Mr. Barrow to Mr. Willughby. 



Mofi dearly Honoured Sir y 



YOUR Obfervation concerning the fpiral Line v 

 fufficiently evinces the invalidity of that demon- 

 ftration concerning its equality with the Semi-periphe- 

 ry; but to remove all doubt, 'tis faid that Monf Ro- 

 bervell hath demonftrated that the fpiral Line is equal 

 to the parabolical Line AMNOZ, whofe Axis AY is 

 equal to the femi- periphery, and YZ (ordinately ap- 

 ply 'd) equal to the Radius. I have not time and fpace 

 to prefent you my Thoughts concerning the Bufi- 

 nefs > only fuppofing EZ parallel to AY be divided 

 into equal parts, EF^ FG, GH, HZ 5 and AE into 

 as many equal Parts, and through the points of the 

 divifion of EF from Vertex A be drawn Lines AF, 

 AG, AH, AZ 3 and through the points of the divi- 

 fion of AE, parallels BZ, CZ, 

 DZ, &c. to AY. The inter- 

 ferons M, N, O, Z, are in the 

 parabolical Line j ( as appears by 

 the f th of Archirn. de Quadra. 

 Parabola) and MZ, NZ, OZ, 

 HZ are in Arithmetical pro- 

 portion, as the Arches of Circles 

 inferibed in the Spiral j from 

 whence appears the great Ana- 

 logy between thefe two Lines, 

 &c. which I leave to your Con- 

 iideration. Upon occafion of Le- 

 ctures I intend upon Archirn. de 

 JEquipond. I have had feveral 

 Thoughts about thefe Matters, which I ftiould be 

 glad to communicate with you, 



C B A 



it'w. CoU March z6, i66z a 



Mr, 



