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 σελίδες |
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Σελίδα
... theorem 213 215 219 225 227 SECTION XVI . OF INTEREST AND ANNUITIES 1. Annuities and Pensions in Arrear , computed at sim- ple interest · · 2. The investigation of Theorems for the solution of the various cases in compound interest and ...
... theorem 213 215 219 225 227 SECTION XVI . OF INTEREST AND ANNUITIES 1. Annuities and Pensions in Arrear , computed at sim- ple interest · · 2. The investigation of Theorems for the solution of the various cases in compound interest and ...
Σελίδα 41
... theorem , given by Sir Isaac Newton , ( demonstrated hereafter ) whereby any power of a binomial a + b , or a — b , may be expressed in simple terms , without the trouble of those tedious multiplications required in the preceding ...
... theorem , given by Sir Isaac Newton , ( demonstrated hereafter ) whereby any power of a binomial a + b , or a — b , may be expressed in simple terms , without the trouble of those tedious multiplications required in the preceding ...
Σελίδα 70
... THEOREM I. Of any four quantities , a , b , c , d , in arithmetical progres- sion , the sum of the two means is equal to the sum of the two extremes . = For since , by supposition , ba is dc , therefore is b + c = d + a , by ...
... THEOREM I. Of any four quantities , a , b , c , d , in arithmetical progres- sion , the sum of the two means is equal to the sum of the two extremes . = For since , by supposition , ba is dc , therefore is b + c = d + a , by ...
Σελίδα 71
... THEOREM III . In any continued arithmetical progression , a , a + d , a + 2d , a + 3d , a + 4d , & c . the last , or greatest term , is equal to the first ( or least , ) more the common difference of the terms drawn into the number of ...
... THEOREM III . In any continued arithmetical progression , a , a + d , a + 2d , a + 3d , a + 4d , & c . the last , or greatest term , is equal to the first ( or least , ) more the common difference of the terms drawn into the number of ...
Σελίδα 72
... THEOREM I. If four quantities , a , b , c , d , ( 2 , 6 , 5 , 15 ) are in geome- trical proportion , the product of the two means bc , will be equal to that of the two extremes , ad . For , since by the ratio of a to b ( or the part ...
... THEOREM I. If four quantities , a , b , c , d , ( 2 , 6 , 5 , 15 ) are in geome- trical proportion , the product of the two means bc , will be equal to that of the two extremes , ad . For , since by the ratio of a to b ( or the part ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 53 - Multiply the numerators together for a new numerator, and the denominators together for a new denominator.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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
Σελίδα 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.
Σελίδα 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.