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N the Study (as well as in the Teaching of any Art or Science, a Gradual Proceeding therein, ought Firft, and Principally, to be confidered: For, It is one thing to Teach; and another How to Teach: And, according to the Adage, Qui bene diftinguit, bene Docet.
Now, the Design of this Book, being for the Directing and Inftru&ting of fuch as would apply themselves to the Study of any Mathematical Science, so as to become fuch a Proficient therein, as to give a Demonftrable Account of what he does; must not attempt, at the firit Onfet, to fall directly upon that Part he principally aims at, but firft acquaint himself well with fuch Elements as concern, and are subservient to, them all.
And to that end, The feveral Parts and Sections of this Book, are difpofed in fuch Order; That, Beginning with the First Part (which is as a KEY to give you entrance into the GATE; which is the Second Part; Through which, having perfectly pafled, you may confidently proceed to fall upon the Study (or Practice) of any Mathematical Science; And not only on thofe that I have here (by my HAND-MAID, in the Third Part) directed you to; but to any other you shall attempt: TRIGONOMETRIA being the Bafis, Foundation; nay, the very Primum Mobile, of all the rest.
For Illuftration whereof, I have applyed the Doctrine of Triangles to Practice (in the feveral Sections of the Third Part) in the Solution of fuch Problems, as are of frequent use in several So in the First, Parts of the Mathematicks. Which teacheth how to take all manner of Heights and Distances, acceffible or inaccessible: And in the Sixth, which treateth of Navigation both by the Plain Sea-Chart, and that called Mercators; in both which, I have first shewed how Geometrically, by Scale and Compaffes, to lay down (upon Paper) a Figure answerable to the Question Propounded: In which Figure, so laid down, you will have conftituted a Right-Lined Triangle or Triangles, of fome kind or other, i. e.
either Right or Oblique-Angled; And in it difcovered what Parts thereof are Given, by the demand in the Question; and then the Part or Parts Unknown will be fuch (as being found) will answer the Queftion demanded: And herein the Excellency of the Doctrine of Plain Triangles is in part made manifeft.
Likewise, In the 1st. 2d. 3d. 4th. and 5th. Sections, which treateth of Cofmography; and therein of Geography, Aftronomy and Dialling: I do firft declare, and fhew how the Operation of the Question or Proportion, is to be performed upon the Terrestrial or Celestial Globe (according as the thing propofed does require.) Which Question being refolved upon the Globe; and the Globe refting in the fame Pofition it was when the Question was refolved thereupon: You will upon the Body of the Globe, (by the great Circles thereon described, and thofe appendant to it) apparently discover a Spherical Triangle or Triangles Conftituted; in which (according to the Tenor of the Question) you will plainly perceive what Parts thereof are Given; and then, the other Parts being found, must neceffarily Answer the Question Propounded: And herein, in fome measure, is the Doctrine of Spherical Triangles made applicable to all the above-named Practices. And Moreover, by Projecting of the Sphere,
as is done for the Geographical Problems in Part III. Section the Second. And for Aftronomical Problems, as is fhewed in PART II. Section II. Of Projection of the Sphere in Plano, &c.
Alfo in the VIIth. Section, Which treats of the Theories, and finding the Places of the Planets, &c. there the Doctrine of Triangles both Plain and Spherical, are joyntly concerned: So that, let your Mathematical Practice or Study be, Opticks, Perspective, Fortification, Gunnery, or any other Mathematical Art: The moft Problems relating to any of them, must be beholding to Trigonometry for their Solutions.
And now I have but one thing more to adver tife the Reader of: That, Whereas in the performances of all the Operations in the several Parts of this Book, the First (which treats of Practical Geometry only) excepted, there is continual Use to be made of a CANON, TRIGONOMETRI CAL; or TABLES of Artificial SINES, GENTS and LOGARITHMS; So that the Reader. cannot expect but that fuch TABLES fhould have been Added unto thefe Precepts. And, indeed, it was fo intended, but that almost in every Book that hath any thing of the Menfuration of Triangles in it, there are fuch Tables Printed; and that one or other of them may be in every Man's Hands; and becaufe all the Problems in this Book