A Treatise of Algebra: Wherein the Principles are Demonstrated ... To which is Added, the Geometrical Construction of a Great Number of Linear and Plane Problems ...M. Carey & sons, 1821 - 408 Seiten |
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Seite
... of converging series extended to surd Equations 174 14. A method of solving high Equations , when two , or more unknown quantities are concerned in each 177 SECTION XIII . OF INDETERMINATE PROBLEMS SECTION XIV . · Contents .
... of converging series extended to surd Equations 174 14. A method of solving high Equations , when two , or more unknown quantities are concerned in each 177 SECTION XIII . OF INDETERMINATE PROBLEMS SECTION XIV . · Contents .
Seite 4
... thus ex- pressed are called radical quantities , or surds ; where- of those , consisting of one term only , as 4 of Notation . A demonstration of Sir Isaac Newton's Binomial The manner of taking away radical quantities from.
... thus ex- pressed are called radical quantities , or surds ; where- of those , consisting of one term only , as 4 of Notation . A demonstration of Sir Isaac Newton's Binomial The manner of taking away radical quantities from.
Seite 5
... surds ; and those consisting of several terms , or members , as ✓a2 - b2 and a2 - b2 + bc , com- pound surds . * the Besides this way of expressing radical quantities , ( which is chiefly followed ) there are other methods made use of ...
... surds ; and those consisting of several terms , or members , as ✓a2 - b2 and a2 - b2 + bc , com- pound surds . * the Besides this way of expressing radical quantities , ( which is chiefly followed ) there are other methods made use of ...
Seite 17
... demonstration of Rule 2 ° . For , it be- ing there proved that Α x C is equal to AC B it is ob- vious that A C X B D can be only the D part of AC i be- B D 4 ° Surd quantities under the same radical sign are of Multiplication . 17.
... demonstration of Rule 2 ° . For , it be- ing there proved that Α x C is equal to AC B it is ob- vious that A C X B D can be only the D part of AC i be- B D 4 ° Surd quantities under the same radical sign are of Multiplication . 17.
Seite 18
... Surd quantities under the same radical sign are mul- tiplied like rational quantities , only the product must stand under the same radical sign . 7bc x 5ad = Thus , 7 × √ 5 = √55 ; √ a × √b = √ab ; 35abcd ; 3ab × 5√ c = 15√abc ...
... Surd quantities under the same radical sign are mul- tiplied like rational quantities , only the product must stand under the same radical sign . 7bc x 5ad = Thus , 7 × √ 5 = √55 ; √ a × √b = √ab ; 35abcd ; 3ab × 5√ c = 15√abc ...
Häufige Begriffe und Wortgruppen
added algebraic arch arithmetical progression ax² become biquadratic circle co-sine coefficient common difference completing the square consequently CONSTRUCTION cube cube root cubic equation DEMONSTRATION denominator dividend divisor draw equa equal example expressed extracting find the numbers former fraction geometrical progression given angle given equation gives greater Hence latter likewise manner Method of Calculation moidores multiplied negative number of terms number sought perpendicular PROBLEM proportion proposed Q. E. D. Method quadratic equation quan question quotient radical quantities radius ratio rectangle reduced remains required numbers right-line rule second term sides sine square root subtracted supposed surd thence theorem third three numbers tion tity trapezium triangle unknown quantity value being substituted vulgar fraction whence wherein whereof whole number
Beliebte Passagen
Seite 241 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.
Seite 53 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Seite 64 - ... then, by adding, or subtracting, the two equations thus obtained, as the case may require, there will arise a new equation, with only one unknown quantity in it, which may be resolved as before.
Seite 251 - ... the sum of the segments of the base is to the sum of the sides as the difference of the sides to the difference of the segments of the base.
Seite 87 - A composition of copper and tin containing 100 cubic inches weighed 505 ounces. How many ounces of each metal did it contain, supposing a cubic inch of copper to weigh of ounces, and a cubic inch of tin to weigh 4т ounces ? Ans. 420 of copper, and
Seite 88 - ... half of what he had left, and half a sheep over ; and, soon after this, a third party met him, and used him in the same manner, and then he had only five sheep left. It is required to find what number of sheep he had at first, Ans, 47 sheep.
Seite 254 - The following particular directions, however, may be of some use. 1st, In preparing the figure, by drawing lines, let them be either parallel or perpendicular to other lines in the figure, or so as to form similar triangles. And if an angle be given, it will be proper to let the perpendicular be opposite to that angle, and to fall from one end of a given line, if possible.