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II. ELEMENTARY MATHEMATICS. (Holograph.) 1. Observations on the Algebra of Kinckhuysen.

2. The first Ten Propositions of the 2nd book of Euclid, succinctly enunciated and demonstrated.

3. Theorem on the Area of a Triangle.

4. Trigonometria succinctè proposita et nova methodo demonstrata a St Joanne Hareo Arm.

5. A few MS. leaves, containing Compendium Trigonometriae. It includes Spherical Trigonometry. Intended for learners.

6. Table of sines to every half degree.

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1. Transcript of a Tract on Fluxions said to have been written by Newton in November, 1666.

2. Tract relating to the History of Fluxions, transcribed from one which was probably written by Jones.

3. Part of Newton's method of Fluxions and Infinite Series, with a fragment of the same treatise. (Holograph.) 4. Part of a Tract on Fluxions.

Some Propositions in Fluxions. ["I think this fragment very proper to be published.” Horsley, Oct. 22, 1777.]

6. Analysis per quantitates fluentes et eorum momenta.
7. Method of Fluxions and Infinite Series.
8. On the solution of Fluxional Equations.
9. Fluxions applied to Curves.

10. Propositions in the Method of Fluxions (dotted letters employed).

11. Propositions in Fluxions (dotted letters employed).

12. An early paper on deducing the subnormal in a curve from a given rational relation between x and y, and the converse operation.

13. Fragments on Fluxions.

14. Method of Curves and Infinite Series, and application to the Geometry of Curves. Complete all but the 1st leaf.



1. An early copy. 2. A later copy.

3. On the curves of the third order, produced by the projections of the Parabola Neiliana.

4. Fragments concerning lines of the third order, and some mistakes of Descartes [not worth publishing.” S. Horsley, Oct. 23, 1777].

V. ON THE QUADRATURE OF CURVES. (Holograph.) 1. A copy which appears to be pretty complete. . 2. A fragment on the same subject. 3. Scattered papers on the same subject, in great confusion 4. Another fragment on the same.

5. Note on Quadrature of Curves, intended as a Supplement to Section 10 of Book I. of the Principia.

6. Fragment on the Quadrature of Curves whose equations consist of but three terms.




1. De Problematum resolutione Synthetica.
2. Geometria. Liber 1. A fragment.
3. Geometry, a fragment on Porisms.
4. Analysis Geometrica.

Regula Datorum. 5. Newton's Regula Fratrum. 6. Fragment relating to Curves. 7. Geometria Curvilinea and Fluxions. 8. Scraps containing Propositions in Geometry; viz. : (a) To describe a Conic Section through five given points ;

and (6) To describe a Conic Section passing through two points

and touching three given straight lines. 9. Tract on the construction of Equations, unfinished. 10. On the Properties of Curves. 11. Part of a Treatise on Geometry (in Latin). 12. De Compositione Locorum Solidorum. 13. Solutio Problematis Veterum de Loco Solido.

14. Fragments relating to the writings of the Ancients in general, but especially to the Porisms of Euclid, and the Loci of


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1. Problemata Numeralia.


3. De serierum proprietatibus.
4. On Quadrature by Ordinates.
5. Regula differentiarum &c.



8. Scraps of calculations.


A. General. 1. Propositions on Elliptic Motion.



4. A small fragment (early) of the Principia.
5. De Motu Corporum.
6. Propositiones De Motu Corporum.

The references do not agree with the Principia. 7. Propositiones de Motu.

Several copies differing somewhat from each other, of which one is printed in Rigaud's “ Historical Essay" Appendix, No 1.


9. Proposed Corrections probably for 1st Edition of the Principia.



12. Additions and Corrections to 1st Edition of the Principia.

13. Additions and Corrections to the 2nd Edition of the Principia.

14. Observations and Calculations about Comets.






B. Lunar Theory. 1. Papers on the Lunar Theory found in interleaved copy of 1st Edition of Principia (damaged by fire).






6. Unarranged fragments connected with points of the Lunar Theory.




(Various statements of the principal points of this Theory.) 11. Propositions. De motu nodorum Lunæ, prepared for the 3rd Edition of the Principia.




15. Comparisons of calculated places of the Moon with Observations.


C. Mathematical Problems. 1. To find the True Anomaly from the Mean. 2. Fragment on the Solid of least resistance.


4. Altitudes by the Barometer.






4. Notæ ad Acta Eruditorum.


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