File:Holditch's Theorem - Original Article.png
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DescriptionHolditch's Theorem - Original Article.png |
English: A single-page article was published by Rev. Hamnet Holditch in January 1857[a] in vol. II, N°5, of The Quarterly Journal of Pure and Applied Mathematics introducing what is now known as Holditch's theorem.
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Date | |
Source | http://resolver.sub.uni-goettingen.de/purl?PPN600494829_0002 |
Author | Göttingen Center for Retrospective Digitization (Göttinger DigitalisierungsZentrum) - Göttingen State and University Library |
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GEOMETRICAL THEOREM
By Rev. Hamnet Holditch
If a chord of a closed curve, of constant length , be divided into two parts of lengths , respectively, the difference between the areas of the closed curve, and of the locus of the dividing point, will be .
Solution. Let be the chord in any position; the dividing point, so that , ; let be the point in which the chord intersects its consecutive position; let be the area of the given curve, , , those of the loci of , , respectively; , .
Then (1),
but also ;
therefore ,
or ;
therefore (2),
Also ,
therefore, by (1),
.
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