BARROW, Isaac Lectiones opticae & geometricae: in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur... London, William Godbid, [1669-] 1674 1674
2 vols in one, 4to (196 x 155 mm), pp [xiv] 127; [iv] 151 [3], with 28 folding engraved plates; corner of imprimatur torn, a fine, crisp copy in contemporary panelled calf, slightly rubbed. £4800
First edition (third issue, see below) of Barrow's Cambridge lectures on optics and geometry, a work edited by Newton. 'Barrow was the first Lucasian professor of mathematics at Cambridge, and resigned in favor of his pupil, Isaac Newton. These lectures, in Latin, form his most important book, in which some of his remarkable optical discoveries are published for the first time and which undoubtedly influenced Newton. In the introductory Letter to the Reader he says: Mr. Isaac Newton, my colleague, a man of great learning and sagacity, revised my copy and noted such things as wanted correction, and even gave me some of his own, which you will see here and there interspersed with mine, not without their due commendations' (Babson catalogue).
The first book, Lectiones opticae, presents the latest theories and discoveries in pre-Newtonian optics, and incorporate some of Newton's earliest work. 'The most original contributions of the work are his method for finding the point of refraction at a plane interface and his point construction of the diacaustic of a spherical interface;: both were at once subsumed by Newton into his own geometrica optics, the the latter (in ignorance) was triumphantly rediscovered by Jakob Bernoulli in 1693' (DSB).
In the second work, Lectiones geometricae, 'he describes tangent problems with methods essentially equivalent to those in differential calculus and area problems with methods similar to those in integral calculus. He furthermore seems to understand that tangent and area problems are inverse to one another... He views both time and geometrical lines as composed of indivisibles, and geometrical magnitudes as generated by flowing points. The work on tangents contains the "characteristic" or "differential" triangle.' (Parkinson Breakthroughs p 110).
'In theory, as Jakob Bernoulli argued in 1691, Barrow's geometrical formulations could well have been the basis on which systematized algorithmic calculus structures were subsequently erected; but in historical fact the Lectiones geometricae were little read even by the few (Sluse, Gregory, Newton, Leibniz) qualified to appreciate them' (DSB).
The Lectiones opticae was published in 1669 and the Lectiones geometricae in the following year. This issue combines the original sheets of the two, with their original titles and dedications, along with a new title page for both works.
Provenance: the Earls of Macclesfield, Shirburn Castle, with engraved bookplate, shelfmark on front pastedown, and blindstamp Macclesfield crest on blank margins of first three leaves
Wing B945; Babson 249; Parkinson p 110; Wallis 358.4
£4800
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