Description

COLLINS, John. The sector on a quadrant: or A treatise containing the description and use of four several quadrants … [including “The description and uses of a great universal quadrant” & “The description and uses of a general quadrant”]; also an Appendix touching reflected dyalling from a glass placed at any reclination [by John Lyon]. London: J. M. for George Hurlock et al., 1659.

First edition, second issue, with cancel title dated 1659. A quadrant is an astronomical calculating device showing a projection of the heavens. By the end of the seventeenth century it was one of the most common astronomical instruments. This volume is actually a combination of four separate works, the last two separately paginated. The first three are by Collins and describe various configurations of quadrants. The final work, an appendix by John Lyon, describes how sundials may be constructed to use light reflected into a room from a mirror on the windowsill.

“The title, linking the sector and quadrant, is rather misleading as the work contains very little material about sector operations. The scales originating from the center of the quadrant (scale of equal parts, tangents and sines) could be used to do arithmetical operations. The text chiefly concerns the usual uses of a quadrant (time, dialing, navigation and surveying). Several different quadrants are described (based on a design by Collins’ friend Thomas Harvey), and Sutton added examples of the astrolabic scales for latitudes from zero to ninety degrees” (Tomash-Williams).

This second issue is almost identical to the first issue (1658) having “printed by J. Macock” in the imprint. In this second issue, the two contents leaves, bound after p. 275 in the original issue, are bound  with the preliminaries, following title page and ‘To the reader’ (A2). The catchword  ‘The’ on the verso of the second contents leaf consequently does not match the first word of the following page (a1).

John Collins, orphaned at the age of thirteen, began work as an apprentice bookseller in Oxford. In 1641, he became a clerk at Court (which had moved to Oxford because of civil war), and John Marr, who was then creating a large set of dials for the king, tutored him in mathematics. Collins later left England and joined the Venetian navy for seven years. Returning to London in 1649, he taught mathematics until 1660 and then held several different accounting positions, eventually becoming the librarian of the Royal Society in 1667. Collins served as unofficial secretary to the Royal Society in the 1670s and 1680s and corresponded with leading mathematicians in Britain and abroad, amongst them Isaac Newton.  

“For his zeal in collecting and diffusing scientific information, and in urging the accomplishment of appropriate and useful tasks, Collins was not undeservedly styled the ‘English Mersennus.’ ‘He was considered as a kind of register of all new improvements in the mathematics, and was constantly stimulating others to useful inquiries and pointing out the defects in different branches of science, and the methods by which those defects might be supplied’. His correspondence with eminent mathematicians, both British and foreign, was an important factor in the progress of his time; he spared no expense in procuring new and rare books, and helped forward many important publications. To him was due the printing of Dr. Barrow’s ‘Optical and Geometrical Lectures,’ as well as of his editions of Apollonius and Archimedes; of Kersey’s ‘Algebra,’ Brancker’s translation of Rhonius’s ‘Algebra,’ and Wallis’s ‘History of Algebra.’ He took besides an active part in seeing Horrocks’s ‘Astronomical Remains’ through the press. About twenty-five years after Collins’s death his books and papers came into the possession of W. Jones, F.R.S. They included a voluminous correspondence with Newton, Leibnitz, Gregory, Barrow, Flamsteed, Wallis, Slusius, and others, providing a repertory of the utmost value to the history of science. From it was selected and published in 1712, by order of the Royal Society, the ‘Commercium Epistolicum,’ by which Newton’s priority over Leibnitz in the discovery of the infinitesimal calculus was established; the first specimens of results from the use of the fluxional method, transmitted 20 July 1669 through Barrow to Collins, and by him made widely known, affording positive proof of Newton’s early possession of it” (DNB). Collins’s papers passed with Jones’s library into the Macclesfield library and are now in Cambridge University library.

Taylor, Mathematical Practitioners (Tudor), pages 228 and 364; Wing C5382; ESTC R32501.

Four parts in one volume, 4to (180 x 140 mm), pp. [16], 284; [2], 54, [8]; [2], 26, with 6 leaves of engraved illustrations of quadrants and scales by Henry Sutton; woodcut text diagrams throughout (light browning). Contemporary gilt-ruled calf (a bit rubbed, rebacked).