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Excerpts from A Treatise of Fluxions

Whitworth's (1981) Isothermal Free-Energy Surface
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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 (1742)
Volume II (2nd Ed., 1801)

Volume I (1st Ed., 1742)

Volume II (2nd Ed., 1801)

Volume I

Dedication (Acknowledgment) 
Preface 
Introduction1
Book 1 (Of the Fluxions of Geometrical Magnitudes)51
      Chapter I (Of the Grounds of this Method) — §§ 1-7751
      Chapter II (Of the Fluxions of plane rectilineal Figures) — §§ 78-104109
      Chapter III (Of the Fluxions of plane curvilineal Figures) — §§ 105-123131
      Chapter IV (Of the Fluxions of Solids, and of third Fluxions) — §§ 124-139142
      Chapter V (Of the Fluxions of Quantities that are in a continued Geometrical Progression, the first term of which is invariable) — §§ 140-150152
      Chapter VI (Of Logarithms, and of the Fluxions of logarithmic Quantities) — §§ 151-179158
      Chapter VII (Of the Tangents of curve Lines) — §§ 180-214178
      Chapter VIII (Of the Fluxions of curve Surfaces) — §§ 215-237199
      Chapter IX ([Identifying Extrema and Inflection Points] of Curves that are defined by a common or by a fluxional Equation) — §§ 238-285214
      Chapter X (Of the Asymptotes of curve Lines, the Areas bounded by them and …) — §§ 286-362240
      Chapter XI (Of the Curvature of Lines … different kinds of Contact [with other Curves] … Caustics … centripetal Forces …) — §§ 363-304
            · Parabola — §371311
            · Any Conic Section — §373312
            · The Second Fluxion of a Curve — §384324
            · Refraction of Light — §413344
            · Centripetal and Centrifugal Forces — §416346
            · Gravity — §419348
            · Circular Motion — §432356
            · When the Center of Forces is the Focus of a Conic Section — §446370
            · When Gravity is Uniform or Varies as any Power of the Distance — §458383
            · Orbit of the Moon, taking into account the Gravity of both the Earth and the Sun — §471391


Volume II

Paragraph and related figure extracted without modification from p. 111 of Colin Maclaurin (1742)

"A Treatise of Fluxions"

Volume 2, Chapter XIV, §630

Maclaurin (1742)
Maclaurin (1742)

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Whitworth's (1981) Isothermal Free-Energy Surface

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