sides remain parallel to their former position. Hence the volume of
a six-face will remain unchanged if, one of its faces, o c D A,
remaining fixed, the opposite face, B E G P, be moved anywhere
parallel to itself in its own plane. We thus find that the volume
of a six-face formed by three pairs of parallel planes is equal to
the product of the area of one of its faces and the perpendicular
distance between that face and its parallel. For this is the volume
of the right six-face into which it may be sheared; and, as we have
seen, shear does not alter volume. The knowledge thus gained of the
volume of a sixface bounded by three pairs of parallel faces, or of
a so-called parallelepiped, enables us to find the volume of an
oblique cylinder. A right cylinder is the figure generated by any
area moving parallel to itself in such wise that any point p ...
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