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COMMITTEE.

Chairman-H. BROUGHAM, Esq., F.R.S., M.P. Vice Chairman-LORD JOHN RUSSELL, M.P.

Rt. Hon. J. Abercrombie.

W. Allen. Esq., F.R.S.

Lord Althorp, M.P.

Rt. Hon. Viscount Ashley, M.P.
Rt. Hon. Lord Auckland.
W. B. Baring, Esq., M.P.

Capt. F. Beaufort, R.N., F.R.S.
C. Bell, Esq., F.R.S. L. & E.

T. F. Buxton, Esq., M.P., F.R.S.
R. Otway Cave, Esq., M.P.
John Conolly, M.D.
William Coulson, Esq.
Wm. Crawford, Esq.

J. Fred. Daniell, Esq., F.R.S.
J. F. Davis, Esq. F.R.S.
T. Denman, Esq.

Hon. G. A. Ellis, M.A., M.P.
T. F. Ellis, Esq, M.A.
Thomas Falconer, Esq.

I. L. Goldsmid, Esq., F.R.S.

Treasurer-WILLIAM TOOKE, Esq., F.R.S.

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Leonard Horner, Esq., F.R.S.
David Jardine, Esq.

Henry B. Ker, Esq., F.R.S.
J. G. S. Lefevre, Esq., F.R.S.
Edward Lloyd, Esq., M.A.
James Loch. Esq., M.P., F.G.S.
George Long, Esq., A.M.

J. W. Lubbock, Esq., F.R. & L.S.
Dr. Lushington, D.C.L., M.P.
B. H. Malkin, Esq., M.A.
Rev. Ed. Maltby, D.D., F.R.S.
James Manning, Esq.
F. O. Martin, Esq.

J. Marshall, Esq., M.P.
John Herman Merivale, Esq.

James Mill, Esq.
James Morrison, Esq.
Sir H. Parnell, Bart., M.P.
Professor Pattison.

T. Spring Rice, Esq., M.P., F.A.S.

Dr. Roget, Sec. R.S.

C. E. Rumbold, Esq., M.P.
J. Smith, Esq., M.P.
Wm. Sturch, Esq.
Rt. Hon. Lord Suffield.
C. P. Thomson, Esq., M.P.
Dr. A. T. Thomson, F.L.S.
A. N. Vigors, Esq., F.R.S.
H. Warburton, Esq., M.P., F.R.S.
H. Waymouth, Esq.

J. Whishaw, Esq., M.A., F.R.S.
Mr. Serjeant Wilde.

John Wood, Esq., M.P.
John Wrottesley, Esq., M.A.

Ashburton-J. F. Kingston, Esq.
Birmingham Local Association.

Rev. Jn. Corrie, Chairman.
Paul Moon James, Esq., Treasurer.
Joseph Parkes, Esq. Honorary
Wm. Redfern, Esq. Secretaries.
Bristol-J. N. Sanders, Esq., Chairman.
J. Reynolds, Esq., Treasurer.

J. B. Estlin, Esq., F.L.S., Secretary.
Cambridge-Rev. James Bowstead, M.A.
Rev. Prof. Henslow, M.A., F.L.S. &
G.S.

Rev. Leonard Jenyns, M.A., F.L.S.
Rev. John Lodge, M.A.

Henry Malden, Esq., M.A.

Fred. Malkin, Esq., M.A.

Rev. Geo. Peacock, M.A., F.R.S. &
G.S.

Marmaduke Ramsay, Esq. M.A.,

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D. Ellis, Esq., F.R.S.

Capt. Basil Hall, R.N., F.R.S.
L. & E.

Francis Jeffrey, Esq.
Prof. Napier, F.R.S.E.
Rev. A. Thomson, D.D.
W. Thomson, Esq.

Etruria Jos. Wedgwood, Esq.
Exeter-Rev. J. P. Jones.

J. Tyrrell, Esq.
Glasgow-K. Finlay, Esq.
D. Bannatyne, Esq.
Rt. Grahame, Esq.
Professor Mylne.
Alexander McGrigor, Esq.
C. Macintosh, Esq., F.R.S.
Mr. T. Atkinson, Hon. Sec.
Hull-Daniel Sykes, Esq., M.P.
Keighley, Yorkshire-Rev. T. Dury, M.A.
Launceston-Rev. J. Barfitt.
Leamington Spa-Dr. Loudon.
Leeds-Benjamin Gott, Esq.

