COMMITTEE.

Chairman-The Right Hon. LORD BROUGHAM, F.R.S., Memb. Nat. Inst. of France.
Vice-Chairman-The Right Hon. Lord J. RUSSELL, M.P.
Treasurer-WILLIAM TOOKE, Esq., M.P., F.R.S.

W. Allen, Esq., F.R. & R.A.S. T. Drummond, Esq., R.E., Rowland Hill, Esq., F.R.A.S.

F.R.A.S.

Capt. F. Beaufort, R.N., F.R.,
and R.A.S., Hydrographer to Right Hon. Viscount Ebring-
the Admiralty.

Sir C. Bell, F.R.S.L. & E.
G. Burrows, M.D.

J. B. Carter, Esq. M.P.
The Rt. Rev. the Bishop
Chichester, D.D.
William Coulson, Esq.
R. D. Craig, Esq.

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

ton, M.P.

T. F. Ellis, Esq., A.M., F.R.A.S.
Sir Henry Ellis, F.R.S., Prin.
Lib. Brit. Mus.

of John Elliotson, M.D., F.R.S.
Thomas Falconer, Esq.

H. T. De la Beche, Esq., V.P.
Geol. Soc.

Edwin Hill, Esq.

The Right Hon. Sir J. C. Hob-
house, Bart. M.P.
Henry B. Ker, Esq.
David Jardine, Esq., M.A.

The Rt. Hon. the Earl of Kerry,

M.P.

Thos. Hewitt Key, Esq., M.A.
George C. Lewis, Esq., M.A.
Loch, Esq., M.P.,

I. L. Goldsmid, Esq., F.R. and James

R.A.S.

F.G.S.

B. Gompertz, Esq., F.R. and George Long, Esq., M.A.
J. W. Lubbock, Esq.,

R.A.S.

G. B. Greenough, Esq., F.R. &
L.S.

R.A., and L.S.S.

H. Malden, Esq., M.A.
A. T. Malkin, Esq. M.A.
James Manning, Esq.

F.R.,

THOMAS COATES, Esq., Secretary, 59, Lincoln's Inn Fields.

LOCAL COMMITTEES.

Chester-Hayes Lyon, Esq.
Henry Potts, Esq.
Chichester-Dr. Forbes, F.R.S.

Ashburton-J. F. Kingston, Esq. C. C. Dendy, Esq.
Barnstaple Bancraft, Esq.
William Gribble, Esq.
Belfast-Dr. Drummond.
Bilston-Rev. W. Leigh.
Birmingham-Rev. John Cor-

rie, F.R.S., Chairman.
Paul M. James, Esq., Trea-

surer.

Bridport-Wm. Forster, Esq.
James Williams, Esq.
Bristol-J. N. Sanders, Esq.,

Chairman.

J. Revnolds, Esq., Treas.
J. B. Estlin, Esq., F.L.S., Sec.
Calcutta-Lord Wm. Bentinck.
Sir Edward Ryan.
James Young, Esq.
Cambridge-Rev. James Bow-
stead, 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.
RW. Rothman, Esq., M.A.,
F.R.A.S. and G.S.

Coventry-Ar. Gregory, Esq.
Corfu-John Crawford, Esq.
Mr. Plato Petrides.
Denbigh-John Madocks, Esq.
Thos. Evans, Esq.
Derby-Joseph Strutt, Esq.

Edward Strutt, Esq., M.P.
Devonport and Stonehouse-
John Cole, Esq.
-Norman, Esq.
Lt.-Col. C. Hamilton Smith,
F.R.S.

Etruria-Jos. Wedgwood, Esq.
Exeter-J. Tyrrell, Esq.

John Milford, Esq. (Coaver.)
Glasgow-K. Finlay, Esq.
Professor Mvlne.
Alexander McGrigor, Esq.
Charles Tennant, Esq.
James Cowper, Esq.
Glamorganshire-

Dr. Malkin, Cowbridge.
W. Williams, Esq., Aberper-

gwm.

Guernsey-F. C. Lukis, Esq.
Hull-J. C. Parker, Esq.

Rev. Geo. Peacock, M.A., Keighley, Yorkshire- Rev. T.

F.R.S. & G.S.

Dury, M.A.

Rev. Prof. Sedgwick, M.A., Launceston-Rev. J. Barfitt.

J. Herman Merivale, Esq.,
M.A., F.A.S.

James Mill, Esq.

Rt. Hon. Lord Nugent.
W. H. Ord, Esq. M.P.
The Right Hon. Sir H. Parnell,
Bart., M.P.

