Norwood, Richard

Trigonometrie: Or, the Doctine of Triangles: Divided into Two Books.

  • Seventh edition of Norwood’s highly important and commercially successful book on mathematics for navigators, originally published in 1631 and used as a reference by Isaac Newton.

    Richard Norwood (1590-1675) set out on his mathematical career when, as a teenager, he joined the crew of a coastal trading vessel and began learning mathematics and navigation. He made a number of long voyages in the coming years and was soon known for his accuracy as a surveyor and navigator. Norwood also spent time as a teacher of mathematics and navigation, and in 1622 married and settled permanently in London where he wrote books and also made important theoretical contributions. Among these were his methods for checking closure and declination of magnetic compasses, and his extremely accurate calculation of the nautical mile, which was undertaken in the mid-1630s and was eventually shown to be only 40 feet too long.

    Many of Norwood’s books “reached several editions and remained in print in the 1690s” (ODNB). Trigonometrie reached its eighth edition in 1685, its popularity resulting from its practical mathematical solutions to astronomical and navigational problems. “With a book like this in his hand there was now no reason why the navigator should not solve all problems of plane and Mercator's sailing logarithmically. Norwood had weaned logarithmical navigation from the lecture hall” (Waters).

    Norwood’s work is also intimately connected with that of Sir Isaac Newton, who owned copies of the 1645 and 1688 editions of Trigonometrie. Norwood was one of Newton’s sources for the measured circumference of the Earth, a key part of his demonstration of universal gravitation - Newton cites Norwood’s measurement of the length of a degree in the second and third editions of the Principia. There has been some controversy over this between scholars who believe that Newton worked out his theory in a flash of insight during his annus mirabilis of 1665-66 and those who argue that he struggled over a much longer period. Norwood published his accurate measurement of 69 miles per degree in A Seaman’s Practice in 1636, but used the commonly accepted and less accurate measurement of 60 miles per degree in Trigonometrie. This less accurate number would not have been ideal for Newton’s calculations, and some scholars have suggested that when he attempted to use it in 1666 he met with poor results and set aside his work until the 1680s, when he was at last successful using the more accurate figure.

    Though Trigonometrie was a best-seller in its time, copies of all editions are now scarce, with only five appearing at auction in the last fifteen years.

  • The first shewing the Mensuration of right lined Triangles: The second of Spherical, with the Grounds and Demonstrations thereof. Both performed by that late and excellent Invention of Logarithms, after a more easie and compendious manner, than hath been formerly taught. Whereunto is annexed (chiefly for the use of Seamen) A Treatise of the application thereof, in the three principal kinds of Sailing. With exact Tables of the Suns Declination… Also other necessary Tables used in Navigation. This Seventh Edition being diligently Corrected in divers difficult Places explained; New Tables of the Stars right ascensions and Declinations added, and the whole Work very much enlarged, by the Author himself. London: by R. W. for William Fisher; T. Passenger; R. Boulter; and R. Smith, 1678. Contemporary speckled sheep rebacked with the original spine laid down, black morocco spine label, marbled edges. Woodcut diagrams throughout the text. Contemporary ownership signature “Strathnaver 1683” to front free endpaper and small contemporary decorative mark to title. Publisher’s ads on the final page. Corners and head of spine worn, joints splitting at the head of the spine, repaired crack to inner side of the lower board, hinges cracked, closed tear to four leaves at the upper part of the gutter, single wormhole to margins of final leaves, the final leaf slightly trimmed at the lower edge cutting off the final line of the advertisement, but not affecting the table on the opposite side. Contents clean save for the occasional spot and minor marginal toning at the front. A very good copy.

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