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 σελίδες |
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Σελίδα 33
... measure of two or more quantities is any quan- tity which measures them all ; and the greatest common measure is the greatest quantity which will so measure them . Thus , 2a is a common measure of the quantities 24ab2 , 16a2bc , and ...
... measure of two or more quantities is any quan- tity which measures them all ; and the greatest common measure is the greatest quantity which will so measure them . Thus , 2a is a common measure of the quantities 24ab2 , 16a2bc , and ...
Σελίδα 34
... measure of a and b . For let x be any common measure of a and b , such that a = mx , and b ― nx , then = a — pb — mx — pnx— ( m — pn ) x d — b — qc = nx— ( qm — pqn ) x— ( n — qm + pqn ) x ; .. x measures d by the units in n ― qm + pqn ...
... measure of a and b . For let x be any common measure of a and b , such that a = mx , and b ― nx , then = a — pb — mx — pnx— ( m — pn ) x d — b — qc = nx— ( qm — pqn ) x— ( n — qm + pqn ) x ; .. x measures d by the units in n ― qm + pqn ...
Σελίδα 35
... measure ( if they have one ) ; arrange their terms accord- ing to the dimensions of the same letter , and divide either , or both of them , by the greatest simple factor which it may contain ; then perform on them the same operation as ...
... measure ( if they have one ) ; arrange their terms accord- ing to the dimensions of the same letter , and divide either , or both of them , by the greatest simple factor which it may contain ; then perform on them the same operation as ...
Σελίδα 36
... measure 6a2 + 7ax - 3x2 3a - x required . 2a + 3x ) - 6a2 + 11ax + 3x2 3a + x Ans . In this example the dimension of ... measure , as before . Required to find the greatest common measure of 7a2 - 23ab + 662 2 . -or or x2 - xy - 2y x2 ...
... measure 6a2 + 7ax - 3x2 3a - x required . 2a + 3x ) - 6a2 + 11ax + 3x2 3a + x Ans . In this example the dimension of ... measure , as before . Required to find the greatest common measure of 7a2 - 23ab + 662 2 . -or or x2 - xy - 2y x2 ...
Σελίδα 37
... measure sought . 722-23ab + 662 7a - 2b -Ans . 5a3 - 18a2b + 11ab2—6b3 5a2 - 3ab + 262 Now , for the last fraction in example second , the greatest common measure of the fraction is x - a ) x2 + ax + a2 x3 + ax2 + a2x + a3 -Ans . x2 + ...
... measure sought . 722-23ab + 662 7a - 2b -Ans . 5a3 - 18a2b + 11ab2—6b3 5a2 - 3ab + 262 Now , for the last fraction in example second , the greatest common measure of the fraction is x - a ) x2 + ax + a2 x3 + ax2 + a2x + a3 -Ans . x2 + ...
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An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ... John D. Williams Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2018 |
An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ... John D. Williams Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ... John D Williams Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2015 |
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.