A Treatise of Algebra, in Three Parts: Containing I. The Fundamental Rules and Operations; II. The Composition and Resolution of Equations of All Degrees, and the Different Affections of Their Roots; III. The Application of Algebra and Geometry to Each Other. To which is Added an Appendix Concerning the General Properties of Geometrical LinesA. Millar and J. Nourse, 1756 - 432 páginas |
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Página 21
... four terms you may find what law the terms obferve : by which means , without any more divifion , you may continue the quotient as far as you please . Thus , în dividing 1 by 1 - a , you find the quotient to be 1 + a + aa + aaa + aaaa + ...
... four terms you may find what law the terms obferve : by which means , without any more divifion , you may continue the quotient as far as you please . Thus , în dividing 1 by 1 - a , you find the quotient to be 1 + a + aa + aaa + aaaa + ...
Página 28
... four Rules are easily demon- ftrated from the definition of a fraction . 1. It is obvious that the fractions are refpectively equal to cbf ebd adf cbf bdf " dbf ' fbd ' 1 C fince if you divide adf by bdf , the quotient will be the fame ...
... four Rules are easily demon- ftrated from the definition of a fraction . 1. It is obvious that the fractions are refpectively equal to cbf ebd adf cbf bdf " dbf ' fbd ' 1 C fince if you divide adf by bdf , the quotient will be the fame ...
Página 29
... four Rules are easily demon- ftrated from the definition of a fraction . 1. It is obvious that the fractions , are refpectively equal to adf cbf ebd " bdf " dbf ' fbd ' C fince if you divide adf by bdf , the quotient will be the fame as ...
... four Rules are easily demon- ftrated from the definition of a fraction . 1. It is obvious that the fractions , are refpectively equal to adf cbf ebd " bdf " dbf ' fbd ' C fince if you divide adf by bdf , the quotient will be the fame as ...
Página 34
... four times to itfelf ; therefore the fecond power of any quantity is had by doubling its exponent , and the third by trebling its exponent ; and , in general , the power expreffed by m if any quantity is had by multiplying the exponent ...
... four times to itfelf ; therefore the fecond power of any quantity is had by doubling its exponent , and the third by trebling its exponent ; and , in general , the power expreffed by m if any quantity is had by multiplying the exponent ...
Página 36
... four times to itself ; therefore the fecond power of any quantity is had by doubling its exponent , and the third by trebling its exponent ; and , in general , the power expreffed by m of any quantity is had by multiplying the exponent ...
... four times to itself ; therefore the fecond power of any quantity is had by doubling its exponent , and the third by trebling its exponent ; and , in general , the power expreffed by m of any quantity is had by multiplying the exponent ...
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Pasajes populares
Página 74 - AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C.
Página 55 - A privateer running at the rate of 10 miles an hour discovers a ship 18 miles off making way at the rate of 8 miles an hour : how many miles can the ship run before being overtaken ? Ans.
Página 107 - ... -{-24, equal to nothing, according to the propofed equation. And it is certain that there can be no other values of x...
Página 367 - This is a quarto volume, containing xxxii + 38 pages, and three plates of figures. The title points out that the work consists of two parts ; we are principally concerned with the first part : on...
Página 193 - The demonftration is deduced from the laft article, as the 7 8th is from the preceding. CHAP. IX. Of the Methods by which you may approximate to the roots of numeral Equations by their limits. §84. TT 7 HEN any equation is propofed W to be refolved, firft find the limits of the roots (by Chap. 5.) as for example...
Página 22 - Rule. Multiply the numerator of the dividend by the denominator of the divifor, their produit ¡hall give the numerator of the quotient. 'Then multiply t be denominator of the' dividend by the numerator of the divifor, and their predu£f jhall give the denominator.