THEutility of GEOMETRY is so well understood,

that it is only neceffary to delineate the particular character of the present work. The aspect of Mathematical Science, as it is commonly exhibited, cannot be denied to be forbiding. Experience evinces that an exceedingly small proportion of those, who are made to attend Lectures on the Mathematics, as essential to a liberal education, become masters of the first fix books of Euclid. Persons less fortunately circumstanced, seldom have opportunity in early life to learn the properties of plane and solid figures; and yet they commonly feel a curiosity to obtain some insight into Natural Philosophy, and the various Arts, in which the principles of Geometry find their application.

These considerations induced the Author, about thirty years ago, to invent mechanical, or palpable demonstrations of the most important propofitions in Geometry. From 1766 to the present time,


he has repeatedly exhibited them in London, Bristol, and other places. In the same way he has exemplified some of their practical uses in Navigation, Architecture, taking of Heights, Mensuration, Gauging, and Surveying. And he has enjoyed the satisfaction of being able to render the truths he wished to communicate, quickly, and distinctly intelligible. Some other Lecturers, he has reason to think, have since partially adopted his plan; and it is possible that similar ideas may have occurred to various persons; but the series of demonftrations, now presented to the public, is entirely his own. Their utility, he presumes, will be acknowledged; though nothing of the kind, as far as he knows, has ever been offered to the public.

In the Prospectus it was promised that the Apparatus should consist of upwards of 50 schemes and models in card-paper, wood, and metal : to render it more useful, it has been considerably extended. By it may be conveyed to very young persons the knowledge of the fundamental propositions in Geometry, as well those of Euclid as some others which do not occur in that author. To acquire mathematical information will be rendered by this contrivance an amusement instead of a task. The repugnance generally excited by the ordinary method will be avoided,


and proficiency in the exact Sciences will be much expedited, by fo advantageous an introduction, Nor can the Apparatus be accounted dear, as by it more propositions may be taught in an Hour than in a Week by Euclid, or any

other Treatise of abstract Geometry. The Author is not fingular in believing that his Work will be found highly useful to all Tutors, whether in private Families, in Boarding Schools or Academies, and even in the Universities themselves.

When the Prospectus of this work was first published, it was not intended to touch on the Fifth Book of Euclid, which treats of the doctrine of proportion; partly on account of its difficulty, and partly from its not being a subject adapted to mechanical proofs. However, as some of the propositions are too valuable to be passed by in filence, an Eighth Book is added, in which it is presumed they are explained in a manner fufficiently clear to be readily understood by young Students; if they have already acquired a general knowledge of the Rule of Three, in common arithmetic.

The Author cannot conclude this Preface without thanking his very respectable Subscribers for their liberal support: to several he is indebted, not only for their subscription, but



for the active part they have taken in recommending the work ; more particularly he must acknowledge his obligations to Thomas Beddoes, M. D.*; as probably the work would never have been published, had it not been for his pressing persuasion, and uncommon activity, in recommending the plan to his literary friends.

* This Gentleman, without any previous knowledge of the Author's invention, had insisted upon the necessity of teaching the Elements of Geometry on this Plan, in a work entitled " Observations on demonftrative Evidence" published by Johnson, St. Paul's Church-Yard,

The BINDER is to observe, that there are two Half-Sheets with the same

Signature H.


Richard Aldridge, Esq. Banker, Bristol
Mr. Samuel Andrews, Wimborné

Richard Banks, Esq. Shropshire
Baptift Academy, Bristol
J. F. Barham, Esq. Exeter
Benjamin Baugh, Esq. Britol
Thomas Beddoes, M. D. Clifton
Mr. William Bell, Hull, 5 Copies
Charles Bernard, Esq. Bristol
Count Betancourt, Spain
Alexander Blair, Esq. Portland-Place, London
William Boscawen, Esq. Portland-Place, London
William Bosville, Esq. Wimpole-Street, London
Rev. Thomas Brachen, Jermyn-Street, London
Mr. Bridel, Academy, Stoke Newington, London
Mrs. Burdet.
Francis Burdet, Esq. M. P.

С William Castleman, Esq. Wimborne Mr. John Clark, Wimborne Mr. William Clayfield, Bristol, 2 Copies Mr. S. T. Coleridge, Derby Mr. Thomas Coulftring, Horfield-Road, Bristol Miss Coutts, London

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