Not only the practical RULES, but also the
REASONS and DEMONSTRATIONS of them;

With so much of

The THEORY, and of universal ARITHMETICK
or ALGEBRA, as are necessary for the better under-
standing the PRACTICE and DEMONSTRATIONS.

WITH

A GENERAL PREFACE, including a PANEGYRIC,

on the Usefulness of Mathematical Learning.

By BENJAMIN DONN,

Of Biddeford, Devon,

Teacher of the Mathematicks, and Natural Philosophy, on

NEWTONIAN Principles.

Nullius in Verba.

LONDON:

Printed for W. JOHNSTON, in St. Paul's Church-Yard
and P. DAVEY and B. Law, in Ave-Mary-Lane.

MDCCLVIII.

C

درد

Quantch 1-25-43 46804

As a proper Judge of the Subject, and

in Gratitude for Favours received, this

Volume is with due Respect dedicated by

His most

Obedient Servant,

1

BENJAMIN DONN.

1

THE

249.

GENERAL PREFACE.

...

T

HE Design of a Preface, in its greatest Extent, is first to give the History of the Art treated of, then to shew that it is a useful Science, and, lastly, to give an Account of the Work. For the first of these, and the Ufefulness of the particular Arts, the Reader is referred to the Preface to the several Essays; it being the Intention of this Preface only to say something on the Usefulness of Mathematical and Mathematico-philosophical Learning in general, and give fome Account of the Design of the intended Work.

It being common to hear many Perfons, and some who would be thought Men of Learning, demanding the Use of the Mathematics, calling the Study of them a dry Study, and affirming that it serves only for Amusement, it is, not only not improper, but in a Manner necessary, to spend a few Pages, in removing these Objections: In which, we shall endeavour to make evident, (not so much by Observations our own, as by * select Passages from esteemed Authors) that the Use of the Mathematics is very great; and, therefore, the above Assertions groundless, and confequently, founded either on Ignorance, or Malice.

It is an Observation of † M. Fontenelle's, " that People very rea" dily call useless what they do not understand. It is a Sort of Re

venge; and, as the Mathematics and Natural Philofophy are "known but by few, they are generally looked upon as useless. "This is the Fate of Sciences which are studied and improved but " by a few."

In this Panegyric, or Eulogium, we shall observe the following Order: 1 To thew the Dignity of those Sciences. 2. Their Ufe to all Men in general, in the Improvement of the Mind. 3. The Advantage of those Sciences in some particular Professions. 4. Laftly, to make fome general Inferences by Way of Conclusion,

1. Of the Dignity of the Mathematical Sciences.

‡ In all Ages and Countries, where Learning hath prevailed, "the Mathematical Sciences have been looked upon as the most * confiderable Branch of it. The very Name. Μάθησις implies