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 12
... multiplied by any pofitive number , + n , the meaning is , That + a is to be taken as many times as there are units in ; and the product is evidently na . Cafe II . When a is multiplied by n , then —ɑ -a is to be taken as often as there ...
... multiplied by any pofitive number , + n , the meaning is , That + a is to be taken as many times as there are units in ; and the product is evidently na . Cafe II . When a is multiplied by n , then —ɑ -a is to be taken as often as there ...
Página 12
... multiplied by + n gives . - na . - - na , In like manner , if we multiply + aa by ―n , the first term of the product being the latter term of the product must be + na , because the two together muft destroy each other , or their amount ...
... multiplied by + n gives . - na . - - na , In like manner , if we multiply + aa by ―n , the first term of the product being the latter term of the product must be + na , because the two together muft destroy each other , or their amount ...
Página 12
... multiplied by adding their exponents . Thus a2 × a3 = a3 , aa × a3 = a1 , a3 × @ = a + . § 16. Sometimes it is ufeful not actually to multiply compound quantities , but to fet them down with the fign of multiplication ( x ) be tween ...
... multiplied by adding their exponents . Thus a2 × a3 = a3 , aa × a3 = a1 , a3 × @ = a + . § 16. Sometimes it is ufeful not actually to multiply compound quantities , but to fet them down with the fign of multiplication ( x ) be tween ...
Página 12
... multiplied by adding them . Thus if you divide a ' by a2 , the quotient is as - 2 or a3 . And divided by b + gives bor b ' ; and a'b ' divided by abs gives a'b ' for the quotient . $ 20 . If the quantity to be divided is com- pound ...
... multiplied by adding them . Thus if you divide a ' by a2 , the quotient is as - 2 or a3 . And divided by b + gives bor b ' ; and a'b ' divided by abs gives a'b ' for the quotient . $ 20 . If the quantity to be divided is com- pound ...
Página 12
... multiply the whole divifor by this part of the quotient , and fubtract the product from the new dividend ; and if there is no remainder , the divifion is finished : If there is a remainder , you are to proceed after the fame manner till ...
... multiply the whole divifor by this part of the quotient , and fubtract the product from the new dividend ; and if there is no remainder , the divifion is finished : If there is a remainder , you are to proceed after the fame manner till ...
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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.