The CONTENTS.

■^CIX. l. 7 te Conßruäion es Cubic and Biqua-drate Aquations, by a Parabola ani aCircle ; by Mr. Edm. Hailey Pag. 632« The Number os Roots in such Aquatioris,w ith iheir Limits ani Signs by Mr. Edm.Hailey 63

XX. The Ext'iäwn of ali Roots, without azy, previous Reduction ; by Mr. Edm* Hailey

3 t

XXL A Method os Raiftng an Infinite Multi-nomial toanyGiven Powers by M. Ab.de Moivre 90

XXII. The Extrablion of the Root of an Infi-nite Equation i L? ^ 1 . Abr. de M»ivre 9;XXIII. The Deärine of Exhaultions - , by Dr.Wallis 58

XXIV. The Approximation of the Ancients in the

Extrading of Roots, improv’d - by Dr.Wallis ibii.

XXV. The Proportion of Infinite Quantitiesy

by Mr. Edm. Hailey j 0 2

XXVI. Infinitely-Infinitq Fractions; by Dr.

R. Wood 104

XXVII. 1. The Anti{uity oj the Nuir.eral Fi-gures in England: by Dr. J. Wallis. 107 »

2. By Mr. Tho. LulFkin' 1-08

XXVIII. The Conflrudion of Logarithms \ byMr. Edm. Hailey ibii.

XXIX. Ptperi of iefs General Vfe Omitted

116

XXX. Accounts of Books, with Additioni, E-

meniatiohs, &c. Omitted ibii.

C H A P. II.

Trigonon;etry x Surveying.

I. K Chorographical Problem, propoßi by

OAr. Richard Townley ; Jblvei byMr. J. Collins Pag. 120

II, Tbree Chorographical Problems ; fovi'i by

aMember es the Philosoph ical Society atOxford 122

III. An Error of Common Surveyors, in com-

par ing Surveys rate» at Long Intervall, ifTime, with the Magnetic Needle, Demon-ftratei, by OAt. W.Molineux 125

IV. A Nerv Level -,.lj Mr. Butterficld 127

V. An Account 0/ a Book Omitted ibii.

C H A P. III.

Opticks.

I« A New Theory about Light ani Co- !jCx lours; byMr.tf. Newton Pag. 128

II. 1. Sonte Experiments Propoi’d in Relation to

thii Theory \ by . 13$

2. Observationi on thu PropofaT, by Dir.Newton ibii.

III. The Genuine Me tho i of Examining this

Theory 3 byMr. Newton 136

IV. 1. Animadversioni on Theory; by

E. P. Ign. Gafton Pardies 137

2. Anfwer'iby W. Newton 139

3. Some further Objcdiow 3 by g.F. Pardies

>4i

4. Anfwer’d by Mr. Newton 142

5. To the Stiisfadion ofV. Pardies 144

V. Some Considerationi on thii Theory ; by. Anfwer’d by Mr. Newton ibii.

VI. i T Sonte Considerationi upon thii Doärifie

tf Colours, front Paris 3 by .

2. Anfwer’d by Mr. Newton . 147

3. A Reply by M. N- 158

4. Anfwer’d by Mr. Newton ib.

VII. 1. Animadversioni en thii T 1 e.'ry ofLight and Colouts •, by Mr. Fr. L uns 161

2. Anfwer'd by . >62

z. A Reply by Mr. Fr. Linus ibii.

4. Anfwer’d by Mr. Newton >6z

5. The Experiment of; Mr. Linus affirm’d 3 by

Mr. Gascoign 164

6 . Anfwer’d h Mr. Newton ibii.

ji Exceptioni by Mr. Lucas J-6$

8. Anfwer’d by Mr. Newton 168

VIII. An Optical Experiment, by Mr. Ste-

phen Cray 172

IX. 1 .A Probiern of Albazen, solvi by M.

Christ- Hugens ibid.

2. wW.Sluiius >7Z

3. Other-