A History of Analysis

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Hans Niels Jahnke
American Mathematical Soc. - Mathematics - 422 pages
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Precursors of Differentiation and Integration
Newtons Method and Leibnizs Calculus
Algebraic Analysis in the 18th Century
The Origins of Analytic Mechanics in the 18th Century
The Foundation of Analysis in the 19th Century
Complex Function Theory 17801900
Theory of Measure and Integration from Riemann to Lebesgue
Foundations of Analysis
A Historical Overview to circa 1900
A Historical Survey
The Origins of Functional Analysis
Index of Names

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Page 9 - Magnitudes are said to be in the same ratio, the first to the second and the third to the fourth, when, if any equimultiples whatever be taken of the first and third, and any equimultiples whatever of the second and fourth, the former equimultiples alike exceed, are alike equal to, or alike fall short of, the latter equimultiples respectively taken in corresponding order.
Page 7 - A ratio is a sort of relation in respect of size between two magnitudes of the same kind. 4. Magnitudes are said to have a ratio to one another which are capable, when multiplied, of exceeding one another.
Page 3 - Two unequal magnitudes being set out, if from the greater there be subtracted a magnitude greater than its half, and from that which is left a magnitude greater than its half, and if this process be repeated continually, there will be hft some magnitude which will be less than the lesser magnitude set out.
Page 11 - If all points of a straight line fall into two classes such that every point of the first class lies to the left of every point of the second class, there exists one and only one point which produces this division of all the points into two classes, this division of the straight line into two parts.
Page 8 - A plane angle is the inclination to one another of two lines in a plane which meet one another and do not lie in a straight line; 9 And when the lines containing the angle are straight, the angle is called rectilineal.

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