## An Introduction to the Summation of Differences of a Function: An Elementary Exposition of the Nature of the Algebraic Processes Replaced by the Abbreviations of the Infinitesimal Calculus |

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An Introduction to the Summation of Differences of a Function: An Elementary ... Benjamin Feland Groat No preview available - 2016 |

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algebra analytic geometry axis binomial theorem CHAPTER choice from rows cofactor complementary minors constituents correspond to columns curve definite integral differ differential calculus differential coefficient Dinostratus eliminant equal roots example Find the sum follows formula function whose derivative geometric series indefinite integral inequalities INFINITESIMAL CALCULUS integral calculus interchange inversions due inversions of natural Let the student letters and suffixes logarithmic logarithmic series method MINOR DETERMINANTS multiplied natural order notation nth order number of inversions odd according odd number order of choice order of factors ordinates permutation positive integer problem quadratrix quantities radius rectangles refer to rows represented respect to rows result row or column rows and columns Scholium Solution Solve square array sum to infinity summation th term Theorem theory of equations tion total number University of Minnesota vanish Whence

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Page 58 - ... from each row, and one and only one from each column, the second suffixes being written in the order 1, 2, 3, are oi,'02,202,8, o^ j, a2-lo'.2a...

Page 63 - Therefore Ai = — As. Let the student give the proof for the case in which two rows are interchanged. 31. Theorem. The determinant of a square array, in which two rows or two columns are identical, is equal to zero. Any interchange in the manner of the theorem should change the sign of A. But the .value of A is evidently identically the same in the two cases. Thus A is unaltered in value by changing its sign. Therefore A = o. • 32. Theorem. If all the constituents of one line be multiplied bv...

Page 23 - EXERCISES 1. Find the equation of the tangent to the curve у = x°- through the point whose abscissa is 2. Thus, xt = 2, \\ = 4. * Barrow's method for drawing a tangent. t Here the symbol = means literally " approaches indefinitely near to.