Solutions of the Cambridge Problems, from 1800 to 1820, Volum 1


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Side 110 - REBATE, is an allowance made on a bill, or any other debt not yet become due, in consideration of present payment.
Side 220 - The sine of an arc is the perpendicular let fall from one extremity of the arc on the diameter which passes through the other extremity.
Side 78 - ... progression, is equal to the sum of the first and last terms multiplied by half the number of terms; therefore, the sum of the moments about R, is 5,000 X 5!L±.§!
Side 220 - A in formulas (11), (10), and (13), we obtain the following results. sin (A + A) = sin A cos A + cos A sin A cos (A...
Side 149 - For transform the proposed equation into one whose roots are the reciprocals of the roots of the proposed equation...
Side 510 - Laplace transformation method — corresponding to eqn. (2.80) — will result in the quotient of two polynomials in s, the degree of the numerator being less than that of the denominator. If this is not so, the quotient must be divided out leaving a polynomial and a "proper" fraction (ie one of the desired form).
Side 107 - The present worth of any sum, due after a certain time, is a sum such that being put out to interest, it would amount to the given sum in that time. The discount of any sum, due after a certain time, is equal to the difference between that sum and its present worth ; or it is equal to the interest of its present worth for that time. Hence, if (P) be the present worth of a sum (A) due after (n) years, we hare PR...
Side 213 - B, it may be shown that sin (A + B) = sin A . cos В + cos A . sin В ; and cos (A + B) = cos A . cos В — sin A . sin В ; . , cos A , cos В .._, *aeüce, dividing by -A 7? . we obtain * cos A . cos В BID (A 4- B) tan A + tan В tîJ" ' " ¿os (A + ß) = 1 -tan Л tana
Side 19 - Similar figures are to one another in the duplicate ratio of their homologous sides " is true of curvilinear figures as well as of rectilinear.
Side 141 - ... whose roots are those of the given equation with their signs changed.

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