PHILOSOPHICAL TRANSACTIONS. 



Ill 



VOL. I.] 



both true. And again, if that proposition be false, his demonstration is so 

 too ; for this depends upon that, and therefore must fall with it. 



His section of an angle in ratione data, has no other foundation than his 

 supposed quadrature. And therefore that being false, this must fall with it. 



His appendix, wherein he undertakes to show a method of finding any num- 

 ber of mean proportionals between two lines given, depends upon the sup- 

 posed truth of his 22d chapter, about dividing an arch in any proportion 

 given, as himself professes ; and as is evident by the construction which sup- 

 poses such a section. And therefore, that failing, this falls with it. 



And so this whole structure falls to the ground. And withal, the proposi- 

 tion 4T , El. 1, doth still stand fast, which he tells us must have fallen, if his 

 demonstrations had stood : and so geometry and arithmetic do still agree, 

 which he tells us had otherwise been at odds. 



It was 



dark- 

 ened. 



^ diam. . .^ 



4 digits. . . , 



^ 5 dig 



1 6 dig-. 



I 7 dig 



L 6 dig 



5 dig. 

 4 dig. 

 3 dig. 

 1 dig. 

 1 dig. 

 O dig. 



Observations^ made in several Places^ of the Eclipse of the Sun, 

 Juns 22, 1666. N' 17, p. 295. 



The observations that were made at London by Mr. Willughby, Dr. Pope, 

 Mr. Hook, and Mr. Philips, are these : — 



The Eclipse began at 5h. 43 m. 



h. m. 



at 6 00 

 at 6 7 



at 6 13 



at 6 21 



at 6 39-1- 



at 6 57 



Its duration hence appears to have been one hour and 54 m. Its greatest 

 obscurity somewhat more than 7 digits. About the middle, between the per- 

 pendicular and westward horizontal radius of the sun, viewing it through Mr. 

 Boyle's 60-foot telescope, there was perceived a little of the limb of the moon 

 without the disk of the sun : which seemed to some of the observers to come 

 from some shining atmosphere about the body either of the sun or moon. 



They observed the figure of this eclipse, and measured the digits, by casting 

 the figure through a five-foot telescoue, on an extended paper fixed at a certain 

 distance from the eye-glass, and havmg a round figure ; all the diameters being 

 divided by six concentric circles into 12 digits. 



The Madrid Observations. 

 The observations made at Madrid by a noble member of the Koyal Society, 



