A   Treatise of Algebra, in Three Parts; Containing I. the Fundamental Rules and Operations. II. the Composition and Resolution of Equations of All De by Colin MaclaurinA   Treatise of Algebra, in Three Parts; Containing I. the Fundamental Rules and Operations. II. the Composition and Resolution of Equations of All De by Colin Maclaurin

A Treatise of Algebra, in Three Parts; Containing I. the Fundamental Rules and Operations. II…

byColin Maclaurin

Paperback | May 5, 2014

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This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1748 edition. Excerpt: ...and Differences. Let r be that Term in any Progreffion that arifes from the Subfiitution cfx=o, and let =pn be the Difference ariftng from fubiratiing that Term from the preceding Ti rm in the Progreffion; lo-flly-, let m be the fore faid Divifor of the highejl Term; thenJhall mxIrtrnx--r be the Divifor that.ought to be tried.1" And one or other of the Divifors found in this Manner will fuc, ceed, if the propofed Equation has a Quadratic Divifor. §69. Suppofe, for Example, the Biquadradratic x--5,J+7,a--5X--6=0, is propofed, which has no fimple Divifor; then to difcover if it has any Quadratic Divifor, the Operation is thus, The firft Arithmetical Progreffion gives the Divifor x--3---2; the fecond gives1--2+3: both which fucceed, fo that the Roots of the twoEquations1--3--2=o,and#--2#--3=o, viz. 3 '7 and idbV--2, are the four Roots 2 of the propofed Equation, the two laft of which are impoffible. The Divifors which the other Arithmetical Progrefiions give, do not fucceed. § 70. After the fame Manner a Rule may be difcovered for finding the Cubic Divifors, or thofe of higher Dimenfions, of any propofed Equation. Suppofe the Cubic Divifor to be tnxs--x-rx+--sy and by fuppofing x equal to the Terms of the Arithmetical Progreffion, it will be as follows; Where the ift Differences are not themfelves in Arithmetical Progreffion, as in the laft Cafe, but the Differences of its Terms, or the fecond Differences, are in Arithmetical Progreffion, the common Difference being 2, whence is known. known. The Quantity r is found in the Column of the 2d Diff. and s is always to be afTumed fome Divifor of the laft Term of the propofed Equation, as m is of the Coefficient of the firft Term. Whence all the Coefficients of a...
Title:A Treatise of Algebra, in Three Parts; Containing I. the Fundamental Rules and Operations. II…Format:PaperbackDimensions:60 pages, 9.69 × 7.44 × 0.12 inPublished:May 5, 2014Publisher:General Books LLCLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:1236319435

ISBN - 13:9781236319432

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