The Mathematician Volume 1 (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. 1856 edition. Excerpt: ...(1) This equation has, therefore, two roots nearly equal to each other, one being 1-236068, and the other 1-2367606, agreeing us far as the third place of decimals inclusive; and by increasing or diminishing the roots, we may form equations at pleasure, and select for practice those which have the smallest co-efficients. By multiplying (1) by a, where a may be any integer number whatever, we should obtain an equation of the fifth degree having two roots nearly equal, and by taking another integer number whose square root coincides to the same extent in the decimal part with the former two, we may form an equation of the sixth degree having three roots nearly equal to each other and so on to any extent. The three following equations were formed by Mr. Lockhart, and proposed to British students for resolution in 1811: xs--824+24043--263942 + 6132--360 = 0 5+1734+2356' + 104682--14101 +4183 = 0 6+ 3785+38189+ 4923683--572554+213720--26352 =0. Several of the roots of each of these equations coincide to six decimal places. ON THE THEORY OF CO-ORDINATES. Mr. Thomas Dobson, Totteridge, Herts. By the aid of co-ordinates and certain conventional meanings attached to algebraical symbols, the Cartesian Geometry enables us to draw, as it were, a geometrical picture of the several states of an algebraical function corresponding to the successive changes of value of the variables of which it is composed; and, conversely, by the same fertile method may be exhibited a faithful analytical representation of a given geometrical figure. Among the numerous systems of co-ordinates which may be employed in the performance of these operations, it is important to distinguish, on the one hand, those which offer the greatest facilities for depicting equations...