To continue a Right Line to a greater Length than can be drawn by a Ruler at one Operation To shew that an Angle, as well as a Line, may be con- To find the Solidity of a Circular, Elliptical, Parabo-- lical, or Hyperbolical Spindle To find the Solidity of a Frustum, or Segment of an Elliptical, Parabolical, or Hyperbolical Spindle To find the Solidity of a Wedge To cut a Tree so that the two Parts measured separately To determine, geometrically, the Point in a given Right Line, from which the Sum of the Distances of two Objects shall be the least possible PLATO, a celebrated Greek Philofopher, who flou rished about 350 Years before Chrift, was used, in his Lec tures, to illustrate and demonstrate to his Pupils the Trut of his Propofitions by Geometry; and EUCLID, who live about fourscore Years after him, being educated in PLATO School, is faid to have compiled his whole System of Ge metrical Elements only in Reference to Applications of tha Kind. But now, the Utility of Geometry extends to ever Art and Science in Human Life. ERRATUM. Page 73, line 7, after the Period, read, " With the fame Extent, a one Foot in b, make a Mark at c." THE YOUNG Geometrician's Companion. T DECIMAL. ARITΗΜΕΤІС. HIS is a particular Kind of Arithmetic, which enables us to treat Fractions as whole Numbers; and it is of the greatest Ufe in all Parts of Mathematical Learning. It receives its Name from Decem (Latin for Ten), because it always supposes the Unit or Integer, let it be what it will, whether i Pound, 1 Mile, 1 Gallon, to be divided into ten equal Parts, and each of those into tο more, and fo on, as far as we please. Definitions. A Fraction is a Number expressing some Part or Parts of an Unit or Integer: So the Half, a Third, or Tenth Part of any Thing are Fractions. Every Fraction consists of two Numbers, the Numerator, and the Denominator. The Denominator shews into how many Parts the Unit or Integer is divided; and the Numerator is the Number expreffing how many of those Parts are intended by the Fraction. |