A Treatise on Algebra Volume 1; Arithmetical Algebra (Paperback)

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. 1842 Excerpt: ...it for granted that each individual labours with the same effect. It is in virtue of such hypotheses, that we conclude, as if with mathematical certainty, that twice or any multiple of the work will be done by twice or the same multiple of the number of men, and consequently, that the quantities of work done in any two cases and the corresponding numbers of men, will constitute the terms of a proportion. 325. The relation of cause and effect, expressed by saying The effect that one is proportional to the other, is more frequently de-the cause, signated by an equivalent phrase, which is, that the effect varies as the cause, or conversely: in both cases, an equally enlarged signification is given to the terms cause and effect, and the connection between them is rendered necessary, either by definition or by hypothesis, or by inferences drawn from observation of the general laws of the physical world. 326. When the causes or agents which produce an effect are Or as the more than one, the effect is said to vary conjointly with the agents concauses which produce it. It remains to consider the law of the jointly, dependence of the effect and agents in such cases, particularly with reference to the proportion which they form. 327. Thus we should say, that the work done would vary Example of conjointly as the number of men employed and the number of van" days they worked: for if the number of days during which the men worked remained the same, m times the same work would be done by m times the same number of men: and if the number of men remained the same, n times the same work would be done in n times the same number of days: it would follow, therefore, that mn times the original work would be done by m times the original number of men, working for n times th...