A Brief History of Mathematics An Authorized Translation of Dr Karl Finks Ges
A Brief History of Mathematics An Authorized Translation of Dr Karl Finks Ges
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Mac- laurin made interesting investigations upon corre- * Baltzer.
tCayley, A. , Address to the British Association, etc. , 1883.
840 HISTORY OF MATHEMATICS.
spending points of a curve of the third order, and thus showed that the theory of these curves was much more comprehensive than that of conies. Euler like- wise entered upon these investigations in his paper Sur une contradiction apparente dans la thtorie des courbes planes (Berlin, 1748), where it is shown that by eight in- tersections of... two curves of the third order the ninth is completely determined. This theorem, which includes Pascal's theorem for conies, introduced point groups, or systems of points of intersection of two curves, into geometry. This theorem of Euler's was noticed in 1750 by Cramer who gave special attention to the sin- gularities of curves in his works upon the intersection of two algebraic curves of higher order; hence the obvious contradiction between the number of points determining a plane curve and the number of inde- pendent intersections of two curves of the same order bears the name of "Cramer's paradox.
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To quickly assess the difficulty of the text, read a short excerpt:
Mac- laurin made interesting investigations upon corre- * Baltzer.
tCayley, A. , Address to the British Association, etc. , 1883.
840 HISTORY OF MATHEMATICS.
spending points of a curve of the third order, and thus showed that the theory of these curves was much more comprehensive than that of conies. Euler like- wise entered upon these investigations in his paper Sur une contradiction apparente dans la thtorie des courbes planes (Berlin, 1748), where it is shown that by eight in- tersections of... two curves of the third order the ninth is completely determined. This theorem, which includes Pascal's theorem for conies, introduced point groups, or systems of points of intersection of two curves, into geometry. This theorem of Euler's was noticed in 1750 by Cramer who gave special attention to the sin- gularities of curves in his works upon the intersection of two algebraic curves of higher order; hence the obvious contradiction between the number of points determining a plane curve and the number of inde- pendent intersections of two curves of the same order bears the name of "Cramer's paradox.
What to read after A Brief History of Mathematics An Authorized Translation of Dr Karl Finks Ges?
You can find similar books in the "Read Also" column, or choose other free books by Zed20translation20of20dr20karl20finks20ges to read onlineMoreLess
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