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 2
... greatest excellence ; the import of thofe fymbols is to be clearly ftated , that no obfcurity or error may arife from the frequent ufe and complication of them . $ 2 . In GEOMETRY , lines are reprefented by a line , triangles by a ...
... greatest excellence ; the import of thofe fymbols is to be clearly ftated , that no obfcurity or error may arife from the frequent ufe and complication of them . $ 2 . In GEOMETRY , lines are reprefented by a line , triangles by a ...
Página 29
... greatest common Measure of two numbers ; that is , the greatest number that can divide them both without a remainder . Rule . Firft divide the greater number by the leffer , and if there is no remainder the leffer number is the greatest ...
... greatest common Measure of two numbers ; that is , the greatest number that can divide them both without a remainder . Rule . Firft divide the greater number by the leffer , and if there is no remainder the leffer number is the greatest ...
Página 30
... greatest common Measure required . Thus the greatest common measure of 45 and 63 is 9 ; and the greateft common measure of 256 and 48 is 16 . 45 ) 63 ( 1 45 18 ) 45 ( 2 36 9 ) 18 ( 2 28 48 ) 256 ( 5 240 16 ) 48 ( 3 48 $ 32 . Much after ...
... greatest common Measure required . Thus the greatest common measure of 45 and 63 is 9 ; and the greateft common measure of 256 and 48 is 16 . 45 ) 63 ( 1 45 18 ) 45 ( 2 36 9 ) 18 ( 2 28 48 ) 256 ( 5 240 16 ) 48 ( 3 48 $ 32 . Much after ...
Página 31
... greatest common measure required . The ground of this operation is , That any quantity that measures the divifor and the re- mainder ( if there is any ) must also measure the dividend ; because the dividend is equal to the fum of the ...
... greatest common measure required . The ground of this operation is , That any quantity that measures the divifor and the re- mainder ( if there is any ) must also measure the dividend ; because the dividend is equal to the fum of the ...
Página 32
... greatest common measure of the numbers and quantities , then the fraction is already in its lowest terms . Thus 3ab be reduced lower . 5dc cannot And numbers whofe greateft common mea- fure is unit , are faid to be prime to one another ...
... greatest common measure of the numbers and quantities , then the fraction is already in its lowest terms . Thus 3ab be reduced lower . 5dc cannot And numbers whofe greateft common mea- fure is unit , are faid to be prime to one another ...
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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.