This section is from the book "The American House Carpenter", by R. G. Hatfield. Also available from Amazon: The American House Carpenter.

The versed sine is equal to the radius, less the square root of the difference of the squares of the radius and half chord; expressed algebraically thus: where r is the radius, v the versed sine, and c the chord. (Equation (161.) reduced.)

Example. - In an arc of a circle whose radius is 75 feet, what is the versed sine to a chord of 120 feet? By the table in the Appendix it will be seen that -

The square of the radius, 75, equals ........ | 5625 |

The square of half the chord, 60, equals.... | 5600 |

The difference is ............................................ | 2025 |

The square root of this is ............................ | 45 |

This deducted from the radius ..................... | 75 |

The remainder is the versed sine, = | 30 |

This is expressed bythe formula, thus -

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