A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical Applications

xxviii+419+errata pages with diagrams. Octavo (8 1/2" x 5 1/4") bound in full leather with black label to spine in gilt lettering. First edition. A Treatise on Plane and Spherical Trigonometry: With Their Most Useful Practical Applications is a historic mathematical textbook written by the prominent English mathematician and educator John Bonnycastle and originally published in 1806.The book is a comprehensive manual designed to bridge classical geometric theory with the operational demands of the 19th century, focusing on fields like navigation, surveying, and astronomy. The treatise is systematically split into two distinct geographical domains of mathematics: Part 1: Plane Trigonometry: Focuses on two-dimensional surfaces. It covers the measurement of angles, trigonometric functions (sine, cosine, tangent, etc.), the construction of logarithmic tables, and methods for solving standard right-angled and oblique triangles. Part 2: Spherical Trigonometry: Focuses on triangles drawn on the surface of a sphere, utilizing spatial intuition. This section includes calculating spherical excess, properties of great and small circles, and formulas crucial for three-dimensional geometry. What made Bonnycastle’s work highly regarded was its departure from purely abstract math to emphasize real-world execution: Astronomy: Calculating the positions, coordinate systems, and paths of celestial bodies on the celestial sphere. Navigation: Determining a ship's position, heading, and great-circle sailing distances across the Earth's curved surface. Geodesy & Surveying: Mapping and measuring large areas of land where the curvature of the Earth must be mathematically factored into the calculations. Bonnycastle's greatest mathematical contribution, namely the books which he has written. The first, written at an early stage in his career, was The Scholar's Guide to Arithmetic (1780). The popularity of the book is clearly seen from the fact that in 1851 the 18th edition was published. No less popular was Introduction to Algebra (1782). The 13th edition of this work, with addenda by his son Charles Bonnycastle, was published in 1824. This was not the only book Bonnycastle published in 1782 for in the same years Introduction to Mensuration and Practical Geometry appeared in print. This was another highly successful work with an 18th edition published in 1823. His next book Introduction to Astronomy (1786) was written for those without a mathematical background. Bonnycastle's Elements of geometry (1789) contains the propositions from Euclid's Elements books, 1-6, 11 and 12 with "critical and explanatory notes" by Bonnycastle. He believed that the approach to geometry exhibited by Euclid provided an outstanding method for teaching young people logical and precise thinking. He therefore followed Euclid's presentation rather closely. He published another geometry book nearly 20 years later, A Treatise on Plane and Spherical Geometry (1806). Condition: Boards scuffed, corners bumped and rubbed, inner hinges cracked, some light notations to end papers, spine head chipped, previous owner's stamp to introduction pages, some internal spotting and soiling else a good copy.…