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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... the care that has been taken in collecting and difpofing them , fo as best to answer the Au- thor's intention , and fill up the Plan he had defigned . * Phil . Tranf . No 408 . He feems , in compofing this Treatise , to have A 3 He.
... the care that has been taken in collecting and difpofing them , fo as best to answer the Au- thor's intention , and fill up the Plan he had defigned . * Phil . Tranf . No 408 . He feems , in compofing this Treatise , to have A 3 He.
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... taken from a Letter of the Author ( 8 Jul . 1743 ) to the Right Honourable the Earl STANHOPE ; communicated to the Publisher , with fome things added by his Lordship , which were wanting to finish the Demonftration . Of thefe Materials ...
... taken from a Letter of the Author ( 8 Jul . 1743 ) to the Right Honourable the Earl STANHOPE ; communicated to the Publisher , with fome things added by his Lordship , which were wanting to finish the Demonftration . Of thefe Materials ...
Página 5
... taken from a leffer of the fame kind , the remainder becomes of the oppofite kind . Thus if we add the lines AB and BD to- gether , their fum is AD ; A C B D but if we are - + . A B to fubtract B C D from AB , then BC BD is to be taken ...
... taken from a leffer of the fame kind , the remainder becomes of the oppofite kind . Thus if we add the lines AB and BD to- gether , their fum is AD ; A C B D but if we are - + . A B to fubtract B C D from AB , then BC BD is to be taken ...
Página 7
... taken twice ; 3a that it is to be taken thrice ; and fo on . When no number is prefixed , unit is understood to be the coefficient . Thus I is the coefficient of a or of b . Quantities are faid to be like or fimilar , that are ...
... taken twice ; 3a that it is to be taken thrice ; and fo on . When no number is prefixed , unit is understood to be the coefficient . Thus I is the coefficient of a or of b . Quantities are faid to be like or fimilar , that are ...
Página 12
... taken as many times as there are units in ; and the product is evi- dently na . Cafe II . When -a is multiplied by n , then → a is to be taken as often as there are units in # , and the product must be na . Cafe III . Multiplication by ...
... taken as many times as there are units in ; and the product is evi- dently na . Cafe II . When -a is multiplied by n , then → a is to be taken as often as there are units in # , and the product must be na . Cafe III . Multiplication by ...
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Términos y frases comunes
adeoque affumed alfo arife arithmetical progreffion autem becauſe biquadratic cafe cafu coefficient common meaſure confequently contactus cube cube root cubic equation curvæ curvam curvaturæ curve demonftrated dimenfions diſcover divided divifor ducantur ducta enim equa equal erit ex puncto exponent expreffed expreffions fame manner fecond term feries fhall fide figns fimple equations fince firft firſt firſt term flexus fome fquare root fraction fubftitute fubtract fuch fuppofe furd give greateſt higheſt impoffible integer interfections itſelf laft term laſt leaft lefs lineæ locus metical muft multiplied muſt negative occurrat odd number parabola parallela pofed pofitive poſitive propofed equation puncto punctum quadratic equation quæ quævis quotient recta rectæ refolved refpectively refult repreſent Rule ſhall ſubſtituted ſuppoſe tangentes tertii ordinis thefe theſe thofe thoſe tion unknown quantity vaniſh whence whofe roots whoſe
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.