ptolemy's table of chords wikipedia - EAS
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See all on Wikipediahttps://en.wikipedia.org/wiki/Ptolemy's_table_of_chordsThe table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's Almagest, a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function.
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See moreA chord of a circle is a line segment whose endpoints are on the circle. Ptolemy used a circle whose diameter is 120 parts. He tabulated the length of a chord whose endpoints are separated by an arc of n degrees, for n ranging
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See moreLengths of arcs of the circle, in degrees, and the integer parts of chord lengths, were expressed in a base 10 numeral system that used 21 of the letters of the Greek alphabet with
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See more• J. L. Heiberg Almagest, Table of chords on pages 48–63.
• Glenn Elert Ptolemy's Table of Chords: Trigonometry in the Second Century...
See moreChapter 10 of Book I of the Almagest presents geometric theorems used for computing chords. Ptolemy used geometric reasoning based on Proposition 10 of Book XIII of Euclid's Elements to find the chords of 72° and 36°. That Proposition states that if
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See more• Exsecant
• Fundamentum Astronomiae, a book setting forth an algorithm for precise computation of sines, published in the late 1500s...
See moreWikipedia text under CC-BY-SA license- https://en.wikipedia.org/wiki/Talk:Ptolemy's_table_of_chords
It was the earliest trigonometric table extensive enough for many practical purposes, including those of astronomy (an earlier table of chords by Hipparchus gave chords only for arcs that were multiples of 7½°). Several centuries passed before more extensive trigonometric tables were created. Page numbers in Glowatzki and Göttsche?
Ptolemy's table of chords - HandWiki
https://handwiki.org/wiki/Ptolemy's_table_of_chords- A chord of a circle is a line segment whose endpoints are on the circle. Ptolemy used a circle whose diameter is 120 parts. He tabulated the length of a chord whose endpoints are separated by an arc of n degrees, for n ranging from 1/2 to 180 by increments of 1/2. In modern notation, the length of the chord corresponding to an arc of θdegrees is 1....
- https://en.wikipedia.org/wiki/Ptolemy's_theorem
In Euclidean geometry, Ptolemy's theorem is a relation between the four sides and two diagonals of a cyclic quadrilateral. The theorem is named after the Greek astronomer and mathematician Ptolemy. Ptolemy used the theorem as an aid to creating his table of chords, a trigonometric table that he applied to astronomy. If the vertices of the cyclic quadrilateral are A, B, C, and D in …
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- https://en.formulasearchengine.com/wiki/Ptolemy's_table_of_chords
- A chord of a circle is a line segment whose endpoints are on the circle. Ptolemy used a circle whose diameter is 120. He tabulated the length of a chord whose endpoints are separated by an arc of n degrees, for n ranging from 1/2 to 180 by increments of 1/2. In modern notation, the length of the chord corresponding to an arc of θdegrees is 1. c h o...
- https://everipedia.org/Ptolemy%27s_table_of_chords
Ptolemy's table of chords The table of chords, created by the Greek astronomer, geometer, and geographer Ptolemy in Egypt during the 2nd century AD, is a trigonometric table in Book I, chapter 11 of Ptolemy's Almagest, [1] a treatise on mathematical astronomy. It is essentially equivalent to a table of values of the sine function.
- https://en.wikipedia.org/wiki/Scale_of_Chords
A scale of chords may be used to set or read an angle in the absence of a protractor. To draw an angle, compasses describe an arc from origin with a radius taken from the 60 mark. The required angle is copied from the scale by the compasses, and an arc of this radius drawn from the sixty mark so it intersects the first arc. ... Ptolemy's table ...
- https://hypertextbook.com/eworld/chords
9 rows · Jun 28, 1994 · Although certainly not the first trigonometric table 1, Ptolemy's On the Size of Chords Inscribed in a Circle (2nd Century AD) is by far the most famous. Based largely on an earlier work by Hipparchus (ca. 140 BC) it was included in Ptolemy's definitive Syntaxis Mathematica, better known by its Arabic name Almagest 2. In this paper I will describe the …
- https://en.wikipedia.org/wiki/Trigonometric_tables
1 day ago · This method was used by the ancient astronomer Ptolemy, who derived them in the Almagest, a treatise on astronomy. In modern form, the identities he derived are stated as follows (with signs determined by the quadrant in which x lies): These were used to construct Ptolemy's table of chords, which was applied to astronomical problems.
- https://en.wikipedia.org/wiki/Regular_polygon
In Euclidean geometry, a regular polygon is a polygon that is direct equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star.In the limit, a sequence of regular polygons with an increasing number of sides approximates a circle, if the perimeter or area is fixed, or a regular apeirogon (effectively …
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