(but to be fure a Father is apt to judge partially of his own Child) it is fo plain and eafy that to be comprehended, it need only to be read. I have taught by this Method for nearly 6 Years, and with fuch Success, that I am induced to lay it open to the World, in hopes that it may faci litate the Acquifition of fo ufeful a Science. I have in the first Place treated on Practical Geometry, but have used only fuch Problems as the Work requires; looking upon any other as Superfluous. You have, in the next Place, given a Compendium of Speculative Geometry, in Order to prepare the Learner for a right Understanding of the Demonflrations of the feveral Rules which are to be found in the Work. Some of the Propofitions I have felected from other Authors. ཉམ། As to the Plan purfued in folving the 3 Varieties &c. of Trigonometry, I fhall not speak of here, as a few Obfervations, by Way of an Advertisement to the Learner, are laid down on the the Subject and placed before the ft. Variety, and therefore fhall only fay, that I have rendered the Application of Trigonometry to Heights and Distances, as useful as poffible, by inferting various Kinds of Examples, feveral of which are borrowed from Dr. HUTTON's excellent Treatife on Menfuration. In short, I have endeavoured throughout the whole, to be as plain and concife as poffible, and indeed too much Pains and Labor cannot be bestowed (to make any Improvement) on the Science of Trigonometry, it is of fuch general Utility. It may with Propriety be termed the Bafis of mathematical Learning. The Surveyor in meafuring and laying out bis Lands knows the Utility of it. The Mariner daily and hourly experiences convincing Proofs of its falutary Effects. But doth it reft here? No-fee it mount up to the Skies to fupport the Aftronomer in his lofty Refearches, leads him on to new Difcoveries, finds the Magnitude, Difiance, Motion, Eclipfes &c. of the Heavenly Bodies, and explains the Caufe of the Diversity of Color in the Rainbow, to the natural PhiloSopher, Jopher. Such are the Powers of Trigonometry. It is to this Science that we owe many valuable Discoveries-Discoveries which would perhaps for ever have been numbered with the Arcana of Nature. Therefore, confidering its general Utility, I would advife every one who means to study to any great Length, to get acquainted with the Principles of it, for I am well assured, that no one who is ignorant of them, can make any great Progrefs in the mixed Mathematics. Ofman-Flat, Oct. 22d. 1792. RICHARD COCKREL. PRACTICAL GEOMETRY. CHA P.. I. SECTION I. I. DEFINITIONS. GR EOMETRY is a Science which treats of extended Quantities. Extention is ift. Length, 2dly, Length and Breadth, and 3dly, Length, Breadth and Thickness. 2. A Point is indivifible and therefore has no Parts. 3. A Line is generated by the Motion of a Point whether it be ftraight as A B, or in a curve as C D. с 4. Parrallel Lines A are fuch as are equidif tant in all their Parts, B B D from each other, as AB, and C D. A 5. Two right Lines as A B, and A Č, do, when A they meet, make what is called an Angle, as A. D 6. When one right Line falls on another right Line, and makes the Angles on each fide equal, it is faid to be perpendicular to the Line on which it falls; and the Angles are called right Angles. Thus: D C is perpendicular to A B; and A C B the Angle A CD equal the Angle D C B, is |