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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... Signs and Coefficients of equa- tions III . Of the Transformation of equations , and exterminating their intermediate terms IV . Of finding the Roots of equations when two or more of the roots are equal to 139 . 148 each other 162 V. Of ...
... Signs and Coefficients of equa- tions III . Of the Transformation of equations , and exterminating their intermediate terms IV . Of finding the Roots of equations when two or more of the roots are equal to 139 . 148 each other 162 V. Of ...
Página 12
... Signs of the factors are unlike , the fign of the product is- . Cafe I. When any pofitive quantity , + a , is multiplied by any pofitive number , + n , the meaning is , That + a is to be taken as many times as there are units in ; and ...
... Signs of the factors are unlike , the fign of the product is- . Cafe I. When any pofitive quantity , + a , is multiplied by any pofitive number , + n , the meaning is , That + a is to be taken as many times as there are units in ; and ...
Página 37
... Signs , When the quantity to be in- volved is pofitive , it is obvious that all its powers must be pofitive . And when the quantity to be involved is negative , yet all its powers whofe ex- ponents are even numbers must be pofitive ...
... Signs , When the quantity to be in- volved is pofitive , it is obvious that all its powers must be pofitive . And when the quantity to be involved is negative , yet all its powers whofe ex- ponents are even numbers must be pofitive ...
Página 62
... sign on the other fide , is to fubtract it from both fides ; and it is certain , that " when from equal quantities you fubtract the fame quantity , the remainders muft be equal . " By this Rule , when the known and unknown quantities ...
... sign on the other fide , is to fubtract it from both fides ; and it is certain , that " when from equal quantities you fubtract the fame quantity , the remainders muft be equal . " By this Rule , when the known and unknown quantities ...
Página 138
... to know when the roots of equations are pofitive and when negative , and how many there . are of each kind , fhall be explained in the next chapter . CHAP . СНАР . II . OF THE SIGNS AND COEFFICIENTS OF 138 A TREATISE of PART II .
... to know when the roots of equations are pofitive and when negative , and how many there . are of each kind , fhall be explained in the next chapter . CHAP . СНАР . II . OF THE SIGNS AND COEFFICIENTS OF 138 A TREATISE of PART II .
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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.