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 ...

A fellow of Trinity College, Cambridge, and of the Royal Society, William Clifford (1845-79) made his reputation in applied mathematics, but his interests ranged far more widely, encompassing ethics, evolution, metaphysics and philosophy of mind. This posthumously collected two-volume work, first published in 1879, bears witness to the dexterity and eclecticism of this Victorian thinker, whose commitment to the most abstract principles of mathematics and the most concrete details of human experience resulted in vivid and often unexpected arguments. Volume 1 includes a detailed biographical introduction by Clifford's colleague, Frederick Pollock, who situates his close friend's interests in Darwin and Spinoza within a larger, life-long devotion to the principles of scientific enquiry and experiment. This volume also features two important essays, 'On Some of the Conditions of Mental Development', his first public lecture delivered at the Royal Institute in London, and 'The Philosophy of the Pure Sciences'.

A fellow of Trinity College, Cambridge, and of the Royal Society, William Clifford (1845-79) made his reputation in applied mathematics, but his interests ranged far more widely, encompassing ethics, evolution, metaphysics and philosophy of mind. This posthumously collected two-volume work, first published in 1879, bears witness to the dexterity and eclecticism of this Victorian thinker, whose commitment to the most abstract principles of mathematics and the most concrete details of human experience resulted in vivid and often unexpected arguments. Volume 2 shows Clifford's thorough engagement with scientific thought as a method for illuminating ethical and moral questions. Essays such as 'Body and Mind', 'On the Scientific Basis of Morals' and 'The Ethics of Belief' all variously demonstrate Clifford's core tenet: that beliefs - whether they guide human action or scientific enquiry - 'can never suffer from investigation'.