The young geometrician's companion [electronic resource] : being a new and comprehensive course of practical geometry; Containing, I. An easy Introduction to Decimal Arithmetic, with the Extractions of the Square, Cube, Biquadrate, and other Roots. II. Such Definitions, Axioms, Problems, Theorems, and Characters, as necessarily lead to the Knowledge of this Science. III. Planometry, or the Mensuration of Superficies; as Squares, Parallelograms, Triangles, Circles, Segments, &c. IV. Stereometry, or the Mensuration of Solids; as Cubes, Parallelopipedons, Prisms, Cones, Pyramids, Cylinders, Spheres, Frustums, &c. V. The Sections of a Cone; as Ellipses, Parabolas, Hyperbolas, Spheroids, Conoids, Spindles, &c. VI. The Platonic Bodies; as Tetraedrons, Hexaëdrons, Octaëdrons, Dodecaëdrons, and Icosaëdrons. To Which is Added A Collection of curious and interesting Problems, shewing that Lines and Angles, (and consequently the least Particle of Matter) may be divided in infinitum; that Superficies and Solids may be so cut as to appear considerably augmented; and, that the famous Problem of Archimedes, of moving the Earth, is capable of an easy and accurate Demonstration. Calculated for the Use of Schools and Academies. And is necessary to be gone through by the Scholar before he proceeds to the higher and more abstruse Branches of the Mathematics, Indivisibles, Infinites, Algebra, and Fluxions. By the Reverend R. Turner, LL. D. Rector of Comberton, and Vicar of Elmly; Author of a View of the Earth, or a Short System of Modern Geography-View of the Heavens-Heavens Surveyed-Plain Trigonometry made Easy-And a New Introduction to Book-Keeping. .