OF Plaiu and Spherical Trigonometry; Together with the GEOMETRY, And the feveral PROJECTIONS of the SPHERE The whole Demonftrated and Illuftrated By J. Harris, A. M. F. R. S. and Chaplain to LONDON: Printed for Dan. Midwinter at the Rofe and Crown 174786 ра TO THE READER. T HO' there are very many Books on this Subject already extant, fome of which are very well done yet I perfuade my self, that the Plainnefs and the Brevity of this Tract will make it very useful and Serviceable to many Perfons to whom fome larger Books may feem both Diffi cult and Tedious: And I am apt to think that a few Hints may be met with here, which will ferve to give the Reader a much clearer and diftin&ter Notion of the Nature of Trigonometry, than is ordinarily to be met with in Books of this Subject; efpecially as to the Rationale of Sta A 2 ting ting a Cafe, and Forming a Canon to work; by which till a Perfon can readily do, he is by no means a Mafter of this Science. For tho' a Man may only by Rules contrived to help the Memory, retain a thing a great while, especially if Practice make it ready and familiar to him; yet 'tis, I think, much better, in order to prevent Miftakes or Blunders sor to avoid being puzzled with Some Difficulties, which either the Nature of a Question, or the Manner of propofing it, may fometimes occafion: 'Tis much better, I fay, That the Learner be let into the whole Mystery, Jee the Thing to the very bottom, and be permitted to take no Steps, but where be bath folid Demonftration to ftand or proceed upon; and then he will be out of danger of either being deceived himself, or expofing the Reputation of bis Teacher. 2 To the Reader I question not but this little Book will be an Inftance of the Poffibility and Facility of proceeding in fuch a Method; and will convince any unprejudic'd Perfon, that the Theory and Practice together, of any Part of Mathematicks, may be taught as foon as the Practice alone without the Theory. The Reafon of its Publication was, that it might be in the Hands of my Auditory at the Publick Mathematick Lecture in Birchin-Lane, when I am explaining this Subject to them; and where, as foon as I have finished Plain Trigonometry, I shall proceed to read Spherick Geometry, and Projection of the Sphere in Plano, and then Spherick Trigonometry; which laft Science cannot be well underflood, without the Learner go in the Order and Method I have now mentioned. And this Hint may ferve to fbew 1 |