pany every Rule, let not that be any Difcouragement; for the Reason of many of the Operations will naturally arise as you go along, from the Connection of the Problems themselves. But if a Youth be unwilling to proceed without a Demonftration of every Thing, he may as well refufe to move or eat, because he has not by him a full Explication of the Caufe of Mufcular Motion, and the Nature of Maftication and Digeftion of his Food. Befides, many of the Rules arife only from Algebraical and Fluxionary Proceffes, which are impoffible for him to understand at present. The Young Geometer must therefore defer them till he has, by the following, or fome other Introduction, initiated himself into a Knowledge of the first Principles of this moft excellent and ufeful Science; which, we flatter ourselves, he may eafily, and in a short Time, accomplifh, by a careful Perufal of the following Work. (v) And, as moft Solutions in Geometry require fome Knowledge of Decimal Arithmetic and the Extraction of Roots, we have therefore judg'd it proper to prefix them, as neceffary to be gone over by the Learner, before he enters fully upon his Geometrical Studies. CONTENTS. To extract the Cube Root of a Vulgar Fraction The Ufe of the Cube Root A General Theorem for extracting the Roots of all PRACTICAL GEOMETRY To erect a Perpendicular on the End of a Right Line 73 To let fall a Perpendicular upon a Right Line given 74 76 PAGE To divide an Angle given into two equal Parts Parts To make an Equilateral Triangle To make a Triangle whofe Sides shall be equal to three given Right Lines To make a Square whofe Sides shall be equal to a given Right Line To make a Parallelogram whofe Length and Breadth fhall be equal to two Right Lines given To make a Rhombus, each of whofe Sides fhall be equal to a given Right Line To divide the Circumference of a Circle To draw a Circle through three given Points To defcribe a Geometrical Oval, the Length only To describe a Geometrical Oval by another Method Two Right Lines being given, to find a third Proportional Three Right Lines being given, to find a fourth Pro portional To find a mean Proportional between two Right Lines 93 94 95 96 97 98 given To divide a Right Line given into extreme and mean To defcribe a Spiral Line about a given Line to it To determine the Height of a Statue GEOMETRICAL THEOREMS The Explanation of fuch Characters as are generally used in the Solution of the following Geometrical Problems PLANOMETRY; OR THE MEASURING OF To measure a Square 100 108 To find the Area of a Parallelogram To find the Area of an Oblique Triangle To find the Area of a Regular Polygon To find the Area of a Circle 119 To find the Area of a Circle by another Method 120 To find the Area of a Circle, Semi-circle, or Quadrant 123 To find the Area of a Sector of a Circle 124 To find the Area of a Segment of a Circle 125 To find the Length of an Arch of any Circle 126 The Chord and Verfed Sine of a Segment of a Circle being given, to find the Diameter of the Circle 127 To find the Area of a circular Ring 128 To find the Area of a Crescent or Lune 129 To find the Area of an Oval 130 To find the Length of the Circumference of an Oval 131 To find the Area of any irregular Figure Application of the foregoing Problems STEREOMETY; OR THE MEASURING To measure, or find the Solid Content of a Cube 240 150 151 To measure the Fruftum of a Cone Another Way to find the Content of a Fruftum of a To measure the Middle Zone of a Sphere or Globe |