330:
148:
341:
of a triangle, the point where the three perpendiculars from the vertices to the sides meet. The orthocentre itself was known previously, but
Chapple writes that its existence was "often taken for granted, but no where demonstrated".
318:. In the same work he stated that, when two circles are the incircle and circumcircle of a triangle, then there is an infinite family of triangles for which they are the incircle and circumcircle. This is the triangular case of
135:"To illustrate the work of Chapple, whose arguments are often confused and whose logic is very poor, even for the standard of his time, is not easy especially when trying to keep as faithful as possible to his thought."
326:
other than circles. It is the first known mathematical publication on pairs of inscribed and circumscribed circles of polygons, and significantly predates
Poncelet's own 1822 work in this area.
273:
548:
Milne, Antony (2015), "The Euler and Grace-Danielsson inequalities for nested triangles and tetrahedra: a derivation and generalisation using quantum information theory",
104:. He married the surveyor's niece, supervised the construction of a new hospital in Exeter, and became secretary of the hospital. He also worked as the estate steward for
308:
219:
199:
179:
77:
14 January 1718], the son of a poor farmer and parish clerk. He was a devoted bibliophile, and gained much of his knowledge of mathematics from Ward's
672:
105:
116:, and spent much of the rest of his life working on it; it was published in part throughout his life, and in complete form posthumously in 1785.
362:, and carried out this valuation for Courtenay. In this, he became one of the first mathematicians to work on this problem, along with Simpson,
516:
667:
120:
415:
401:
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43:
371:
319:
152:
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367:
534:
Magna
Brittanica; being a concise topographical account of the several counties of Great Britain, Vol. VI: Devonshire
93:
662:
508:
Leases for Lives: Life
Contingent Contracts and the Emergence of Actuarial Science in Eighteenth-Century England
279:
227:
119:
He died in early
September 1781. A tablet in his memory could be found in the west end of the nave of the
79:
The Young
Mathematician's Guide: Being a Plain and Easie Introduction to the Mathematicks, in Five Parts
657:
652:
355:
88:
83:
50:
613:
633:
595:
596:"An essay on the properties of triangles inscribed in, and circumscribed about two given circles"
557:
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284:
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567:
469:
123:, prior to that church's demolition in 1971. Chapple Road in Witheridge is named after him.
581:
481:
431:
577:
477:
412:, Devonshire Association for the Advancement of Science Literature & the Arts: 217–348
109:
460:
Del
Centina, Andrea (2016), "Poncelet's porism: a long story of renewed discoveries, I",
359:
311:
204:
184:
164:
28:
617:
646:
489:
314:, who published them in 1765, they were found earlier by Chapple, in a 1746 essay in
24:
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402:"Prince's "Worthies of Devon" and the "Dictionary of National Biography", part III"
181:
between the incentre and circumcentre of a circle, as a function of the inradius
87:, especially concerning mathematical problems. He also later contributed work on
338:
36:
572:
473:
70:
147:
81:. He became an assistant to the parish priest, and a regular contributor to
20:
139:
Nevertheless, Chapple made several significant discoveries in mathematics.
100:
His correspondence led him to become, in 1738, the clerk for a surveyor in
57:
He was also one of the earliest mathematicians to calculate the values of
337:
In 1749, Chapple published the first known proof of the existence of the
322:, which applies more generally to polygons of any number of sides and to
351:
58:
101:
562:
328:
323:
146:
618:"A Possibly First Proof of the Concurrence of Altitudes"
406:
Report & Transactions of the
Devonshire Association
333:
Three altitudes of a triangle meet at the orthocentre
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230:
207:
187:
167:
53:
on triangles with a common incircle and circumcircle.
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267:
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350:Chapple learned of the problem of valuation of
44:distance between the incentre and circumcentre
27:. His mathematical discoveries were mostly in
8:
500:
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511:, Cambridge University Press, p. 79,
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571:
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237:
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106:William Courtenay, 1st Viscount Courtenay
278:An immediate consequence is the related
108:. In 1772 he began work on an update to
35:the first proof of the existence of the
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393:
391:
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387:
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310:. Although these results are named for
462:Archive for History of Exact Sciences
426:
424:
7:
268:{\displaystyle d={\sqrt {R(R-2r)}}.}
598:, Miscellanea Curiosa Mathematica,
673:People from North Devon (district)
14:
161:gives a formula for the distance
354:through his correspondence with
131:Andrea del Centina writes that:
634:Chapple's letter with the proof
602:, vol. 4, pp. 117–124
416:"Chapple, William", pp. 316–318
121:Church of St Mary Major, Exeter
257:
242:
1:
436:Witheridge Historical Archive
114:Survey of the County of Devon
537:, Thomas Cadell, p. 215
505:Bellhouse, David R. (2017),
127:Contributions to mathematics
159:Euler's theorem in geometry
19:(1718–1781) was an English
689:
320:Poncelet's closure theorem
153:Poncelet's closure theorem
594:Chapple, William (1749),
573:10.1007/s00022-014-0257-8
474:10.1007/s00407-015-0163-y
73:on 25 January 1719 [
600:The Gentleman's Magazine
316:The Gentleman's Magazine
303:{\displaystyle R\geq 2r}
94:The Gentleman's Magazine
531:Lysons, Daniel (1822),
151:The triangular case of
668:English mathematicians
334:
304:
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215:
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400:Pengelly, W. (1887),
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614:Bogomolny, Alexander
414:. See in particular
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89:West Country English
69:Chapple was born in
550:Journal of Geometry
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300:
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211:
191:
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42:a formula for the
663:English surveyors
432:"William Chapple"
364:Abraham de Moivre
260:
214:{\displaystyle R}
201:and circumradius
194:{\displaystyle r}
174:{\displaystyle d}
84:The Ladies' Diary
51:Poncelet's porism
49:the discovery of
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110:Tristram Risdon
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17:William Chapple
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11:
5:
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556:(3): 455–463,
540:
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420:
382:
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360:Thomas Simpson
347:
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312:Leonhard Euler
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143:Plane geometry
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47:
46:of a triangle,
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39:of a triangle,
29:plane geometry
13:
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6:
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3:
2:
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518:9781108509121
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372:William Jones
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34:
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31:and include:
30:
26:
25:mathematician
22:
18:
625:, retrieved
622:Cut The Knot
621:
608:
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553:
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543:
533:
526:
507:
468:(1): 1–122,
465:
461:
439:, retrieved
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368:James Dodson
349:
336:
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157:
138:
130:
118:
113:
99:
92:
82:
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68:
56:
16:
15:
658:1781 deaths
653:1719 births
632:. See also
627:17 November
441:18 November
339:orthocentre
37:orthocentre
647:Categories
378:References
280:inequality
71:Witheridge
563:1404.0525
490:253898210
356:John Rowe
352:annuities
292:≥
249:−
59:annuities
21:surveyor
582:3420559
482:3437893
346:Finance
580:
515:
488:
480:
370:, and
324:conics
102:Exeter
558:arXiv
486:S2CID
629:2019
513:ISBN
443:2019
358:and
75:O.S.
65:Life
23:and
568:doi
554:106
470:doi
112:'s
91:to
649::
620:,
616:,
578:MR
576:,
566:,
552:,
497:^
484:,
478:MR
476:,
466:70
464:,
450:^
434:,
423:^
410:19
408:,
404:,
386:^
374:.
366:,
221::
97:.
61:.
636:.
570::
560::
472::
418:.
298:r
295:2
289:R
263:.
258:)
255:r
252:2
246:R
243:(
240:R
235:=
232:d
209:R
189:r
169:d
Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
