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THE

J.A Young Trigonometer's Compleat GUIDE. Spherical Trigonometry

Being the Mystery and RATIONALE of

Made CLEAR and EASY. VOL. II. or TwoPARTS. PART I. Containing Fifty Two Definitions. II. The Ortho

graphic Proje&tion 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 Equino&tial, 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 ali their Va.

rieties, and the Solution thereof by the following Methods, viz. I. By the Logarithmetic Canon., VI. By Scale and Compases. 11. By Natural Sines Tangents,

VII. By the Globe or Spbere. &c.

VIII. By the Stereographic ProIII. By the Lord Neiper's five jection. Circular Parts.

. IV. By the Settor.

. V. By the Sliding Rule. With the Do&trine of Oblique Spherical Triangles, and the Synopsis

and Solution of all the cases and their Ambiguities, in several Methods. The Mensuration of the Area of a Spherical Trian.

gle and Completion of a Solid Body. PART II. Containeth the Application of the Do&trine of Spherical

Trigonometry to the following Mathematical Arts and Sciences. 1. To Astronomy

IV. Great Circle-Sailing. 11. Aftrology:

V. Sailing by the Glob. Chart. III. Geography.

VI. Dialling. In both Volumes the chiefest Care has been to collea all the scat

tered Appurtenances of this Art necessary to compleat it ; to explain it in a more easy and perspicuous Method, through all its Parts : And to Thew its extenGive Use in all the Parts of Ma.

thematical Science. By BENJAMIN MARTIN, Teacher of the Mathema

ticks in Chichefter, and Author of the Philosophical Grammar, LONDON: Printed for 7. Noon, at the White-Hart in Cheap

fide, near Mercers-Chapel. MDCCXXXVI.

1936

QA 533 M38

vi?

iii

51-17686

THE

PREFACE.

N my Preface to the first Volume, I have given a general Account of the

Nature, Design, 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 perspicuous; so that I hope what has been thought perplexing and abstruse, will be with pleasure rendered attainable. 'Tis necessary in order to make a Progress in this Science, for the young Student to be furnished with good Mathematical Instruments. It be understood a little of the Latin and Greek Languages, it must be allowed that he would have a more satisfaktory Notion of the Terms of the Art, whereby he would have a more clear and lasting Idea of it impressed on his Mind. He that will be a considerable Proficient in

the

the Mathematicks, must not make it the Amusement of a few leisure Hours, but with great Refolution and Application of Mind, fet himself to the Study of it ; for to arrive to a good Degree of Perfection, will require the Work and Toil of some Years. Though it ma) not be in the Power of fome to commence compleat Masters in the higher Geometry, for want of Leisure, Materials, Capacity, &c. Yet they may learn how to stear a Ship. by Rules of Art, to Fortify a City, to Calt a Bomb witł Certainty, to Measure Heights and Distances to Measure or Plot Land, to Calculate Eclipses, and make all sorts of Dials, &c. . These Things are the most useful, and to make the Means of attaining these both easy and plain and delightful to such as desire to be let inte the Knowledge of those Excellent Sciences, ha been my chief Care and Study.

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