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Excerpts from A Treatise of Fluxions
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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.
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Title Pages with Google-Books Links |
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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 |
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| · Prolate Spheroidal Fluid Figure — §491 | 409 |
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| · The Earth's Equilibrium Shape — §492 | 410 |
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| 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 |
| · Of the Gravitation towards Spheres and Spheroids — §628 | 110 |
| · Of the Figures of Planets — §636 | 116 |
Maclaurin's Discussion of
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Paragraph (and partial print of related figure) extracted† from Colin Maclaurin (1742)
"A Treatise of Fluxions"
Volume II, Chapter XIV, §630 | |
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†The paragraph has been extracted from p. 111 of Google's digitized volume and displayed here without modification. The (partial) figure has been extracted from the collection of figures that appears near the beginning of the same digitized file; apparently this figure was not scanned in properly from the original source. |
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Paragraph (and related figure) extracted† from Colin Maclaurin (1742)
"A Treatise of Fluxions"
Volume II, Chapter XIV, §628 | |
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†As displayed here, this paragraph has been pieced together from two text segments found on separate but sequential pages (pp. 110-111) of Google's digitized volume. The figure has been extracted from the collection of figures that appears near the beginning of the same digitized file, and has been displayed here without modification. |
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