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. J. Herman Merivale, Esq.,

F.R.A.S.
Edwin Hill, Esq.

M.A., F.A.S.
Capt. F. Beaufort, R.N., F.R.,
and R.A.S., Hydrographer to Right Hou. Viscount Ebring- The Right Hon. Sir J. C. Hob- James Mill, Esq.
the Admiralty.
ton, M.P.

house, Bart, M.P.

Rt. Hon. Lord Nugent.
T.F. Ellis, Esq., A.M., F.R.A.S. Henry B. Ker, Esq.

David Jardine, Esq., M.A.
Sir C. Bell, F.R.S.L. & E.

W. H. Ord, Esq. M.P.

The Right Hon. Sir H. Parnell, G. Burrows, M.D.

Sir Henry Ellis, P.R.S., Prin. The Rt. Hon, the Earl of Kerry, Bart., M.P. J. B. Carter, Esq. M.P.

Lib. Brit. Mus.

M.P.

Dr. Roget, Sec. R.S., F.R.A.S.
The Rt. Rev. the Bishop of John Elliotson, M.D., F.R.S. Thos. Hewitt Key, Esq., M.A. Sir M. A. Shee, P.R.A., F.R.S.
Chichester, D.D.

Thomas Falconer, Esq. George C. Lewis, Esq., M.A. J. Abel Smith, Esq., M.P.
William Coulson, Esq. I. L. Goldsmid, Esq., F.R. and James Loch, Esq., M.P., Rt. Hon. Earl Spencer,
R. D. Craig, Esq.

R.A.S.

F.G.S.

John Taylor, Esq., F.R.S. J. Fred. Daniell, Esq., F.R.S. B. Gompertz, Esq., F.R. and George Long, Esq., M.A. Dr. A. T. Thomson, F.L.S. J. F. Davis, Esq., F.R.S.

R.A.S.

J._W. Lubbock, Esq., F.R., H. Waymouth, Esq. H. T. De la Beche, Esq., V.P. G. B. Greenough, Esq., F.R. & R.A., and L.S.S.

J. Whishaw, Esq., M.A., F.R.S. Geol. Soc.

L.S.

H. Malden, Esq., M.A. John Wood, Esq.
The Right Hon. Lord Den- H. Hallam, Esq., F.R.S., M.A. A. T. Malkin, Esq. M.A. John Wrottesley, Esq., M.A.
M. D. Hill, Esq.
James Manning, Esq.

F.R.A.S.

man.

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

surer.

Esq.
Esq.

LOCAL COMMITTEES.
Anglesed-Rev. E. Williams. Chester-Hayes Lyon, Esq.

Maidenhead-R. Goolden, Esq., Ripon – Rev. H. P, Hamilton,
Rev. W. Johnson.
Henry Potts, Esq.

P.L.S.

A.M., F.R.S. and G.S.
Mr. Miller.
Chichester-Dr. Forbes, F.R.S. Maidstone-

Rev. P. Ewart, M.A.
Ashburton-J. F. Kingston, Esq. C. C. Dendy, Esq.

Clement T. Smyth, Esq. Ruthen-Rev. the Warden of. Barnstaple- - Bancraft, Esq. Coventry-Ar. Gregorv, Esq. John Case, Esq.

Humphreys Jones, Esq. William Gribble, Esq. Corfu-John Crawford, Esq.

Malmesbury-B.C.Thomas, Esq. Ryde, Isle of Wight-
Belfast-Dr. Drummond. Mr. Plato Petrides.

Manchester Local Association- Sır Rd. Simeon, Bart., M.P.
Bilston-Rev. W. Leigh. Denbigh-John Madocks, Esq. G.W. Wnod, Esq., Chairman. Sheffield-J. H. Abraham, Esq.
Birmingham-Rev. John Cor-
Thos. Evans, Esq.

Benj. Heywood, Esq., Treas. Shepton Mallet-
rie, F.R.S., Chairman, Derby-Joseph Strutt, Esq. T. W. Winstanley, Esq., Hon. G. F. Burroughs, Esq.
Paul M. James, Esq., Trea- Edward Strutt, Esq., M.P.

Sec.

Shrewsbury-R. A. Slaney, Esq.,
Devonport and Stonehouse- Sir G, Philips, Bart., M.P. M.P.
Bridport-Wm. Forster, Esq. John Cole, Esq.

