EXHIBITS

Turner's Compendium: Applications

Applications

Now that the reader knows how to solve both right and oblique triangles by using Turner's four axioms, Turner continues his book by detailing 24 example problems that involve solving triangles in the real world. These range from assessing the height of a tower, mountain, or cloud, to determining the distance to a ship, building, or planet. They also include measuring the depth of a well, length of the earth's shadow, and duration of an eclipse. Turner even details, in problem 24 (seen below), how the reader can use trigonometry to find the location of a beehive and its honey!

Turner concludes this book by writing: "Thus by one plain Geometrical Figure, having three Sides and three Angles, and assisted by the Rule of Three, you see what amazing Truths may be discover'd" [1].

Example problem two: Finding the height of a tower without being able to walk to its base.

Example problem seven: Finding how far a ship is out to sea by use of a tower in the harbor.

Example problem twenty-three: Finding the distance to an object without walking to the object or using any angle measurements.

Example problem twenty-four: Finding the location of a beehive by catching and releasing bees.

Work Cited:

Richard Turner, Plain Trigonometry, 39, as found in A View of the Heavens: being a short but comprehensive system of modern astronomy…, (London: Printed for S. Crowder, in Pater-noster-Row; and S. Gamidge, bookseller, in Worcester, 1765), in Utah State University, Merrill-Cazier Library Department of Special Collections and Archives, COLL V OV 74 pt. C.

Image Source:

Richard Turner, A View of the Heavens: being a short but comprehensive system of modern astronomy…, (London: Printed for S. Crowder, in Pater-noster-Row; and S. Gamidge, bookseller, in Worcester, 1765), in Utah State University, Merrill-Cazier Library Department of Special Collections and Archives, COLL V OV 74 pt. C.