Writing to you last Weeke I accquainted you that I had received somewhat more from Mr Baker in two Letters in the former he accquaints me with the Paines he hath been taking viz, what he hath written namely
A Treatise of Trigonometry done 26 yeares since, not only simple and vulgar, but such as Bartholinus pretends to have found out that is compound or a new way of resolving two things at once, A Demonstration of Vietas Way and the Prostaphereticall way in one sheete Geometrically done
A Treatise of Angular Sections
A Treatise of Conick Sections in an Analyticall method
A Treatise of Cubick æquations &c, with a Miscellany of Problems of Deschartes, Monsieur de Montfort and diverse other besides, with an infinite Company of his owne Invention
And having lately facilitated the Solution of such æquations even of many Dimensions whose rootes are in Arithmeticall or Geometricall Progression he thereupon undertooke the Solution of Dr Davenants Probleme, about finding those 4 continuall Proportionalls, the Summes of whose Squares and Cubes are given which you have over the leafe after the same manner done, as those Papers you have already seene, there is a very notable large Letter from Leibnitz lately arrived, which is not yet in my hands, I hope next Weeke to transcribe, and send a Duplicate, of it to you, I remaine

Your most humble thankfull Servitor

John Collins

Farthing Office
fanch{urch} streete
the 3{1} of August 1676


To Mr Isaac Newton fellow
of Trinity Colledge

In Cambridge



Æquatio Prob: 1° et 2° inserviens 0 Probl: 1 . Dat {b=aa+mm+nn+ee d=a3+m3+n3+e3 Qr { a,m,n,eQr } pqrstx x73bx5+16dx421bbx3+12bdxx9b3+8ddx+12bbd=0 Prob 2 . { Dat {b=aa+mm+nn+ee d=a3m3+n3e3 Qr { a,m,n,eQr } 0 0 Æquatio Prob: 3° et 4° inserviens 0 Probl: 3 . Dat {b=aa+mm+nn+ee d=a3m3n3+e3 Qr { a,m,n,eQr } pqrstxyz x93bx7+8dx69bbx512bdx4+23b3+8ddx312bbdxx12b4x+8b3d=0 .Innotescat verox=X; Dico Probl 4 . { Dat }b=aa+mm+nn+ee d=a3+m3n3e3 Qr; } a,m,n,e?Qr } 0 . 0Solutio Prob1iet3ij x2+b4x12bb4xx+xx2b2,±:b4xbb4xx+xx2b2,bb8xx+3b8xx8:={a__e 12bb4xx+xx2b2,b4x±:x2+b4xbb4xx+xx2b2,bb8xx+b83xx8:={m__n } Solutio Prob2iet4i0 { :b4xbb4xx+xx2b2,bb8xx+3b8xx8:±x2+b4x12bb4xx+xx2b2={a__e :x2+b4xbb4xx+xx2b2,bb8xx+3b8xx8:±b4x12bb4xx+xx2b2={m__n } 0 0 Æquatio Prob: 5° et 6° inserviens 0 Probl 5 . Dat {b=aammnn+ee d=a3+m3+n3+e3 Qr { a,m,n,e?Qr } 0000000000 pqrst x6+7bx416dx3+3bbxx+8bdx3b3=0 . Innotescat veròx=X; Dico 0000000000 Probl 6 . Dat {b=aammnn+ee d=a3m3+n3e3 Qr, { a,m,n,eQr } 0 0 Æquatio Prob: 7° et 8° inserviens 0 Probl: 7 . Dat {b=aammnn+ee d=a3m3n3+e3 Qr { a,m,n,eQr } 0 0 Solutio Prob 5iet7i x4+b4x±3x4b4xb2xxb={a__e x4b4x±x4b4xb2xxb={m__n 000 0pqrsxx616d9bx5+b3x4+8d9x35bb9xx+b39=0 . Innotescat verox=XDico 000 Probl 8 . [Dat {b=aammnn+ee d=a3+m3n3e3 Qr { a,m,n,e?]Qr } 0 0 Solutio Probl: 6iet8i b4x3x4b2xxb,±b4x+x4={a__e b4xx4b2xxb,±b4xx4={m__n 0


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Professor Rob Iliffe
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Faculty of History, George Street, Oxford, OX1 2RL - newtonproject@history.ox.ac.uk

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