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V. Some Geometrical Porisms, with Examples of their Application to the Solution of Problems
Published online by Cambridge University Press: 17 January 2013
Extract
The nature of those mathematical propositions, which were called Porisms by the ancient geometers, is now no longer a matter of uncertainty. The relation which they bear to other mathematical truths, the way in which they may at first have been observed, the kind of analysis to be employed in their investigation, their application to the solution of problems, have all been considered by some eminent mathematicians of the present age.
- Type
- Papers Read Before the Society
- Information
- Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 4 , Issue 2 , 1798 , pp. 107 - 134
- Copyright
- Copyright © Royal Society of Edinburgh 1798
References
page 119 note * It may be proper to remark here, that, in the preceding propositions, the straight lines given by position, as well as the indeterminate straight line, which is cut by them into segments, having to each other given ratios, and which also cuts off from them segments adjacent to given points, and having to each other given ratios, are tangents to a parabola, of which the point that is required to be found is the focus. This consideration suggests some curious propositions, relating to tangents to the parabola. Some of them have been observed by Dr Halley, in his translation of the Sectio Rationis of Appollonius.
One very obvious application of the propositions above hinted at, is, to describe parabolas that shall pass, through given points, and touch straight lines given by position.
page 125 note * The manner of doing this has been shown in Prop. 1.