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 99
... least numbers in any proportion . always measure any other numbers that are in the fame proportion . Suppofe a and b to be the least of all integer numbers in the fame proportion , and that c and d are other numbers in that proportion ...
... least numbers in any proportion . always measure any other numbers that are in the fame proportion . Suppofe a and b to be the least of all integer numbers in the fame proportion , and that c and d are other numbers in that proportion ...
Página 101
... least numbers in the fame proportion with a and b . For if there could be any other numbers in that proportion lefs than c and d , fuppofe them to be e and ƒ , and these , being in the fame pro- portion as a and b , would measure them ...
... least numbers in the fame proportion with a and b . For if there could be any other numbers in that proportion lefs than c and d , fuppofe them to be e and ƒ , and these , being in the fame pro- portion as a and b , would measure them ...
Página 102
... least number which they can both measure . For if they could measure a lefs number than ab , as c , suppose that nb ; and fince c is less is equal to ma , and to than ab , therefore ma will be less than ab , and m less than b ; and nb ...
... least number which they can both measure . For if they could measure a lefs number than ab , as c , suppose that nb ; and fince c is less is equal to ma , and to than ab , therefore ma will be less than ab , and m less than b ; and nb ...
Página 103
... least quantity na , which is measured by a and b , will also mea- fure c . For if you fuppofe as before that c = la , you will find that n muft meafure 1 , and na must measure la or c . m n § 107. Let a exprefs any integer number , and ...
... least quantity na , which is measured by a and b , will also mea- fure c . For if you fuppofe as before that c = la , you will find that n muft meafure 1 , and na must measure la or c . m n § 107. Let a exprefs any integer number , and ...
Página 118
... least number n whose power n is divifible by AABB , the quotient being & Compute A + B X √e in the nearest integer number , which suppose to be r . Divide A✓by its greatest rational divisor , C r + and let the quotient be s , and let ...
... least number n whose power n is divifible by AABB , the quotient being & Compute A + B X √e in the nearest integer number , which suppose to be r . Divide A✓by its greatest rational divisor , C r + and let the quotient be s , and let ...
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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
Pasajes populares
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.