J. Marshall, Jun., Esq.
Lewes J. W. Woollgar, Esq.
Liverpool Local Association.

Dr. Traill, Chairman.

J. Mulleneux, Esq., Treasurer.
Rev. W. Shepherd.

J. Ashton Yates, Esq.

Maidenhead-R. Goolden, Esq., F.L.S..

Manchester Local Association.
G. W. Wood, Esq., Chairman.
B. Heywood, Esq., Treasurer.
T. W. Winstanley, Esq., Hon. Sec.
Sir Geo. Philips, Bart., M.P.
Monmouth J. H. Moggridge, Esq.
Newcastle-James Losh, Esq.
Rev. W. Turner.
Newport-Abraham Clarke, Esq.
T. Cooke, Jun. Esq.

R. G. Kirkpatrick, Esq.

Newport Pagnell-James Millar, Esq.
Norwich-Rich. Bacon, Esq.

Plymouth-Geo. Harvey, Esq., F.R.S.
Portsmouth-E. Carter, Esq.

G. Grant, Esq.

D. Howard, Esq.

Rev. Dr. Inman, Nav. Col.
Sheffield-J. H. Abraham, Esq.

Shrewsbury-R. A. Slaney, Esq., M.P.
South Petherton-Jolin Nicholetts, Esq.
Tavistock-Rev. Wm. Evans.

John Rundle, Esq.

Truro-William Peter, Esq.

Waterford-Sir John Newport, Bart. M.P.
Wolverhampton-J. Pearson, Esq.

Worcester-Dr. Corbet, M.D.

Dr. Hastings, M.D.

C. H. Hebb, Esq.
Mr. H. Martin.

¡THOMAS COATES, Secretary, 4, South Square, Gray's Inn.

London: Printed by WILLIAM CLOWES, Stamford Street.

ELEMENTARY COURSE.

In compiling the present Treatise, the leading object has been to furnish the "Library
of Useful Knowledge" with a body of geometrical information, in which nothing
might be wanting that seemed necessary or desirable, whether to the correct expla-
nation and solid establishing of the science, or to its application in the different
branches of natural philosophy. Such an object, it is plain, can never be accom-
plished by a mere elementary course, which has solely in view the instruction of
beginners: it implies many discussions and distinctions, many theorems, scholia,
and even whole sections of matter, which it is better that a beginner should pass by,
while he confines his attention to the few and simple but important propositions to
which perpetual reference is made, and which may be regarded as constituting the
high road of Geometry. At the same time, the purposes of instruction have not
been lost sight of; and accordingly, while the present work may be considered
sufficiently extensive to answer every useful purpose, it will be found also to
include an elementary course of study complete in itself, by the help of which a
person totally unacquainted with the subject may become his own instructor, and
advance by easy steps to a competent knowledge of it. With this view, the
beginner has only to confine himself to the following portions of the entire work.

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first perusal, to avoid this difficulty by making, at once, the following assumption:
Through the same point there cannot pass two different straight lines, each of
which is parallel to the same straight line."

The converse part of Prop. 14, viz. that "parallel straight lines are at right
angles to the same straight line," will then be demonstrated as follows:-
Let A B be parallel to CD, and from any point E of

For, if A B be not at right angles to E F, through the
point E let A' B' be drawn at right angles to EF (post. 5.).
Then, by the former part of the proposition, because A' B'
and CD are, each of them at right angles to E F, A'B' is parallel to CD. But
A B is parallel to CD. Therefore, through the same point E there pass the two
straight lines A B and A'B', each of which 'is parallel to CD. But it is assumed
that this is impossible. Therefore, the supposition that A B is not at right angles
to E F is impossible; that is, A B is at right angles to E F.

It will be found that the Course just laid down, excepting the sixth Book of it
only, is not of much greater extent, nor very different in point of matter from that
of Euclid, whose “Elements" have at all times been justly esteemed a model not
only of easy and progressive instruction in Geometry, but of accuracy and perspi-
cuity in reasoning. A perusal of this work, as translated and edited by Simson,
though certainly not essential to an acquaintance with geometry, is strongly re-
commended to the student.

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