APPENDIX TO THE PREFACE. XX111 



2. If the curve line DnNgG be such that the surface of the 

 solid generated by its revolution feels the least resistance of any 

 solid with the same top and bottom BG and CD, then the resistance 

 of the two narrow annular surfaces generated by the revolution of 

 the [infinitely little lines nN~\ and Gg is less then if the intermediate 

 solid bgNM be removed [along CB without altering Mb, until 

 bg comes [to BG], supposing as before that on is equal to Jig,] and by 

 consequence it is the least that can be, and therefore gG qq is to nN qq 

 as BG x Bb [is to MN x Mm]. 



*[Also if] gh be equal to hG so that the angle [gGh is 45 de s r ] then 

 will Bb qq be [to nN qq as BG x Bb is to] MN x Mm, and by conse- 

 quence BG qq is to GR qq as BG q is to MN x BR or BG q x BR is to 

 GR^ [as GR to MN}. 



Whence the proposition to be demonstrated easily follows. 



But its to be noted that in the booke pag 327 lin. 7 instead of 

 Quod si figura DNFB it should be written Quod si figura DNFGB, 

 and that DNFG is an uniform curve meeting with the right line GB 

 in G in an angle of 135degr. 



I have not yet made any experiments about the resistance of the 

 air and water nor am resolved to see Oxford this year. But perhaps 

 the next year I may. I had answered your letter sooner but that I 

 wanted time to examin this Theorem and the Lem. 1 in the 3 d Book. 

 I do not see how to derive the resistance of the air from the ascent of 

 water. The reasoning which must be about it seems too complicate 

 to come under an exact calculus, and what allowance must be made 

 for the retardation of the water by the contact of the pipe or hole at 

 its going out of the vessel is hard to know. 



II. LIST OF PROPOSITIONS APPARENTLY INTENDED TO BE INSERTED 

 IN A 2ND EDITION OF THE PRINCIPIA. 



In Theoria Lunae tractentur hae Propositiones. 



8 PROP. XXV. PROB. v. PAGE 434, PRINCIP. 

 Orbem Lunae ad aequilibrium reducere. 



* If the altitude of the frustum of the cone spoken of in the preceding para- 

 graph be infinitely small, the semi-angle of the cone becomes equal to 45. 

 Hence when the total resistance is a minimum, the curve meets the extreme 

 ordinate GB at an angle of 45. 