Benj. Gott, Esq.

South PethertonJames Williams, Esq.

- Norman, Esq.

Merthyr Tydvil-J. J. Guest, J. Nicholetts, Esq. Bristol.-J. N. Sanders, Esq., Lt.-Col. C. Hamilton Smith, Esq., M.P.

St. Asaph-Rev. Geo. Strong. Chairman.

F.R.S.

Minchinhampton - John Ball, Stockport — Henry Marsland,
J. Revnolds, Esq., Treas. Etruria-Jos. Wedgwood, Esq.

Esq., Treasurer.
J. B. Estlin, Esq., F.L.S., Sec. Exeter-J. Tyrrell, Esq. Monmouth-J. H. Moggridge, Henry Coppock, Esq., Sec.
Calcutta-Lord Wm. Bentinck. John Milford, Esq. (Coaver.)

Tavistock-Rev. W. Evans.
Sir Edward Ryan.
Glasgmo-K. Finlay, Esq.

Neath-John Rowland, Esq. John Rundle, Esq.
James Young, Esq.

Professor Mvlne.

Newcastle-Rev. W. Turner. Truro-Richard Taunton, M.D. Cambridge-Rev. James Bow- Alexander McGrigór, Esq. Newport, Isle of Wight

Henry Sewell Stokes, Esq. stead, M.A. Charles Tennant, Esq.

Abr. Clarke, Esq.

Tunbridge Wells - Dr. Yeats, Rev. Prof. Henslow, M.A., James Cowper, Esq.

T. Cooke, Jun., Esq.

M.D.
F.L.S. & G.S.
Glamorganshire-

R. G. Kirkpatrick, Esq. Warwick-Dr. Conolly.
Rev. Leonard Jenyns, M.A., Dr. Malkin, Cowbridge. Neroport Pagnell - J. Millar, The Rev. W. Field, (Leam.)
F.L.S.
W. Williams, Esq., Aberper- Esq.

Waterford-Sir John Newport,
Rev. John Lodge, M.A.

gwm.

Newtown, Montgomeryshire- Bart.
RW. Rothman, Esq., M.A., Guernsey-F.C. Lukis, Esq.

William Pugh, Esq. Wolverhampton - J. Pearson,
F.R.A.S. and G.S.
Hull-J. C. Parker, Esq.
Rich. Bacon, Esq.

Esq.
R'v. Geo. Peacock, M.A., Keighley, Yorkshire- Rev. T. Oxford-Dr. Daubeny, F.R.S., Worcester-Dr. Corbet, M.D.
F.R.S. & G.S.
Dury, M.A.

Professor of Chemistry. Dr. Hastings, M.D.
Rev. Prof. Sedgwick, M.A., Launceston-Rev. J. Barfitt. Rev. Professor Powell.

C. H. Hebb, Esq.
F.R.S. & G.S.
Leamington Spa-Dr. Loudon,

Rev. John Jordan, B.A. Wrexham-Thomas Edgworth,
Professor Smyth, M.A.

M.D.
E. W. Head, Esq., M.A.

Esq.
Rev. C. Thirlwall, M.A. Leeds J. Marshall, Esq. W. R. Browne, Esq., M.A. J. E. Bowman, Esq., F.L.S..
Canterbury-Alex. B. Higgins, Lewes-J. W. Woollgar, Esq. Penang-Sir B. H. Malkin.

Treasurer.
Esq.

Liverpool Local Association--Plymouth - H. Woollcombe, Major William Lloyd. John Brent, Esq.

w. w.jCurrie, Esq., Chair- Esq., F.A.S., Chairman. Yarmouth - C. E. "Rumbold, William Masters, Esq.

Snow Harris, Esq., F.R.S. Esq., M.P.
Cardigan-The Rev. J. Black. J. Mulleneux, Esq., Treas. E. Moore, M.D., F.L.S., Sec. Dawson Turner, Esq.
well.
Rev. W. Shepherd.

G. Wightwick, Esq.

York-Rev. J. Kenrick, A.M. Carnarvon-R.-A. Poole, Esq. J. Ashton Yates, Esq.

Presteign-Dr. A. W. Davies, J. Phillips, Esq. F.R. S., William Roberts, Esq. Ludlow-T. A. Knight, Est.

M.D.

