Elements of conic sections in three books: in which are demonstrated the principal properties of the parabola, ellipse, and hyperbola

xii+332 pages with woodcut ornament to title and 9 folding engraved plates, Octavo (8" x 5 1/4") bound in period mottled calf, spine in compartments and with modern (to style) brown leather label. (ESTC T140561) Fist edition. Elements of Conic Sections in Three Books: In Which Are Demonstrated the Principal Properties of the Parabola, Ellipse, and Hyperbola is an influential 18th-century mathematical treatise written by the Scottish mathematician Richard Jack and originally published in 1742. The work is highly regarded as a classical reference for university-level study in synthetic geometry. It provides definitions, theorems, and proofs using purely geometric methods over algebraic abstractions. Book I: The Parabola – Focuses heavily on how the curve is generated and details key features like its axis, vertex, focus, directrix, diameters, ordinates, and tangents. Book II: The Ellipse – Establishes properties regarding conjugate diameters, axes, foci, and tangents, demonstrating foundational rules for how ellipses are structurally characterized. Book III: The Hyperbola – Explores the unique attributes of the hyperbola, focusing extensively on its asymptotes, conjugate diameters, foci, and tangency criteria. Richard Jack (d.1759) gave lectures on natural and experimental philosophy, first in Edinburgh and later in London. He also worked as a military engineer. The work was well-regarded and its subject matter features in a substantial article on conic sections in the first edition of the Encyclopaedia Britannica, 1771, which is credited to Jack. Condition: Corners bumped and rubbed, boards scuffed some internal spotting else good to very good.…