 After some analytical discussion, Prof. Sylvester adds : " My reader will now be prepared to see why it is that all the geometrical demonstrations given of this theorem are indirect, I believe I may venture to say necessarily indirect. It is because the...  Proceedings of the Edinburgh Mathematical Society - Page 21by Edinburgh Mathematical Society - 1900Full view - About this book
 | Edinburgh Mathematical Society - Electronic journals - 1901 - 232 pages
...259-260 (August) pp. 356-358 (Dr Zech) XVIII (1852) pp. 357-359 (ะก. Schmidt) XX (1853) pp. 459-461 (Dr Clausen) XLI (1864) pp. 151-152 (A. Niegemann)...no other form of proof than that of the reductio ad absurdum is possible in the nature of things." Prof. Sylvester appends to his paper the following remarks... | |
 | Physics - 1852 - 590 pages
...geometrical demonstrations given of this theorem, even in the simplest case of all, viz. when n=2, are indirect, I believe I may venture to say necessarily...the truth of the theorem depends on the necessary non-ex'stence of real roots (between prescribed limits) of the analytical equation expressing the conditions... | |
 | Physics - 1852 - 1172 pages
...geometrical demonstrations given of this theorem, even in the simplest case of all, viz. when n=2, are indirect, I believe I may venture to say necessarily...the truth of the theorem depends on the necessary non-ex'stence of real roots (between prescribed limits) of the analytical equation expressing the conditions... | |
 | 672 pages
...geometrical demonstrations given of this theorem, even in the simplest case of all, namely when n = 2, are indirect, I believe I may venture to say necessarily...geometrical method, that whenever this is the case no other * In the first of these cases, if the base of the triangle is supposed given, the locus of the vertex... | |
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