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Excerpts from A Treatise of Fluxions

Both Volume I and Volume II of Colin Maclaurin's "A Treatise of Fluxions" can now be accessed online via Google Books. (Check out Wolfram's explanation of the term, fluxion.) In what follows, we present selected excerpts from these two books.

Title Pages with Google-Books Links
Volume I (1st Ed., 1742)	Volume II (2nd Ed., 1801)

Volume I

Dedication (Acknowledgment)
Preface
Introduction	1
Book 1 (Of the Fluxions of Geometrical Magnitudes)	51
Chapter I (Of the Grounds of this Method) — §§ 1-77	51
Chapter II (Of the Fluxions of plane rectilineal Figures) — §§ 78-104	109
Chapter III (Of the Fluxions of plane curvilineal Figures) — §§ 105-123	131
Chapter IV (Of the Fluxions of Solids, and of third Fluxions) — §§ 124-139	142
Chapter V (Of the Fluxions of Quantities that are in a continued Geometrical Progression, the first term of which is invariable) — §§ 140-150	152
Chapter VI (Of Logarithms, and of the Fluxions of logarithmic Quantities) — §§ 151-179	158
Chapter VII (Of the Tangents of curve Lines) — §§ 180-214	178
Chapter VIII (Of the Fluxions of curve Surfaces) — §§ 215-237	199
Chapter IX ([Identifying Extrema and Inflection Points] of Curves that are defined by a common or by a fluxional Equation) — §§ 238-285	214
Chapter X (Of the Asymptotes of curve Lines, the Areas bounded by them and …) — §§ 286-362	240
Chapter XI (Of the Curvature of Lines … different kinds of Contact [with other Curves] … Caustics … centripetal Forces …) — §§ 363-	304
· Parabola — §371	311
· Any Conic Section — §373	312
· The Second Fluxion of a Curve — §384	324
· Refraction of Light — §413	344
· Centripetal and Centrifugal Forces — §416	346
· Gravity — §419	348
· Circular Motion — §432	356
· When the Center of Forces is the Focus of a Conic Section — §446	370
· When Gravity is Uniform or Varies as any Power of the Distance — §458	383
· Orbit of the Moon, taking into account the Gravity of both the Earth and the Sun — §471	391
· Prolate Spheroidal Fluid Figure — §491	409
· The Earth's Equilibrium Shape — §492	410
End of Book I, Chapter XI, § 494	413

Volume II

Table of Principal Contents (5 pp.)
Figures (30 pp.)
Book 1 (continued)	1
Chapter XII (Of the Methods of Infinitesimals …) — §§ 495-570	1
· Centre of Gravity — §510	13
· Of the Collision of Bodies — §511	14
· Of the Descent of Bodies that Act upon One Another — §521	27
· Of the Centre of Oscillation — §533	40
· Of the Motion of Water Issuing from a Cylindric Vessel — §537	44
· Of the Catenaria — §551	59
· General Observations Concerning the Angles of Contact, etc. — §554	61
· General Observations Concerning centripetal Forces, etc. — §563	67
Chapter XIII (Determining the Lines of swiftest Descent in any Hypothesis of Gravity …) — §§ 571-608	74
· When Gravity is Directed Towards a Given Centre — §578	80
· Isoperimetrical Problems — §588	88
· The Solid of Least Resistance — §606	100
Chapter XIV (Of the Ellipse Considered as the Section of a Cylinder … Of the Figure of the Earth …) — §§ 609-	101
· Properties of the Ellipse — §609	101

Maclaurin's Discussion of

Paragraph and related figure extracted† without modification from p. 111 of Colin Maclaurin (1742) "A Treatise of Fluxions" Volume 2, Chapter XIV, §630

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