Dr. Roget, Sec. R.S., F.R.A.S.
Sir M. A. Shee, P.R.A., F.R.S.
J. Abel Smith, Esq., M.P.
Rt. Hon. Earl Spencer.
John Taylor, Esq., F.R.S.
Dr. A. T. Thomson, F.L.S.
H. Waymouth, Esq.

J. Whishaw, Esq., M.A., F.R.S.
John Wood, Esq.

John Wrottesley, Esq., M.A.
F.R.A.S.

Neath-John Rowland, Esq.
Newcastle-Rev. W. Turner.
Newport, Isle of Wight-
Abr. Clarke, Esq.
T. Cooke, Jun., Esq.
R. G. Kirkpatrick, Esq.
Newport Pagnell-J. Millar,
Esq.
Newtown, Montgomeryshire-
William Pugh, Esq.
Rich. Bacon, Esq.
Oxford-Dr. Daubeny, F.R.S.,
Professor of Chemistry.
Rev. Professor Powell.
Rev. John Jordan, B.A.
E. W. Head, Esq., M.A.
W. R. Browne, Esq., M.A.
Penang-Sir B. H. Malkin.
Plymouth-H. Woollcombe,

Esq., F.A.S., Chairman.
Snow Harris, Esq., F.R.S.
E. Moore, M.D., F.L.S., Sec.
G. Wightwick, Esq.
Presteign-Dr. A. W. Davies,
M.D.

- Rev. H. P. Hamilton,
A.M., F.R.S. and G.S.
Rev. P. Ewart, M.A.
Ruthen-Rev. the Warden of.
Humphreys Jones, Esq.
Ryde, Isle of Wight-

Sir Rd. Simeon, Bart., M.P.
Sheffield-J. H. Abraham, Esq.
Shepton Mallet-

G. F. Burroughs, Esq. Shrewsbury-R. A. Slaney, Esq.,

M.P.

South Petherton

J. Nicholetts, Esq.
St. Asaph-Rev. Geo. Strong.
Stockport-Henry Marsland,
Esq., Treasurer.

Henry Coppock, Esq., Sec.
Tavistock-Rev. W. Evans.
John Rundle, Esq.
Truro-Richard Taunton, M.D.
Henry Sewell Stokes, Esq.
Tunbridge Wells-Dr. Yeats,
M.D.

Warwick-Dr. Conolly.

The Rev. W. Field, (Leam.)
Waterford-Sir John Newport,
Bart.

Wolverhampton - J. Pearson,
Esq.

Worcester-Dr. Corbet, M.D.
Dr. Hastings, M.D.
C. H. Hebb, Esq.
Wrexham-Thomas Edgworth,
Esq.

J. E. Bowman, Esq., F.L.S..
Treasurer.

Major William Lloyd.
Yarmouth-C. E. Rumbold,
Esq., M.P.

Dawson Turner, Esq.
York-Rev. J. Kenrick, A.M.
J. Phillips, Esq. F. R. S.,
F. G.S.

THE THEORY OF PROJECTION, SO FAR AS IT IS
AUXILIARY TO GEOMETRY;

WITH AN ACCOUNT OF THE

PLANE SECTIONS OF THE CONE AND CYLINDER,

IN WHICH CERTAIN GENERAL PROPERTIES OF THE CONIC SECTIONS ARE
DEMONSTRATED BY HELP OF THE FOREGOING THEORY,"

PUBLISHED UNDER THE SUPERINTENDENCE OF THE SOCIETY
FOR THE DIFFUSION OF USEFUL KNOWLEDGE.

LONDON:

BALDWIN AND CRADOCK, PATERNOSTER-ROW.

MDCCCXXX.

Chairman-H. BROUGHAM, Esq., F.R.S., M.P.

Vice Chairman-LORD JOHN RUSSELL, M.P.

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

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

London: Printed by WILLIAM CLOWES, Stamford Street.

4. Regular polygons, and approximation to the area of the circle

91

5. The circle a maximum of area, and a minimum of perimeter

6. Simple and plane loci

99

106

7. Problems

112

BOOK IV.

Page

125

Section 1. Of lines, perpendicular, or inclined, or parallel, to planes.

2. Of planes which are parallel, or inclined, or perpendicular, to other

Section 1. Surfaces and contents of the right cylinder and right cone

Surface and content of the sphere

3. Surfaces and contents of certain portions of the sphere

BOOK VI.

3. Of equal portions of spherical surface, and the measure of solid angles 194

4. Problems

203

Part

APPENDIX.

208

214

I. Of projection, by lines diverging, and by lines parallel

II. Of the plane sections of the right cone, or conic sections

III. Plane sections of the oblique cone, of the right cylinder, and of the