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IX. On a new property of the tangents of three arches trisecting the circumference of a circle, by Nevil Maskelyne, D. D. F. R. S. and Astronomer Royal
- Source :
- Philosophical Transactions of the Royal Society of London. 98:122-123
- Publication Year :
- 1808
- Publisher :
- The Royal Society, 1808.
-
Abstract
- Mr. William Garrard having shewn me a curious property of the tangents of the three angles of a plane triangle, or in other words, of the tangents of three arches trisecting a semicircle, in a paper which I have communicated to this Society, I was led to consider whether a similar property might not belong to the tangents of three arches trisecting the whole circumference; and, on examination, found it be so. Let the circumference of a circle be divided any how into three arches A, B, C; that is, let A + B + C be equal to the whole circumference. I say, the square of the radius multiplied into the sum of the tangents of the three arches A, B, C, is equal to the product of the tangents multiplied together. I shall demonstrate this by symbolical calculation, now commonly called (especially by foreign mathematicians) analytic calculation.
- Subjects :
- Property (philosophy)
Tangent
Geometry
Arch
Circumference
Mathematics
Subjects
Details
- ISSN :
- 20539223 and 02610523
- Volume :
- 98
- Database :
- OpenAIRE
- Journal :
- Philosophical Transactions of the Royal Society of London
- Accession number :
- edsair.doi...........a3b33475495e03148e31fb11fc16b5d9