## The Mathematical Papers of Isaac Newton:, Volume 4; Volumes 1674-1684This volume reproduces the texts of a number of important, yet relatively minor papers, many written during a period of Newton's life (1677-84) which has been regarded as mathematically barren except for his Lucasian lectures on algebra (which appear in Volume V). Part 1 concerns itself with his growing mastery of interpolation by finite differences, culminating in his rule for divided differences. Part 2 deals with his contemporary advances in the pure and analytical geometry of curves. Part 3 contains the extant text of two intended treatises on fluxions and infinite series: the Geometria Curvilinea (c. 1680), and his Matheseos Universalis Specimina (1684). A general introduction summarizes the sparse details of Newton's personal life during the period, one - from 1677 onwards - of almost total isolation from his contemporaries. A concluding appendix surveys highlights in his mathematical correspondence during 1674-6 with Collins, Dary, John Smith and above all Leibniz. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

141r144r A first | 3 |

82r84r Tabular computation of differences and their use | 4 |

the series is assumed and its coefficients are then successively determined term by term from | 5 |

68v A configuration illustrating linesegments determinable one from another by simple | 10 |

Newtons ignorance of Briggs and Harriot 4 Possible | 13 |

3r4v A discarded sheet from Newtons epistola posterior to Leibniz | 32 |

deriving centraldifference interpolation formulas 1 A detailed tabulation of unit | 64 |

3 Lemma | 72 |

39r40r A first draftpreliminary revise of the third | 343 |

2 Observations on asymptotes and diameters in the general cubic curve 1 private | 351 |

THE GEOMETRIA CURVILINEA AND MATHESEOS | 407 |

are examined most simply and clearly by Euclidean geometry augmented by fluxional | 410 |

Newtons attack on Cartesian algebraic analysis 409 The theory | 413 |

Its sudden abandonment after Halleys visit to Cambridge in August 1684? | 419 |

Definitions of fluxional increment and decrement 424 Axioms and postulates | 426 |

mented right triangle 428 The model abandoned and the theorems restated in abstract | 442 |

91v The resolution of geometrical questions regarding numbers | 110 |

CODIFICATIONS OF ELEMENTARY PLANE AND SPHERICAL | 116 |

33r44v The elaborated augmented compendium ofTrigono | 164 |

derivation from the collapsed net of standard theorems relating | 184 |

MS Wharton 592 Whartons transcript | 191 |

MISCELLANEOUS NOTES ON ANNUITIES AND ALGEBRAIC | 203 |

Tabulation of results and examination of their pattern 207 The quadratic factori | 212 |

Newtons early knowledge not profound of classical geometry 217 His study of Pappus | 229 |

problems 1 Various ways ofgiving determining a triangle by a simple relationship | 268 |

RESEARCHES INTO THE GREEK SOLID LOCUS | 274 |

passim Solution of the Ancients problem of the 4line solid | 286 |

considering their points at infinity | 335 |

on the fluxions of the sides basesegments and perpendiculars of a general scalene | 462 |

61v A first sketch | 504 |

53v Two trivial variants on Proposition 20 | 518 |

of the Geometria | 524 |

13r14r The revised computation of series Chapter | 592 |

Chapter 2 on transmuting series whose alternate terms have the same sign The basic | 616 |

Examples of this 622 General observations on the relative efficacy of ways of deriving | 633 |

llr12v Preliminary versions of Chapter 2 of the | 652 |

and November 1676 mark the opening and close of Newtons mathematical | 667 |

manuscripts and his debt therein to Wallis 672 The central passages in the epistola borrow | 674 |

### Other editions - View all

### Common terms and phrases

angle anguli angulorum Apollonius arcus Arithmetica cancelled casu circle circulo compare note complementi conic corresponding cosine cross-ratio crura crus cube cubic cubus curva curve datam datis dato datur Descartes differentiae Diophantus ejus equal equation equivalent Ergo erit erunt etiam Fermat figure geometry given in position given points half sum hyperbola hypotenuse inter interpolation intersections Invenire Isaac Newton latera laterum latus latus rectum Leibniz Lemma lineae loci locus logarithms Mathematical numeros Pappus parallel perpendicular plane Pone positione Prob problem Prop proportionale Proposition puncta punctum quadrant quae quam quod quorum summa radius rational recta rectangulum reproduced Roger Cotes secants sectionem semissis semisummae sides sine sint sinum sinus sive solution spherical triangle square straight line sunt T. L. Heath tangent tangentem termini terminorum Theorem trianguli trigonometry