Lectiones opticae & geometricae: in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur. 2 parts in 1 volume

London: William Godbid for Robert Scott, 1674. 1st Edition. Hardcover. Very Good. 1st Edition. Hardcover. 4to - over 9¾ - 12" tall. 4to (202 x 152 mm). [12], 127 [1], [2], 147, [3] pp., 27 folding engraved plates. With the 'Benevolo Lectori' preliminary leaf bound before the 'Lectiones Geometricae.' Bound in a contemporary English speckled calf with a spine divided by raised bands into 6 richly gilt compartments. The book-block is strong and the hinges hold very firmly. The leather upon the front hinge is lightly cracked, but the cords hold firmly. The boards themselves, the edges and the corners show only slightest wear. Internally, the leaves are toned, but generally clean, with ample margins and clear print throughout. There is light occasional spotting and little marginal staining, which remains quite unobtrusive. The title page show a very small burn hole not affecting text, the second F2 got a small burn-hole in the outer margin, not affecting text as well. The 27 folding engraved plates are excellent impressions, some browned a bit stronger. This is an unusually attractive example of a rare work. ----

Wing B 945; Babson 249; Wallis 358.4; Sotheran 5816 (2); DSB I, 475. Very rare early issue of the first edition without the 'Addenda Lectionibus Geometricis' (pp. 149-151) and plate 13 of the second part found in later issues. In this issue, plate 12 is in uncorrected state with missing lines in figure 220 finished by hand. This plate was re-ingraved for the later issues. "Many problems connected with the reflexion and refraction of light are treated with ingenuity. The geometrical focus of a point seen by reflexion or refraction is defined; and it is explained that the image of an object is the locus of the geometrical foci of every point on it. Barrow also worked out a few of the easier properties of thin lenses; and considerably simplified the Cartesian explanation of the rainbow. The geometrical lectures contain some new ways of determining the areas and tangents of curves. The most celebrated of these is the method given for the determination of tangents to curves" (Sotheran).
Isaac Barrow (October 1630 - 4 May 1677) was an English Christian theologian, and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for the discovery of the fundamental theorem of calculus. His work centered on the properties of the tangent; Barrow was the first to calculate the tangents of the kappa curve. Isaac Newton was a student of Barrow's, and Newton went on to develop calculus in a modern form. In 1662 he was made professor of geometry at Gresham College, and in 1663 was selected as the first occupier of the Lucasian chair at Cambridge. During his tenure of this chair he published two mathematical works of great learning and elegance, the first on geometry and the second on optics. In 1669 he resigned his professorship in favour of Isaac Newton. In 1669 he issued his 'Lectiones XVIII,' which would come to be known as the 'Lectiones Opticae.' The 'Lectiones Geometricae' were first published in 1670, and the two volumes together, revised, corrected, edited and slightly expanded by Collins and Newton, were first published in 1674 (the edition offered here). It is said in the preface that Newton revised and corrected the 'Lectiones Opticae.'
In this 1674 first complete edition, the title and preliminary matter for the 'Lectiones Geometricae' were supposed to be cancelled. Indeed, ESTC states that "no copy is recorded with the original second title page retained." In addition to the new title-page, this copy actually contains the uncancelled preliminary material. Barrows work was edited by John Collins and Isaac Newton, and corrected and revised by Issac Newton, thus constituting one of Newton's earliest publications.