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
... difference . And when a greater quantity is 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. b but if we are + + to fubtract C ...
... difference . And when a greater quantity is 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. b but if we are + + to fubtract C ...
Página 6
... difference . This change of quality however only takes place . where the quantity is of fuch a nature as to ad- mit of fuch a contrariety or oppofition . We know nothing analogous to it in quantity abstractly confidered ; and cannot ...
... difference . This change of quality however only takes place . where the quantity is of fuch a nature as to ad- mit of fuch a contrariety or oppofition . We know nothing analogous to it in quantity abstractly confidered ; and cannot ...
Página 26
... . Rule . Reduce them to a common denominator , and add or fubtract the numerators , the fum or difference fet over the common denominator , is the fum or remainder required . Thus a C d Thus + + b d = ade 26 PART 1 . A TREATISE of.
... . Rule . Reduce them to a common denominator , and add or fubtract the numerators , the fum or difference fet over the common denominator , is the fum or remainder required . Thus a C d Thus + + b d = ade 26 PART 1 . A TREATISE of.
Página 34
... difference the exponent of the quotient . " a6 as Thus = a6-4 = 42 ; and 23 63 a⭑ as = 463 3 = ab2 a + b §37 . If you divide a leffer power by a greater , the exponent of the quotient must , by this Rule , be negative . Thus = a + ...
... difference the exponent of the quotient . " a6 as Thus = a6-4 = 42 ; and 23 63 a⭑ as = 463 3 = ab2 a + b §37 . If you divide a leffer power by a greater , the exponent of the quotient must , by this Rule , be negative . Thus = a + ...
Página 39
... difference ( viz . unit ) and that in the laft term it is never found . The powers of b are in the contrary order ; it is not found in the first term , but its exponent in the fecond term is unit , in the third term its ex- ponent is 2 ...
... difference ( viz . unit ) and that in the laft term it is never found . The powers of b are in the contrary order ; it is not found in the first term , but its exponent in the fecond term is unit , in the third term its ex- ponent is 2 ...
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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.