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In Euclidean geometry, the intersecting chords theorem, or just the chord theorem, is a statement that describes a relation of the four line segments created by two intersecting chords within a circle. It states that the products of the lengths of the line segments on each chord are equal. It is Proposition 35 of Book 3 of Euclid's Elements.
In the 2nd century AD, Ptolemy compiled a more extensive table of chords in his book on astronomy, giving the value of the chord for angles ranging from 1 / 2 to 180 degrees by increments of 1 / 2 degree. Ptolemy used a circle of diameter 120, and gave chord lengths accurate to two sexagesimal (base sixty) digits after the ...
The fractional parts of chord lengths required great accuracy, and were given in sexagesimal notation in two columns in the table: The first column gives an integer multiple of 1 / 60 , in the range 0–59, the second an integer multiple of 1 / 60 2 = 1 / 3600 , also in the range 0–59.
A standard 8 + 1 ⁄ 2 by 11 inches (220 mm × 280 mm) sheet of paper has three holes with spacing of 4 + 1 ⁄ 4 inches (110 mm). There is a variant for half-letter size pages (8 + 1 ⁄ 2 by 5 + 1 ⁄ 2 inches or 220 mm × 140 mm), whose three rings are 2 + 3 ⁄ 4 inches (70 mm) apart. "Ledger" size binders hold 11-by-17-inch (28 by 43 cm ...
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4 ft 8 in gauge railways are railways with a track gauge of 4 ft 8 in / 1,422 mm. This gauge is 1 ⁄ 2 inch (13 mm) less than 4 ft 8 + 1 ⁄ 2 in ( 1,435 mm ) standard gauge The first such railways were the Killingworth Railway [ 1 ] [ 2 ] and the Stockton and Darlington Railway [ note 1 ]