# 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

H.W. Wilson, 1902 - Calculus - 43 pages

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### Contents

 Section 1 1 Section 2 8 Section 3 12 Section 4 29
 Section 5 40 Section 6 49 Section 7 51

### Popular passages

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.