which, I discover'd feveral Errors, here and there, as I went along, in them, as exact as they were, which accordingly correcting in mine, I can, I prefume, justly pronounce my Tables the most certain and exact, as well as the most compendious of any in being.

Having thus largely declared the feveral Parts of this Work, and fhewn the Reader what an ufeful Variety he may expect to meet with both in the Theory, Praxis, and Tables, of this most useful and excellent Art; I must leave it to himself, to use or reject it, as he fall judge of the Merits thereof.

THE

(ix)

THE

TABLE of CONTENTS.

OF

PART I.

CHA P. I.

F the DEFINITION, ORIGIN, and NATURE

of LOGARITHMS.

CHA P. II.

p. I

Of the Method of making a TABLE of LOGA-

RITHMS by PLAIN ARITHMETIC.

CHA P. III.

9

The DOCTRINE of the NATURE and PROPERTIES

of LOGARITHMS farther explain'd and illuftrated

by means of the LOGARITHMIC CURVE.

CHA P. IV.

18

The NATURE of LOGARITHMS and their INDICES,

when the Numbers are FRACTIONS, farther ex-

plain'd by the LOGARITHMIC CURVE.

CHAP. V.

25

The Original Conftruction of LOGARITHMS by the

Lord NEPER, and the Change thereof to the pre-

fent Form by Himfelf and Mr. BRIGGS, explain'd

and illuftrated by the LOGARITHMIC CURVE. 35

CHAP. VI.

A Method of Conftructing the LOGARITHMS, de-

rived and demonftrated from the Nature of NUM-

BRS only, by Dr. EDMUND HALLEY.

2

40

CHAP.

CHAP. VII.

The LOGARITHMIC SERIES aforegoing demonftrated

alfo by FLUXIONS; and from the Nature of the

HYPERBOLA.

CHAP.

VIII.

P. 50

The Method of Conftructing LOGARITHMS by the

INFINITE SERIES, exemplified and illuftrated. 53

CHA P. IX.
Р.

Of the LOGARITHMIC SPIRAL; and the Nature

and Conftruction of a Table of MERIDIONAL

PARTS or Nautical MERIDIAN LINE, deduced

therefrom.

СНАР. Х.

64

Of the Conftruction of a Large LOGARITHMIC

SCALE, exhibiting, by Inspection, a distinct IDEA

of the Nature and Agreement of NUMBERS and

their LOGARITHMS.

CHAP. XI.

Of the Conftruction of the Artificial LINES of NUM-

BERS, SINES, and TANGENTS, by means of Lo-

GARITHMS.

CHAP. XII.

75

Of the MANNER of ufing the TABLES of LOGĄ ¬

RITHMS in PRACTICE; and of the PREREQUI-

SITES thereto.

СНАР. XIII

82

Of the Origin and Conftruction of SHAKERLEY'S

and STREET'S LOGISTICAL LOGARITHMS. 93

Of the Rules of ADDITION, SUBSTRACTION, MUL-

TIPLICATION, and DIVISION of the Indices of.

LOGARITHMS,

103

СНАР.

CHAP. II.

Of MULTIPLICATION and DIVISION of WHOLE

NUMBERS and DECIMALS by LOGARITHMS.108

CHA P. III.

Of Raifing POWERS and the EXTRACTION of ROOTS

by LOGARITHMS.

CHA P. IV.

p. 115

Of the various RULES OF PROPORTION, and of finding

MEAN PROPORTIONALS by LOGARITHMS. 121

СНАР. V.

SIMPLE INTEREST by LOGARITHMS.

CHAP. VI.

COMPOUND INTEREST by LOGARITHMS.

CHA P. VII.

VULGAR FRACTIONS by LOGARITHMS.

CHAP. VIII.

128

138

148

DUODECIMAL ARITHMETIC perform'd by LOGA -

RITHMS.

CHA P. IX.

153

The OPERATION of the common RULES of ARITH-

METIC by INSTRUMENTS; viz. the LOGA-

RITHMIC SCALE, and GUNTER'S LINE with

the COMPASSES, and on the SLIDING-RULE. 158

CHA P. X.

Sheweth the ANALOGIES for the SOLUTION of all

the CASES of PLAIN and SPHERICAL TRIAN

GLES, both Right and Oblique angled.

СНАР. XI.

167

The SOLUTION of PLAIN TRIANGLES by the CA-

NON of LOGARITHMICSINES and TANGENTS;

by GUNTER'S SCALE and COMPASSES, and by the

L IDING-RULE.

CHAP. XII.

173

The SOLUTION of SPHERICAL TRIANGLES by

LOGARITHMS, by GUNTER'S SCALE, and by

the SLIDING-RULE.

186

CHAP.

CHAP. XIII.

MERCATOR'S SAILING perform'd by the CANON

of LOGARITHMIC TANGENTS, without the

Meridional Parts.

CHA P. XIV.

P. 200

Of the MENSURATION of SUPERFICIES and So-

LID BODIES by Logarithms.

CHAP. XV.

207

The Doctrine of MENSURATION applied to ĠAUG-

ING, Measuring TIMBER, and SURVEYING;

wherein the Practical Ufe of the PLAIN SCALE,

and SLIDING RULE for thefe Purpofes, is clearly

explain'd.

CHA P. XVI.

222

The Practical USE of the LOGISTICAL LOGA-

RITHMS.

239

PART III.

CANON of LOGARITHMS for NATURAL NUM-

BERS, from 1 to 10000.

249

A CANON of LOGARITHMIC SINES and TAN-

GENTS.

A CANON or TABLE of LOGISTICAL LOGA-

RITHMS.

LOGA