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

With fo much of

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

WITH

AGENERAL PREFACE, including a PANEGYRIC,
on the Usefulness of Mathematical Learning.

By BENJAMIN DO N N,
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.

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+ One of His Majefty's Juftices of the Peace,

AND

Deputy Lieutenant, for the County of Devon;

As a proper Judge of the Subject, and

in Gratitude for Favours received, this

Volume is with due Refpect dedicated by

His most

Obedient Servant,

BENJAMIN DONN.

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GENERAL PREFACE.

HE Defign of a Preface, in its greatest Extent, is firft to give the Hiftory of the Art treated of, then to fhew that it is a useful Science, and, laftly, to give an Account of the Work. For the firft of these, and the Ufefulness of the particular Arts, the Reader is referred to the Preface to the feveral Effays; it being the Intention of this Preface only to fay fomething on the Usefulness of Mathematical and Mathematico-philofophical Learning in general, and give fome Account of the Defign of the intended Work.

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It being common to hear many Perfons, and fome who would be thought Men of Learning, demanding the Ufe of the Mathematics, calling the Study of them a dry Study, and affirming that it ferves only for Amusement, it is, not only not improper, but in a Manner neceffary, to spend a few Pages, in removing thefe Objections: In which, we shall endeavour to make evident, (not fo much by Observations our own, as by felect Paffages from efteemed Authors) that the Ufe of the Mathematics is very great; and, therefore, the above Affertions groundless, and confequently, founded either on Ignorance, or Malice.

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*

It is an Obfervation of †M. Fontenelle's, " that People very readily call useless what they do not understand. It is a Sort of Revenge; and, as the Mathematics and Natural Philofophy are "known but by few, they are generally looked upon as ufelefs."This is the Fate of Sciences which are studied and improved but "by a few."

In this Panegyric, or Eulogium, we fhall obferve the following Order: 1 To thew the Dignity of thofe Sciences. 2. Their Ufe to all Men in general, in the Improvement of the Mind. 3. The Advantage of thofe Sciences in fome particular Profeffions. 4. Laftly, to make fome general Inferences by Way of Conclufion,

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 Mános implies * We have chofen this Method, because it is natural to fuppofe, that the Authority of great Names will be much more perfuafive, than any Affertions barely

our own..

In his Preface to the Memoirs of the Royal Academy of Sciences at Paris, in the Year 1699; and tranflated in Mifcellanca Curiofa.

‡ Essay on the Usefulness of Mathematical Learning,

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