## The Mathematical Papers of Isaac Newton:, Volume 7; Volumes 1691-1695Newton's mathematical researches during the last five years of his stay in Cambridge before leaving in April 1696 to take up his duties at the Mint in London have three main centres of interest: methods of fluxions and series, classical pure geometry, and Cartesian analytical geometry. Part 1 reproduces Newton's advances at this time in further extending the techniques of his combined calculus of fluxions and fluent, and of expansion into infinite series. Part 2 gives publication of Newton's lengthy excursions in the early 1690s into the modes of geometrical analysis used by the 'ancient' geometers, based - by way of Commandino's Latin translation - on the account of this little understood field of the Greek 'topos analuomenos' which was given by Pappus in the prolegomenon to the seventh book of his Mathematical Collection. Part 3 gives prominence to the final text of the Enumeratio Linearum Tertii Ordinis which Newton put together in June 1695. |

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### Contents

LIST OF PLATES xlviH | xlviii |

given a fluxional equation to determine the corresponding fluent relationship 70 The | 1 |

Appendix Variant preliminary drafts for the final Liber secundus 1 Add 3962 | 3 |

Newton employs Oughtredian notation for the sum and difference | 4 |

62r63r A first reshaping of Proposition IV of the 1691 De quadratura to be the | 10 |

subordinate kinds 487 Hyperbolic and parabolic branches and the deficient curves | 11 |

John Craiges visit to Cambridge in 1685 to talk of the quadrature of curves 3 Newton shows | 18 |

31r40r56r56v38ar38br + private The unfinished preliminary text | 24 |

on the equality of the products of alternate intercepts cut in the extended sides of a given | 276 |

an incomplete opening and a Chapter 2 1 Add | 294 |

is the universal Apollonian sectio spatii 314 Porism 11 is the Fermatian extension 316 | 336 |

A yet more general Porism 12 effecting the same by an arbitrary 11 correspondence | 350 |

of the Arithmetica again 362 Ways in which a quadrilateral may be given both in species | 380 |

further sorts of postulate which can be made | 394 |

THE FINAL GEOMETRIC LIBRI DUO | 402 |

segments of a triangle 452 Further such theorems but it is enough to have disclosed | 460 |

for compounding quadratures of related | 32 |

where by distinguishing related groups of terms in it the equation is seen to be directly | 80 |

cannot distinguish between a general fluxional derivative and a particular value of it | 98 |

by means of the preceding to solve problems Testing for maxima | 114 |

Again instanced in the ellipse 116 The converse construction of properties of curves | 128 |

University Library Cambridge | 130 |

whose equations are trinomial 130 Newton for the first time introduces his standard | 143 |

1059 | 160 |

Two reworked propositions on the fluxions and fluents of complex | 164 |

The restyled excerpts from the De quadratura communicated to Wallis | 177 |

PART 2 | 183 |

a comprehensive modern treatise on curves 193 The distinction of curves into grades | 199 |

27r28r A preliminary account ofAnalysis Geometrica | 222 |

PART 3 | 241 |

FIRST ESSAYS AT A MULTIPARTITE GEOMETRIA | 248 |

where the ordination angle also is permitted to vary 502 And yet more complicatedly | 503 |

CARTESIAN ANALYSIS OF HIGHER PLANE CURVES | 563 |

David Gregorys thoughts in 1698 of editing the tract soon abandoned Newtons | 566 |

IMPROVED ENUMERATION OF THE CUBIcs SPECIES | 579 |

lr14r The finished enumeration into 72 species Division of straight | 602 |

The four monodiametral ones species 2831 and the unique tridiametral instance | 616 |

The seven monodiametral ones species 3945 620 The seven parabolic hyperbolas | 635 |

16v A first | 648 |

AND QUARTIC CURVES | 656 |

44r42r42v Determining the simplest forms of general Cartesian | 663 |

second f double point as origin 666 The defining equation of 106 terms when sub | 670 |

derived from first principles by supposing a cubic approximating parabola 675 3 Add | 679 |

2 Determining the slope of the apparent path of the comet of 16801 at its sighting | 686 |

611r Case 5 where there are seven | 702 |

### Other editions - View all

The Mathematical Papers of Isaac Newton:, Volume 7; Volumes 1691-1695 Isaac Newton No preview available - 2008 |

The Mathematical Papers of Isaac Newton:, Volume 7; Volumes 1691-1695 Isaac Newton No preview available - 2008 |

### Common terms and phrases

abscissa aequatio algebraic alia altera angle Apollonius Appendix area curvae autem Cambridge casu circle circuli Collectiones conic Correspondence cross-ratio cujus curvae cujus curvature curve datis dato datum datur David Gregory draft eadem earum ejus ellipse equal equivalent Ergo erit etiam Euclid figure fluent quantities fluxion fluxionem Geometria given in position given point given ratio haec hujus hyperbola ibid ideoqj igitur ilia infinitum inter intersection ipsius Isaac Newton latus rectum Leibniz libri loci locus manuscript Mathematical method Newton omnes ordinata ordinate ordinatim applicata osculating circle Pappo Pappus parabola Porism positione datam potest preceding problem Problemata Proposition punctis punctum quadratura Curvarum quadrature quae quam quantitatem quibus quod recta recta linea rectangle rectangulum relatio reproduced sectione sequel seriei sint straight line summa sunt T. L. Heath tangent termini terminorum Theor Theorem vero Wallis