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. 1867 Excerpt: ...are among them n--1 Equations, which have their F-Block not evanescent; and, when such a set of n--1 Equations is selected and taken along with each of the remaining Equations successively, each set of n Equations, so formed, has its i?-Block evanescent; the n+r Equations are consistent; (ch. III. Prop. VIII. Cor. ...
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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. 1867 Excerpt: ...are among them n--1 Equations, which have their F-Block not evanescent; and, when such a set of n--1 Equations is selected and taken along with each of the remaining Equations successively, each set of n Equations, so formed, has its i?-Block evanescent; the n+r Equations are consistent; (ch. III. Prop. VIII. Cor. their i?-Block is evanescent. (chap. III. Prop. XIII. Cor. Therefore, if there be, &c. Q. E. D. Proposition III. Th. If there be a Block, having one of its Minors of the kth degree, where k is less than the degree of a secondary Minor, not evanescent; and if, of the oblong Blocks formed from it by selecting k-t-1 of its longitudinals, each one, which contains that non-evanescent Minor, be evanescent: every other oblong Block, so formed, is evanescent. And the same is true of its laterals. Call the two dimensions of the Block 'm' and '-'. Let the Block be placed in either position, and let the k rows, and also the k columns, which contain the non-evanescent Minor, be placed first; and let each of the columns, except the last, be multiplied throughout by the symbol of a Variable; and let each row be equated to zero; and let the Equations, so formed, be represented by Prop. II. Thus, if, in the oblong Block J. e f g h V, it be given that (Uo.md that _j k I m J' a b d 'bed efh =0, and I / g h j km k I m--0: the whole Block is evanescent. then the first + 1 Equations contain m--1 Variables, and there are among them k Equations whose F-Block is not evanescent; and the iS-Block of these k +1 Equations is evanescent; First, let m--1 = k+; then the Equations are consistent; and the Variable xm_1 may have an arbitrary value assigned to it; and the /fc+ll01 Equation is dependent on the first k Equations; (ch. III. Prop. IX. also, ...
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