Youth ought to learn the Elements from shorter Treatifes, and afterwards at their leifure should read gene ral Systems, in order to perfect them.

For thefe Reafons, I have ventured to publish this Small Treatife; wherein I have made it my chief Bufinefs to keep a due Medium betwixt the two Extremes, into which the fpeculative Writers on the one Hand, and the practical ones on the other are apt to run. I have laid down all the ufeful Rules, and troubled the Reader with no more of the Theory than is necessary to explain them. I have also explained the principles of Menfuration, Surveying, aud Gauging, and fhewed how they are applied to Practice, in order that my Book might better anfwer the particular end for which it is defigned, namely the Instruction of the young Gentlemen of Mr WATTS Academy.

As for the particular Contents of each Section, the Reader will find them at the end of the Book, and therefore they need not be repeated here. I shall only obferve, that I have defignedly omitted Great Circle Sailing, as being only fpeculative, and depending on Spherical Trigonometry, which would require a particular Volume to explain it. There are indeed two or three Problems neceflary in Practice, which depend on the Refolution of Spherical Triangles; but for the Solution of thefe, I have laid down fuch clear and fhort

mistake the manner of applying Rules that no body can

L

I know, fome are of Opinion, that the Demonftrations are not to be easily learnt by every Capacity, on which account they teach the Practice only. This Book is therefore fo written as to ferve for their purpose likewife, because they may take the Rules alone without their Rea fons. It is true indeed, that there may be great Difficul ty in finding out a proper Demonftration, but after it is found, it is easier to be understood than that of which it is the Reafon and therefore they who are not capable of understanding the Demonftrations, are much less capable of understanding the Practical Rules which depend on

them. And I am inclined to believe, that what is commonly attributed to want of Genius in the Scholar, is often owing to want of Method and Perfpicuity in the Mafter.

In preparing this Treatife for the Press, I own myself obliged to Mr STIRLING, F.R.S. (of the Academy in Tower-Street) who on his first feeing my Papers, fo far approved both of the Matter they contained and of the Order in which they were put together, as to think them fit to be made publick with very little Alteration.

I acknowledge myself alfo obliged to that most excellent Book of Mr HODGSON, entituled a Syftem of Mathematicks, which I take to be by far the most compleat Treatife on this Subject, both as to Theory and Practice. And on this occafion I cannot but take notice of a late Writer, who has accufed him and all Writers on Navigation of being guilty of a very grofs Error; which is, that they took Departure and Meridional Distance to be the fame. Indeed in Plain Sailing he took them to be the fame and is still of the fame Opinion, notwithftanding what has been faid to the contrary. But that be did not in other Cafes take them to be the fame will appear by the following Paffage of bis Book at the end of Mercator's Sailing. "To give the Learner all the

Helps neceffary to a right Understanding of this "most useful Part of Sailing, I fhall endeavour

66

(before I conclude this Part) to fet his Notions right, concerning Difference of Longitude, Me"ridional Distance, and Departure; and let him "fee, that tho' these are fynonymous Terms in "Plain Sailing, conftantly fignifying the fame

thing, and in every Question are reprefented by "the fame Right Line, yet in the true Sailing they "are effentially different one from another; and "and in the fame Problem, are, as they really "fhould be, reprefented or expreffed by different "Lines, and are of different Values.

Now

Now after reading this Paffage, I fall leave it to the Publick to judge as they think fit of the Writer, who owns that he has feen Mr HODGSON's Syftem of Mathematicks by bis quoting it, and at the fame time affirms that he never met with an Author who made any Distinction between Departure and Meridional Distance.

And I hope I may be excufed for vindicating the Author to whom I have profeffed myself fo much obliged, left, from my Silence on this Head, it fhould be fufpected that I were guilty of the fame Error which is unjustly laid to bis Charge.

SECT. I.

Of fuch Geometrical Propofitions as are abfolutely neceffary for NAVIGATION.

ART. I.

nitude.

GE

EOMETRY is that Science whereI in we confider the Properties of Mag

2. A Point is that which is not made up of Parts, or which is of itself indivifible, as A.

3. A Line is a Length without Breadth, as B.

4. The Extremities of a Line are Points; as the Extremities of the Line AB, are the Points A and B.

5. If the Line A B be the nearest Distance between its Extreams A and B, then it is call'd a strait Line, as AB in the former Figure; but if it be not the nearest Distance, then it is called a curve Line, as A B.

6. A Surface is that which is confidered as having only Length and Breadth, but no Thickness, as B.

.

B

7. The Terms of a Surface are Lines.

8. A plain Surface is that which lies equally between its Extremes.

9. The Inclination between two Lines meeting one another, (provided they do not make one con