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 LinesF. Wingrave; T. Longman; W. Richardson; G. G. and J. Robinson; F. and C. Rivington; W. Lowndes; and Cadell and Davies., 1796 - 504 páginas |
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Página 5
... tion above the horizon , and depreffion below it . When two quantities equal in refpect of magnitude , but of thofe oppofite kinds , are I joined together , and conceived to take place in I the fame fubject , they deftroy each other's ...
... tion above the horizon , and depreffion below it . When two quantities equal in refpect of magnitude , but of thofe oppofite kinds , are I joined together , and conceived to take place in I the fame fubject , they deftroy each other's ...
Página 6
... tion , when they are equal as to quantity . Thus 330 , and a- -α = 0. But though + a anda are equal as to quantity , we do not fuppofe in Algebra that + a = —a ; because to infer equality in this fcience , they must not only be equal as ...
... tion , when they are equal as to quantity . Thus 330 , and a- -α = 0. But though + a anda are equal as to quantity , we do not fuppofe in Algebra that + a = —a ; because to infer equality in this fcience , they must not only be equal as ...
Página 27
... tion , you may reduce it to the form of a frac- tion by placing unit under it . EXAMPLES . 3 537 X = 4 17 3 3 51 X 4 12 39 X alm 3 x 3 18 bx = = 6 ; b + 3 a CHAP . 6 . 27 ALGEBRA .
... tion , you may reduce it to the form of a frac- tion by placing unit under it . EXAMPLES . 3 537 X = 4 17 3 3 51 X 4 12 39 X alm 3 x 3 18 bx = = 6 ; b + 3 a CHAP . 6 . 27 ALGEBRA .
Página 28
... ; and ebd divided by fb d the fame quotient as e divided by f . 2. Fractions reduced to the fame denomina- tion are added by adding their numerators and a a + fubfcribing the common denominator . a I 1 fub- 28 A TREATISE of PART I.
... ; and ebd divided by fb d the fame quotient as e divided by f . 2. Fractions reduced to the fame denomina- tion are added by adding their numerators and a a + fubfcribing the common denominator . a I 1 fub- 28 A TREATISE of PART I.
Página 32
... tion to a fraction equal to it that shall have a given denominator , you must multiply the nu- merator by the given denominator , and divide the product by the former denominator , the quotient fet over the given denominator is the ...
... tion to a fraction equal to it that shall have a given denominator , you must multiply the nu- merator by the given denominator , and divide the product by the former denominator , the quotient fet over the given denominator is the ...
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adeoque affumed afymptote alfo alſo arife arithmetical progreffion autem becauſe biquadratic cafe cafu coefficient common meaſure confequently conic fection contactus Corol cube cubic equation curvæ curvam curvature demonftrated dimenfions divided divifor drawn ducantur ducta enim equa equal erit expreffed fame manner fame right line fecond term feries fhall fide figns fimple equations fince firft firſt flexus fome fquare root fubftitute fubtract fuch fuppofe furd greateſt harmonical mean impoffible interfections laft term laſt leaft lefs lineæ locus meet the curve metical multiplied muſt negative occurrat parallel pofitive PROP propofed equation puncto punctum px² quadratic equation quæ quævis quotient recta rectæ refolved refult Rule ſhall ſuppoſe tangents tertii ordinis thefe theſe third order thofe tion touching the curve unknown quantity vaniſh whence whoſe
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Página 88 - 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 431 - APM, cut a geometrical line of any order in as many points as it has dimensions, the product of the segments of the first terminated by P and the curve, will always be to the product of the segments of the latter, terminated by the same point and the curve, in an invariable ratio.
Página 426 - And by iimilar equations geometrical lines of fuperior orders are defined. § 2. A geometrical line may meet a right line in as many points as there are units in the number which denotes the order of the equation or line, and never in more. The number of times that any curve will meet its...
Página 43 - The general Theorem vhich we gave for the Involution of binomials will' ferve alfo for their Evolution ;" becaufe to extract any root of a given quantity is the fame thing as to raife that quantity to a power whofe exponent is a fraction that has...
Página 61 - 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.