# Draft Letter from John Collins to Newton, dated 12 October 1678

A Curve passing through the ends |of| The Rayes PA PC PD being \& which are supposed to be/ in cont Propcon and makeing equall angles at the Pole P \I call the rumb Spirall/ it is desired to draw \a/ touch line to the said Curve both by ayd of a Series and, a geometricall approach

Or conversly if any two Rayes

and this tis presumed according to D^{r} Wallis in Libro de Cycloide cannot be done without streightening the Curve

Conversly if one Ray as PA and the angle the touch line makes therewith be given FAP, it is desired \from this {sic} data/ to describe the Spirall

The Rayes PC or PD and PA may be conceived to be the tang^{ts} of \halfe/ the Comp^{lts} of the Latitudes of two Places numbred with the double arke or whole Comp^{lt}, and the angle DPA to be the difference of Longitude, the drawing of a touch line to such Spirall which gives the \angle of the/ rumbe from one place to the other, a Problem of great use in Navigation and no Construction or \good/ approach for it, yet in lines not or at least not commonlyknowne, vouchsafe therefore to consider this most usefull Probleme and impart the same as an Appendage to your Letters to Leibnitz which we hope you will consent to have printed in English

|About the Rumb Spirall to M^{r} Newton 12 Oc^{r} 1678|

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