Letters From Dr James Gregory of Edinburgh in Defence of His Essay On the Diff
Letters From Dr James Gregory of Edinburgh in Defence of His Essay On the Diff
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The best of these that I can remember at present, is the sophism, (attribu- ted to ZENO, but on what authority I know not, ) that two right lines inclined and approaching to one another never can meet, though protracted ad injinitum. If you do not know the proposition, and the pseudo-demonstration of it, leading to the necessary consequence, that one side of a triangle would be equal to the other two, which is impos- sible, your friend MR. PATERSON, I dare say, can help you out. It would be an ...useful and wholesome exercise to you, to endeavour to point out the difference between that notorious sophism and the valid demonstration with respect to the hyperbola and its asymptote. In both, the argu- mentum ad absurdum is employed; in both, the proposition to be demonstrated appears at first sight absurd and impossible; nay, the absurdity and impossibility appear, at first sight, to be the same in both : in both, the contradictory proposition, assumed in order to be disproved, by shewing that it implies by necessary consequences an inference which is certainly impossible, appears, at first sight, a self-evident truth : and lastly, in both these arguments, the inference given as a necessary consequence of the supposition assumed in order 190 to be disproved, is false and impossible.
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To quickly assess the difficulty of the text, read a short excerpt:
The best of these that I can remember at present, is the sophism, (attribu- ted to ZENO, but on what authority I know not, ) that two right lines inclined and approaching to one another never can meet, though protracted ad injinitum. If you do not know the proposition, and the pseudo-demonstration of it, leading to the necessary consequence, that one side of a triangle would be equal to the other two, which is impos- sible, your friend MR. PATERSON, I dare say, can help you out. It would be an ...useful and wholesome exercise to you, to endeavour to point out the difference between that notorious sophism and the valid demonstration with respect to the hyperbola and its asymptote. In both, the argu- mentum ad absurdum is employed; in both, the proposition to be demonstrated appears at first sight absurd and impossible; nay, the absurdity and impossibility appear, at first sight, to be the same in both : in both, the contradictory proposition, assumed in order to be disproved, by shewing that it implies by necessary consequences an inference which is certainly impossible, appears, at first sight, a self-evident truth : and lastly, in both these arguments, the inference given as a necessary consequence of the supposition assumed in order 190 to be disproved, is false and impossible.
What to read after Letters From Dr James Gregory of Edinburgh in Defence of His Essay On the Diff?
You can find similar books in the "Read Also" column, or choose other free books by James Gregory to read onlineMoreLess
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