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nydus/A History of MathematicsPublic

This text examines the transition from the Middle Ages to the Modern era, highlighting how the fall of Constantinople and the invention of the printing press catalyzed a revival of classical learning. It traces the shift toward scientific inquiry through the rise of pure mathematics and astronomy, detailing the intellectual struggle against established scholastic and ecclesiastical authority.

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Table of Contents

Applied Mathematics

sea. He and A. Oberbeck showed that when the waves on the

sea attain lengths of from 16 to 33 feet, the air waves must attain lengths of from 10 to 20 miles, and proportional depths. Superposed strata would thus mix more thoroughly, and their energy would be partly dissipated. From hydrodynamical equations of rotation Helmholtz established the reason why

the observed velocity from equatorial regions is much less in a latitude of, say, 20° or 30°, than it would be were the movements unchecked.

About 1860 acoustics began to be studied with renewed

zeal. The mathematical theory of pipes and vibrating strings had been elaborated in the eighteenth century by Daniel Bernoulli,

D'Alembert, Euler, and Lagrange. In the first part of

the present century Laplace corrected Newton's theory on the

velocity of sound in gases, Poisson gave a mathematical discussion

of torsional vibrations; Poisson, Sophie Germain, and

Wheatstone studied Chladni's figures; Thomas Young and the

brothers Weber developed the wave-theory of sound. Sir J. F. W. Herschel wrote on the mathematical theory of sound for

the Encyclopædia Metropolitana, 1845. Epoch-making were Helmholtz's experimental and mathematical researches. In his hands and Rayleigh's, Fourier's series received due

attention. Helmholtz gave the mathematical theory of beats, difference tones, and summation tones. Lord Rayleigh (John William Strutt) of Cambridge (born 1842) made extensive

mathematical researches in acoustics as a part of the theory of vibration in general. Particular mention may be made of his discussion of the disturbance produced by a spherical obstacle on the waves of sound, and of phenomena, such as sensitive flames, connected with the instability of jets of fluid. In 1877

and 1878 he published in two volumes a treatise on The Theory of Sound. Other mathematical researches on this subject have been made in England by Donkin and Stokes.

The theory of elasticity[]42 belongs to this century. Before

1800 no attempt had been made to form general equations for the motion or equilibrium of an elastic solid. Particular problems had been solved by special hypotheses. Thus, James Bernoulli considered elastic laminæ; Daniel Bernoulli and

Euler investigated vibrating rods; Lagrange and Euler, the

equilibrium of springs and columns. The earliest investigations of this century, by Thomas Young ("Young's modulus of

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