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With their Application to the SOLUTIONS of a

Variety of PROBLEMS, which are of great Use
in measuring Heights and Distances of Places, sur-
veying of Counties, Sea-Coafts, &c.

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By BENJAMIN DONN,
Teacher of the Mathematics, and Lecturer in experimental

Philofophy,
Author of the Essays on Arithmetic, Book-keeping, the Britisa

Mariner's Afstant, &c.

The SECOND EDITION.

Quicquid in astronomicis, geographicis, vel nauticis, efficiendum,

geometriæ et trigonometria attribuendum eft.

LONDON
Sold by J. JOHNSON, in St. PAUL'S CHURCH-YARD.

M.DCC.LXXV.

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46901

TO THE
TUTORS IN THE UNIVERSITIES,

MASTERS OF ACADEMIES,

AND

OTHER

TEACHERS of GEOMETRY,

IN GREAT-BRITAIN.

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GENTLEMEN,
T is probable that many of you, as well as myself,

have found it frequently difficult to initiate young Gentlemen into a necessary Acquaintance with Geometry by the Elements of Euclid, and therefore have wished for a more easy Introduction to that valuable Science, which, at the same time as it facilitated the Attainment of Geometry, might not depart (as many do) too much from the geometrical Spirit of the Ancients, which is so necessary for acquiring a Habit of reasoning with Propriety and Judgement.

Such a Treatise, with its Application to Trigonometry, I have now attempted, and beg Leave to offer to the Public, under your Protection; and, if it should be so far approved of, by you, as to be put into the Hands of your Pupils, I Aatter myself you will find the Science will be acquired by thein in much less Time than is usual, and with greater

Ease to yourselves. If this meets with your Encouragement, it will induce me to pursue my original Design, of presenting the Public, with other Efsays, for rendering the several Branches of mathematical Litera. ture, both ancient and modern, more pleasant in the Study, and more easily to be attained, than by any other Course, hitherto published, in our Language.

I am, Gentlemen,
Kingfon, near Taunton,
July 5; 177.5.

Your humble Servant,

B. DONN.

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THE

P R E F A C E.

IN

IN the general Preface to the Essays on Arithmetic,

published in the Year 1758, the Public were acquainted with our Design of presenting them with a new Course of mathematical Learning, a Thing generally allowed to be much wanted : For the great and numerous Improvements, which have been made since any Course has been published in the English Language, make a new Course absolutely necessary. For, as those Sciences, with their Improvements, are dispersed in a Multitude of Authors, the young

Student knows not how to proceed; and, even to a Master, it is no easy Talk to direct : Whereas, if these Sciences are brought into a regular Coursë, as they depend on each

other, the Student will learn with more Ease, Pleasure, and Dispatch,

As

* " Mathematical Learning, during the last and present “ Centuries, has made a most surprizing Progress; and Truth, $$ affifted by the uncontroverted Principles of this Science, has ço banished hypothetical Chicanery from the Regions of Philo

sophy. It is, therefore, no Wonder that a great Variety of " Authors, desirous of extending so valuable a Branch of Sci

ence, fhould have written on every Part of mathematical " Learning

But still a Course of Mathematics and Natural“ Philosophy, tracing the Science from its first Principles, and

exhibiting the Demonstrations on which each Rule or Problem ss is founded, is still wanting; there being none, in our own “ Language, that can, with any Show of Justice, be called a “ Course of Mathematics and Natural-Philosophy, according " to the modern Improvements, and properly adapted to Learn

This Defect Mr. Donn has undertaken to supply." Monthly Review for July, 1758.

5 ers.

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