Books

Bound in contemporary vellum, manuscript title to spine (slightly worn, lightly soiled, small loss to spine). A very good copy with intermittent foxing and a small stain to the upper margin. A slim worm-trail has been discreetly filled in the upper blank margin of the opening leaves. 17th c. owner's inscription to title-page. Complete with the errata leaf and the leaf added after p. 26 referring to 'propositio' LXIV. First edition of the foundation work that "changed the course of optics" (DSB), containing both the first accurate theory of lenses and the formation of images by the eye. The book is a direct result of the recently published "Sidereus Nuncius" (1610), in which Galileo announced his observations made with the telescope, among them that the Moon, thought to be smooth, was in fact mountainous and craggy; and that Jupiter had moons of its own. "In order that the enormous possibilities harbored in [the telescope] could develop it was necessary to clear up the theoretical laws by which it worked. And this achievement was reserved solely for Kepler. With the energy peculiar to him, inside of a few weeks, in the months of August and September of 1610, he composed a book tracing basically once and for all the laws governing the passage of light through lenses and systems of lenses." (Caspar) The book also contains Kepler's description of his own modified version of the telescope, known to us as the "astronomical" or "Keplerian" telescope (see below.) In his preface, Kepler discusses the further discoveries that Galileo had made with his telescope subsequent to the publication of his "Sidereus Nuncius", and includes four letters by Galileo, dated 13 October 1610, 11 December 1610, 1 January 1611, and 26 March 1611, which he sent to Kepler via the Medici ambassador at Prague. These new Galilean discoveries include his observations that Saturn is not a single orb, but rather three orbs close together (the telescope was too weak to clearly reveal the planet's rings); and that Venus has phases and reflects the Sun's light (rather than generating its own), which evidence proves that Venus orbits the Sun. "[Kepler's 'Dioptrice'] is divided into 141 theorems which are distinguished as definitions, axioms (theorems needing no proof), problems (theorems to be proved by experiments), and propositions (theorems which follow out of definitions and axioms by logical conclusions). "The author begins with the law of refraction which, indeed, he was here as little able to express exactly as in his earlier work about optics. Since in the 'Dioptrice' however, only small angles of incidence are dealt with, he managed well by assuming the proportionality between the angle of incidence and that of refraction. He himself determined the ratio by measurements. By investigating the path of a ray in a glass cube and three-sided prism he discovered total reflection. "Next in his exposition comes the treatment of the double-convex converging lens. He sets to work with great thoroughness. There appear the ideas well known to us of the real and virtual, the upright and inverted image, the distance of the image and the object, the magnification or reduction of the image. From the path of the ray for a simple lens he proceeds to two- and three-lens systems. In problem eighty-six in which he shows 'how with the help of two convex lenses visible objects can be made larger and distinct but inverted' he develops the principle on which the so-called astronomical telescope is based, the discovery of which is thus tied up with his name for all time. "Further on follows the research into the double concave diverging lens and the Galilean telescope in which a converging [convex] lens is used as objective and a diverging [double concave] lens as eyepiece. By the suitable combination of a converging lens with a diverging lens in place of a simple object lens he discovers the principle of today's so-called telescopic lens by which an inverted real image of an object can be<f232/>