THE Young Trigonometer's Compleat GUIDE Being the MYSTERY and RATIONALE Of Spherical Trigonometry Made CLEAR and EASY. VOL. II. In Two In Two PARTS. PART I. Containing Fifty Two Definitions. II. The Orthographic Projection of the Sphere in Twelve Theorems, and Ten Problems. III. The Stereographic_Projection in Eleven Theorems, and Nine Ppoblems. IV. The Projection of the Sphere on the Plane of the General Meridian, the Horizon, the Ecliptic, the Equinoctial, the Tropic of Capricorn, and of an Oblique Circle. V. Forty One Theorems explaining the Nature and Rationale of Spherical Triangles. VI. A Synopsis of all the Cafes of a Right Angled Spherical Triangle in all their Varieties; and the Solution thereof by the following Methods, viz. 1. By the Logarithmetic Canon. || VI. By Scale and Compaffes. II. By Natural Sines Tangents, VII. By the Globe or Sphere. VIII. By the Stereographic Pro &c. III. By the Lord Neiper's five IV. By the Sector. V. By the Sliding Rule. jection. IX. By the Orthog. Planifph. With the Doctrine of Oblique Spherical Triangles, and the Synopfis and Solution of all the Cafes and their Ambiguities, in feveral Methods. The Menfuration of the Area of a Spherical Triangle and Completion of a Solid Body. PART II. Containeth the Application of the Doctrine of Spherical Trigonometry to the following Mathematical Arts and Sciences. 1. To Aftronomy. 11. Aftrology. III. Geography. IV. Great Circle-Sailing. V. Sailing by the Glob. Chart. In both Volumes the chiefeft Care has been to collect all the feattered Appurtenances of this Art neceffary to compleat it; to explain it in a more eafy and perfpicuous Method, through all its Parts And to fhew its extenfive Ufe in all the Parts of Mathematical Science. By BENJAMIN MARTIN, Teacher of the Mathematicks in Chichefter, and Author of the Philofophical Grammar. LONDON: Printed for 7. Noon, at the White Hart in Cheapfide, near Mercers Chapel, MDCCXXXVI, 1736 51-17686 THE iii PREFACE. N my Preface to the first Volume, I have given a general Account of the Nature, Defign, and Use of this Work. In this Second are contained all the Parts of Spherical Trigonometry, which I have endeavoured to explain in a Method (as I think) the most easy and perfpicuous; fo that I hope what has been thought perplexing and abftrufe, will be with pleasure rendered attainable. 'Tis neceffary in order to make a Progrefs in this Science, for the young Student to be furnished with good Mathematical Inftruments. If he understood a little of the Latin and Greek Languages, it must be allowed that he would have a more fatisfactory Notion of the Terms of the Art, whereby he would have a more clear and lafting Idea of it impreffed on his Mind. He that will be a confiderable Proficient in the the Mathematicks, must not make it th musement of a few leifure Hours, but great Refolution and Application of Mind himfelf to the Study of it; for to arri a good Degree of Perfection, will requir Work and Toil of fome Years. Though it not be in the Power of fome to commence pleat Mafters in the higher Geometry, for of Leifure, Materials, Capacity, &c. Yet may learn how to tear a Ship by Ru Art, to Fortify a City, to Caft a Bomb Certainty, to Measure Heights and Difta to Measure or Plot Land, to Calculate E fes, and make all Sorts of Dials, &c. Things are the most useful, and to mak Means of attaining thefe both eafy and and delightful to fuch as defire to be let the Knowledge of thofe Excellent Sciences. been my chief Care and Study. Vale. |