Å General View of the Contents of this Work. a THE System of Geometry is divided into two parts. The first contains Geometrical Definitions respecting Lines, Angles, Superficies; &c. The second part contains a number of Geometrical Problems necessary for Trigonometry and Surveying. The System of Trigonometry is also divided into two parts ; and teaches the solution of Questions in Right and Oblique angled Trigonémetry, by Logarithms and also by Natural Sines. The Treatise on Surveying is divided into three parts. Part first treats of measuring Land, and is divided into three Sections. The first contains several Problems respecting Mensuration, and for finding the Area of various Right-lined Figures and Circles. The second Section teaches different methods of taking the Survey of Fields; also to protract them, and find their Area in the manner commonly practised, and likewise by Arithmetical and Trigonometrical calculations, without measuring Diagonals and Perpendiculars with a Scale and Dividers ; interspersed with sundry useful rules and directions. The third Section is a particular explanation and demonstration of Rectangular Surveying, or the method of computing the Area of Fields from the Field Notes, by Mathematical Tables, without the necessity of plotting the Field. To this Section is added a use. ful Problem for ascertaining the true Area of a Field which has been measured by a Chain too long or too a elements of Surveying upon a larger scale ; and the system of Geometry and Trigonometry with which it is introduced, with the Problems for the mensuration of Superficies, as also the Mathematical Tables at the end, will be found useful for many other It would be well, therefore, for those who do not intend to become practical Surveyors, to acquaint themselves with what is here taught ; and with this view the following work is very proper to be introduced into Academies, and those nigher Schools which are designed to fit young men for active business in life. Indeed every person who frequently buys and sells land should learn to calculate the Contents of a Field Arithmetically ; a knowledge which may be acquired in a very little a time, from the particular explanation here given of that method. Notwithstanding the many Books already published on the subjects here treated upon, it was thought a work of this kind was really wanted, and that if judiciously executed it would be useful. It is more particularly , necessary at the present time in Connecticut, as the Legislature of the State have lately enacted a Law on the subject of Surveying, in consequence of which more attention must be paid to the Theory of that Art than has been common. These considerations induced the Compiler to select from various publications what appeared to him important; and to arrange the whole in a method best adapted, in his view, for teaching that useful Art, How far he has succeeded in his endeavor to simplify the subject, and render it easy to the Learner, must be submitted to the test of experience. À General View of the Contents of this work. a THE System of Geometry is divided into two parts. The first contains Geometrical Definitions respecting Lines, Angles, Superficies, &c. The second part contains a number of Geometrical Problems necessary for Trigonometry and Surveying. The System of Trigonometry is also divided into two parts ; and teaches the solution of Questions in Right and Oblique angled Trigord metry, by Logarithms and also by Natural Sines. The Treatise on Surveying is divided into three parts. Part first treats of measuring Land, and is divided into three Sections. The first contains several Problems respecting Mensúration, and for finding the Area of various Right-lined Figures and Circles. The second Section teaches different methods of taking the Survey of Fields; also to protract them, and find their Area in the manner commonly practised, , and likewise by Arithmetical and Trigonometrical calculations, without measuring Diagonals and Perpendiculars with a Scale and Dividers; interspersed with sundry useful rules and directions. The third Section is a particular explanation and demonstration of Rectangular Surveying, or the method of computing the Area of Fields from the Field Notes, by Mathematical Tables, without the necessity of plotting the Field. To this Section is added a use. ful Problem for ascertaining the true Area of a Field which has been measured by a Chain too long or too a Part second treats of laying out Land in various shapes. Part third contains sundry Problems and Rules for dividing Land and determining the true Course and Distance of dividing Lines, or from one part of a Field a to another. To this are added some observations réspecting the Variation of the Compass and the Attraction of the Needle ; with Rules for finding the Variation of the Compass and for drawing a Meridian Line. The Mathematical Tables are, A Traverse Table or Table of Difference of Latitude and Departure, calculated for every Degree and quarter of a Degree, and for any distance up to 50; a Table of Logarithms comprised in four pages, yet sufficiently extensive for common use ; a Table of Logarithmic or Artificial Sines, Tangents and Secants, calculated for every 5 Minutes of a Degree ; and a Table of Natural Sines calculated for every Minute. To these Tables are prefixed particular explanations of the manner of using them. GEOMETRY G EOMETRY is a Science which treats of the properties of Magnitude. PART I. a Geometrical Definitions. 1. A Point is a small Dot; or, Mathematically considered, is that which has no parts, being of itself indivisible. 2. A Line has length but no breadth. 3. A Superficies or Surface, called also Area, has length and breadth, but no thickness. 4. A Solid has length, breadth and thickness. 5. A Right Line is the shortest that can be drawn between two Points. 6. The inclination of two Lines meeting one another, or the opening between them, is called an Angle. Thus at B. Plate I. Figure 1. is an Angle, formed by the meeting of the Lines AB and BC. 7. If a Right Line CD. Fig. 2. fall upon another Right Line AB, so as to incline' to neither side, but make the Angles on each side equal, then those Angles are called Right Angles ; and the Line CD is said to be Perpendicular to the other Line. 8. An Obtuse Angle is greater than a Right Angle; as ADE. Fig. 3. |