An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to Simplify ... that Science ... With Notes and Illustrations ... To which is Added an Appendix, on the Application of Algebra to GeometryHilliard, Gray, & Company, 1840 - 605 sider |
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Side
... Hence A - 1 , Put L for the logarithm , and L ' for the arith . comp . of a log . Since ( 1 + 7 ) " = TM , therefore n = P L.m + L'.p M - P = L. ( r + 1 ) L ( 1 + r ) * Case 18. Given a , p , and r , to find the value of n . Since ( 1 + ...
... Hence A - 1 , Put L for the logarithm , and L ' for the arith . comp . of a log . Since ( 1 + 7 ) " = TM , therefore n = P L.m + L'.p M - P = L. ( r + 1 ) L ( 1 + r ) * Case 18. Given a , p , and r , to find the value of n . Since ( 1 + ...
Side 41
... Hence za is the simple divisor . ? —a2 ) 1 a * —b1 ) a®_b® ( a2 aR — a2b1 + a2b - b This , divided by b , gives ab2 ) a * —b1 ( a2 a1 — a22 This , again divided , abb by b2 , gives a2b2 ) a2 — b2 ( 1 a2 ba Therefore a2 - b2 is the ...
... Hence za is the simple divisor . ? —a2 ) 1 a * —b1 ) a®_b® ( a2 aR — a2b1 + a2b - b This , divided by b , gives ab2 ) a * —b1 ( a2 a1 — a22 This , again divided , abb by b2 , gives a2b2 ) a2 — b2 ( 1 a2 ba Therefore a2 - b2 is the ...
Side 43
... Hence the fractions re- quired are 9cx 4ab 6acd ' 9 and bac bac 6ac 1X3cX2a6ac , com . denom . Here the three fractions when reduced are 3 2x 4x 5a + 4x 4 ' 3 and a + = 5 5 3 × 3 × 5 = 45 2xX4X5-40x ( 5a + 4x ) × 4 × 3—60a ++ 48x 4X3X5 ...
... Hence the fractions re- quired are 9cx 4ab 6acd ' 9 and bac bac 6ac 1X3cX2a6ac , com . denom . Here the three fractions when reduced are 3 2x 4x 5a + 4x 4 ' 3 and a + = 5 5 3 × 3 × 5 = 45 2xX4X5-40x ( 5a + 4x ) × 4 × 3—60a ++ 48x 4X3X5 ...
Side 61
... Hence , if the signs of all the terms on each side of an equation be changed , the two sides still remain equal ; because in this change every term is transposed . Cor . 2. Hence , when the known and unknown quantities are connected in ...
... Hence , if the signs of all the terms on each side of an equation be changed , the two sides still remain equal ; because in this change every term is transposed . Cor . 2. Hence , when the known and unknown quantities are connected in ...
Side 62
... Hence also any term of an equation may be made a square , by multiplying all the terms of the equation by the quan- tities necessary ; as , if ax2 + bcxcd , the first term may be made a square by multiplying each term by a , and a2x2 + ...
... Hence also any term of an equation may be made a square , by multiplying all the terms of the equation by the quan- tities necessary ; as , if ax2 + bcxcd , the first term may be made a square by multiplying each term by a , and a2x2 + ...
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An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ... John D Williams Ingen forhåndsvisning tilgjengelig - 2015 |
Vanlige uttrykk og setninger
Algebra amount angle annuity answer arithmetical progression arithmetical series Assume bushels cent coefficients compound interest consequently continued fraction converging fractions cube cubic equation denominator denote the numbers difference divided divisor dollars expression factors Find the sum find the value formula four roots geometrical progression gives greater Hence infinite infinite series infinitum integral least value less logarithms miles multiplied number of days number of solutions number of terms proposed equation quadratic equation question quotient ratio reduced remainder Required the number Required the sum required to find rule scale of relation shillings side square numbers square root substituted subtracted Suppose surd taken at pleasure third three numbers tion transposition triangle unknown quantity value of x whence whole numbers yards
Populære avsnitt
Side 126 - In one of the given equations obtain the value of one of the unknown quantities in terms of the other unknown quantity; Substitute this value in the other equation and solve.
Side 544 - Two travellers, A and B, set out to meet each other, A leaving the town C at the same time that B left D.
Side 94 - A person has two horses, and a saddle worth £50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.
Side 258 - Then, as the difference of these results is to the difference of the two assumed numbers, so is the difference between the true result, and either of the former, to the correction of the number belonging to the result used ; which correction being added to that number when it is too little, or subtracted from it when it is too great, will give the root required, nearly.
Side 492 - There is a rectangular field, whose length is to its breadth in the proportion of 6 to 5. A part of this, equal to -£ of the whole, being planted, there remain for ploughing 625 square yards. What are the dimensions of the field ? 1 3.
Side 97 - If A and B together can perform a piece of work in 8 days, A and C together in 9 days, and B and C in 10 days : how many days would it take each person to perform the same work alone ? Ans.
Side 435 - At the 50th mile stone from London, A overtook a drove of geese which were proceeding at the rate of three miles in two hours ; and two hours afterwards met a stage waggon, which was moving at the rate of 9 miles in 4 hours.
Side 439 - There are four numbers in geometrical progression, the second of which is less than the fourth by 24 ; and the sum of the extremes is to the sum of the means, as 7 to 3. What are the numbers ? Ans.
Side 497 - Is. ; for each of which I paid as many shillings per yard as there were yards in its side. Now had each of them cost as many shillings per yard as there were yards in a side of the other, I should have paid 17s.
Side 96 - Divide the number 90 into 4 such parts, that the . first increased by 2, the second diminished by 2, the third multiplied by 2, and the fourth divided by 2, shall all be equal.