A Brief History of Mathematics;
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By Lam^ the theory of curvilinear co-ordinates, of which he had investigated a special case in 1837, was developed in 1859 into a theory for space in his Lemons sur la thiorie des coordonn^es curvilignes.
The expression for the Gaussian measure of curva- ture as a function of curvilinear co-ordinates has given an impetus to the study of the so called differential invariants or differential parameters. These are cer- tain functions of the partial derivatives of the coeffi- cients in the expressi...on for the square of the line- ele- ment which in the transformation of variables behave like the invariants of modern algebra. Here Sauc6, Jacobi, C. Neumann, and Halphen laid the founda- tions, and a general theory has been developed by Beltrami.* This theory, as well as the contact-trans- formations of Lie, moves along the border line be- tween geometry and the theory of differential equa- tions.!
"Mem. di Bologna, VIII. t Loria.
270 HISTORY OF MATHEMATICS.
With problems of the mathematical theory of light are con- nected certain investigations upon systems of rays and the prop- erties of infinitely thin bundles of rays, as first carried on by Du- pin, Malus, Ch.
What to read after A Brief History of Mathematics;?
You can find similar books in the "Read Also" column, or choose other free books by Karl Fink to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
By Lam^ the theory of curvilinear co-ordinates, of which he had investigated a special case in 1837, was developed in 1859 into a theory for space in his Lemons sur la thiorie des coordonn^es curvilignes.
The expression for the Gaussian measure of curva- ture as a function of curvilinear co-ordinates has given an impetus to the study of the so called differential invariants or differential parameters. These are cer- tain functions of the partial derivatives of the coeffi- cients in the expressi...on for the square of the line- ele- ment which in the transformation of variables behave like the invariants of modern algebra. Here Sauc6, Jacobi, C. Neumann, and Halphen laid the founda- tions, and a general theory has been developed by Beltrami.* This theory, as well as the contact-trans- formations of Lie, moves along the border line be- tween geometry and the theory of differential equa- tions.!
"Mem. di Bologna, VIII. t Loria.
270 HISTORY OF MATHEMATICS.
With problems of the mathematical theory of light are con- nected certain investigations upon systems of rays and the prop- erties of infinitely thin bundles of rays, as first carried on by Du- pin, Malus, Ch.
What to read after A Brief History of Mathematics;?
You can find similar books in the "Read Also" column, or choose other free books by Karl Fink to read onlineMoreLess
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