F.G.S.

man,

THE THEORY OF PROJECTION, SO FAR AS IT IS

AUXILIARY TO GEOMETRY;

WITH AN ACCOUNT OF THE

PLANE SECTIONS OF THE CONE AND CYLINDER,

ARE

IN WHICH CEPTAIN GENERAL PROPERTIES OF THE CONIC SECTIONS

DEMONSTRATED BY HELP OF THE FOREGOING THEORY,

PUBLISHED. UNDER THE SUPERINTENDENCE OF THE SOCIETY

FOR THE DIFFUSION OF USEFUL KNOWLEDGE,

LONDON:
BALDWIN AND CRADOCK, PÂTERNOSTER-ROW.

MDCCCXXX.

COMMITTEE.

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

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

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.RS.
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.

B. Gompertz, Esq., F.R.S.
H. Hallam, Esq., F.R.S., M.A.
M. D. Hill, E3q.
Rowland Hill, Esq.
E. Hill, Esq.
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., MA.
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. 0. 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., MP., 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.

D. Ellis, Esq., F.R.S. Birmingham Local Association,

Capt. Basil Hall, R.N., F.R.S. Rev. Jn. Corrie, Chairman.

L. & E. Paul Moon James, Esq., Treasurer.

Francis Jeffrey, Esq. Joseph Parkes, Esq. Į Honorary

Prof. Napier, F.R.S.E.
Wm. Redfern, Esq. 1 Secretaries.

Rev. A Thomson, D.D.
Bristol-J. N. Sanders, Esq., Chairman. W. Thomson, Esq.
J. Reynolds, Esq., Treasurer.

Etruria,Jos. Wedgwood, Esq.
J. B. Estlin, Esq., F.L.S., Secretary. Exeter-Rev. J. P. Jones.
Cambridge-Rev. James Bowstead, M.A. J. Tyrrell, Esq.

Rev. Prof. Henslow, M.A., F.L.S. & Glasgow --K. Finlay, Esq.
G.S.

D. Bannatyne, Esq.
Rev. Leonard Jenyns, M.A., F.L.S. Rt. Grahame, Esq.
Rev.John Lodge, M.A.

Professor Mylne. Henry Malden, Esq., M.A.

Alexander McGrigor, Esq. Fred. Malkin, Esq., M.A.

C. Macintosh, Esq., F.RS. Rev. Geo. Peacock, M.A., F.R.S. & Mr. T. Atkinson, Hon. Sec. G.S.

Hull-Daniel Sykes, Esq., M.P. Marmaduke Ramsay, Esq. M.A., Keighley, Yorkshire-Rev. T. Dury, M.A. F.L.S.

Launceston-Rev. J. Barfitt. Rev. Prof. Sedgwick, M.A., F.R.S. Leamington Spa-Dr. Loudon. & G.S.

Leeds-Benjamin Gott, Esq. Professor Smyth, M.A.

J. Marshall, Jun., Esq. Rev. C. Thirlwall, M.A.

Lewes--J. W. Woollgar, Esq. Derby - Joseph Strutt, Esq.

Liverpool Local Association. Wm. Strutt, Esq.

Dr. Traill, Chairman. Devonport-Major J. Hamilton Smith, J. Mulleneux, Esq., Treasurer. F.R. and L.S.

Rev. W. Shepherd. Dublin-Hon. Thos. Vesey.

J. Ashton Yates, Esq. Edinburgh-R. Greville, LL.D.

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.
Nenport-Abraham Clarke, Esq.

T. Cooke, Jun. Esq.

R. G. Kirkpatrick, Esq.
Neni port Pagnell-James Millar, Esq.
Nornich-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.
Shefield-J. H. Abraham, Esq.
Shrensbury--R. A. Slaney, Esq., M.P.
South Petherton-John 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.

Section 1. First properties of the circle

2. Of angles in a circle

3. Rectangles under the segments of chords

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

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

6. Simple and plane loci

7. Problems

78

84

88

91

99

106

112

a

BOOK IV.

Page

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

125

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

planes

133

3. Of solids contained by planes

138

4. Problems

150

.

BOOK V.

.

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

2. Surface and content of the sphere

3. Surfaces and contents of certain portions of the sphere

156

175

179

BOOK VI.

.

.

Section 1. Of great and small circles of the sphere

185

2. Of spherical triangles

189

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

4. Problems

203

APPENDIX.

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

208

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

214

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

oblique cylinder

229