Isaac Barrow / Sir Isaac Newton (editor) / Edmund Stone (translation) - Geometrical Lectures: Explaining the Generation, Nature and Properties of Curve Lines. Read in the - 1735

Geometrical Lectures: Explaining the Generation, Nature and Properties of Curve Lines. Read in the University of Cambridge, By Isaac Barrow, D.D. Professor of the Mathematicks and Master of Trinity College &c. Translated from the Latin Edition, revised, corrected and amended by Sir Isaac Newton. By Edmund Stone, F.R.S. – Isaac Barrow / Sir Isaac Newton (editor) / Edmund Stone (translation)

London: Printed for Stephen Austen, at the Angel and Bible in St. Paul’s Church Yard, 1735. [2], vi, 309, [3] pages, 11 fold-out plates. 18.8cm x 12cm. Quarter leather binding with marbled boards and a gilt lettered spine with 5 raised bands. First English edition of this cornerstone of mathematical history, containing the seminal geometric lectures delivered by Isaac Barrow at the University of Cambridge. Translated from the original 1670 Latin Lectiones Geometricae by the Scottish mathematician Edmund Stone, this volume represents a critical evolutionary step in the development of modern infinitesimal calculus. The book features 11 fold-out engraved copperplate illustrations containing the complete suite of intricate geometric diagrams and curve constructions necessary to demonstrate the mathematical proofs. Originally revised, corrected, and amended by Barrow’s most famous pupil, Sir Isaac Newton, these lectures systematically investigate the generation, nature, and properties of curved lines through motion and velocity. The text introduces Barrow's pioneering geometric methods for determining tangents, maxima, and minima, famously featuring the "differential triangle" that provided the foundational conceptual framework later formalized by Newton and Leibniz into differential and integral calculus. An essential, highly significant work bridging seventeenth-century geometry and the dawn of modern mathematical analysis.

Rubbing, bumping, wear, and discoloration to the boards and spine. The top and the bottom of the spine are cracked at both hinges. Defunct library sticker on the bottom of the spine. Pen and pencil markings on the front pastedown endpaper. The front free endpaper has some damage at the bottom and is nearly fully loose. Defunct library sticker on the verso of the front free endpaper. The frontispiece is missing, but otherwise the book is complete. Pen and pencil markings on the title page and pencil markings on its verso. Page numbering corrected with pen on page 225. Some of the fold-out plates are cut short at the top, affecting the content slightly (see photos, all plates are photographed). Some browning, spotting, fingerprints, and the occasional creasing of the corners throughout. The text and illustrations are clear, and the binding is a bit soft in the front, but holds well for the rest. Overall, a well-preserved copy lacking the frontispiece in good condition.