The book The Common Sense of the Exact Sciences was written by author Clifford, William Kingdon, 1845-1879 Here you can read free online of The Common Sense of the Exact Sciences book, rate and share your impressions in comments. If you don't know what to write, just answer the question: Why is The Common Sense of the Exact Sciences a good or bad book?
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Similarly b' a" equals h a' times the area A b ; but the area A B itself is a^. Thus we see that the identity P . o'^Q = a' b" — b' a" 204 THE COMMON SENSE OP THE EXACT SCIENCES, may be read {aa + 6y3) (a'o + h' ^) = {aV - I a') a^. Or, the determinant is equal to tlie parallelogram on the alternate units magnified in the ratio of 1 to ab' — h a'. It obviously vanishes it ah' —ha' = 0, or if ajb = a'jV. Iq this case p and q lie, by the property of similar triangles, on the same straight line th...rough o, and therefore, as we should expect, the determinant p . o Q is zero. The reader will find little diflBculty in discovering like properties for a determinant formed from three alternate units. In this case there will be a geometrical relation between certain volumes, which may be ob- tained by stretches in the manner explained on p. 139.' We have in this section arrived at a legitimate interpretation of the product of two directed steps or vectors. We find that their product is an area^ or ac- cording to our previous convention (see p.
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