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Similar to when I was a kid reading World Books, I’m reading my copy of Thomas Dobson’s encyclopedia (first American encyclopedia; 1798,) and learning about something I knew nothing about.
“PORISM”
Here’s the plate, a small thread.
@mathshistory @rmathematicus
“PORISM”
Here’s the plate, a small thread.
@mathshistory @rmathematicus
The gist (I think): Euclid found a class of propositions which were ‘porismata’, or acquired while working on other problems. Euclid’s porisms were lost, but Pappus of Alexanderia mentions them in a criticism. It refers to a figure ‘now lost’; even Halley can’t figure it out.
Fermat gives it a shot, but it is Scottish mathematician Robert Simpson (1687-1768) who “by patient inquiry and some lucky thoughts” restores Euclid’s porisms in a “just” manner that corresponds with Pappus description of them.
Simpson provides the first ‘modern’ definition, restated by the author of the article as, “a proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate; or capable of innumerable [infinite] solutions.”
![Simpson provides the first ‘modern’ definition, restated by the author of the article as, “a proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate; or capable of innumerable [infinite] solutions.”](https://pbs.twimg.com/media/ElBY_ZUX0AEV2V9.jpg "Simpson provides the first ‘modern’ definition, restated by the author of the article as, “a proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate; or capable of innumerable [infinite] solutions.”")
![Simpson provides the first ‘modern’ definition, restated by the author of the article as, “a proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate; or capable of innumerable [infinite] solutions.”](https://pbs.twimg.com/media/ElBY_a6WMAI5_Fr.jpg "Simpson provides the first ‘modern’ definition, restated by the author of the article as, “a proposition affirming the possibility of finding such conditions as will render a certain problem indeterminate; or capable of innumerable [infinite] solutions.”")
Several more important points (no time to retype here, I actually have to accomplish a few things today 
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A few full pages with some of the math for clarification. Anyway, read an encyclopedia and you may end up learning about something you knew little or nothing about. Have a great day.
