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GEOMETRICIAN:

CONTAINING

ESSAYS

Ο Ν

PLANE GEOMETRY,

AND

TRIGONOMETRY:

With their Application to the SOLUTIONS of a
VARIETY OF PROBLEMS, which are of great Use
in measuring Heights and Distances of Places, fur-
veying of Counties, Sea-Coafts, &c.

BY BENJAMIN DON N,
Teacher of the Mathematics, and Lecturer in experimental
Philofophy,

Author of the Effays on Arithmetic, Book-keeping, the British
Mariner's Affiftant, &c.

The SECOND EDITION.

Quicquid in aftronomicis, geographicis, vel nauticis, efficiendum,
geometrie et trigonometria attribuendum eft.

LONDON:

Sold by J. JOHNSON, in ST. PAUL'S CHURCH-YARD.
M.DCC.LXXV.

10-25-44 EMP

Thorp
2-11-43

46901

TO THE

TUTORS IN THE UNIVERSITIES,

MASTERS OF ACADEMIES,

AND OTHER

TEACHERS OF GEOMETRY,
IN GREAT-BRITAIN.

GENTLEMEN,

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T is probable that many of you, as well as myself, have found it frequently difficult to initiate young Gentlemen into a neceffary Acquaintance with Geometry by the Elements of Euclid, and therefore have wished for a more eafy Introduction to that valuable Science, which, at the fame 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 fo neceffary for acquiring a Habit of reasoning with Propriety and Judgement.

Such a Treatife, 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 fo far approved of, by you, as to be put into the Hands of your Pupils, I flatter myself you will find the Science will be acquired by them in much less Time than is usual, and with greater Ease to yourselves. If this meets with your Encouragement, it will induce me to purfue my original Defign, of presenting the Public with other Effays, for rendering the feveral Branches of mathematical Literature, 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,

Kingfton, near Taunton,
July 5, 1775.

Your humble Servant,
B. DONN.

THE PREFACE.

IN

N the general Preface to the Efays on Arithmetic, published in the Year 1758, the Public were acquainted with our Design of prefenting 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 fince any Courfe has been published in the English Language, make a new Courfe abfolutely neceffary. For, as thofe Sciences, with their Improvements, are difperfed in a Multitude of Authors, the young Student knows not how to proceed; and, even to a Mafter, it is no eafy Tafk to direct : Whereas, if these Sciences are brought into a regular Course, as they depend on each other, the Student will learn with more Eafe, Pleasure, and Dispatch,

As

"Mathematical Learning, during the laft and prefent "Centuries, has made a moft furprizing Progrefs; and Truth, affifted by the uncontroverted Principles of this Science, has banifhed hypothetical Chicanery from the Regions of Philofophy. It is, therefore, no Wonder that a great Variety of "Authors, defirous of extending so valuable a Branch of Sci❝ence, should have written on every Part of mathematical "Learning. But ftill a Course of Mathematics and NaturalPhilofophy, tracing the Science from its firft Principles, and exhibiting the Demonftrations on which each Rule or Problem is founded, is ftill wanting; there being none, in our own "Language, that can, with any Show of Juftice, be called a Courfe of Mathematics and Natural-Philofophy, according "to the modern Improvements, and properly adapted to LearnThis Defect Mr. Donn has undertaken to fupply." MONTHLY REVIEW for JULY, 1758.

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