282 PHILOSOPHICAL TRANSACTIONS. [aNNO 16'/6. 



Correct time of Clock. Distances and Altitudes. 



5h 37m Qs From the cusp 36' 35^ 



5 41 10. . The moon's altitude being 10-i-°, the diameter about 31 53 



5 48 30. . DifF. of altitude of Jupiter and the moon's lower limb 23 1 



5 52 40. . Jupiter from the nearest cusp 41 40 



6 9 40. . From the cusp, dubious 47 29 



u4n Account of Books. N° 123, p. 567. 



auTTiv u7rcjw,i/r)|tAa5 &c. Cum Versione et Notis Joh. Wallis, SS. Th. Doct. Geo- 

 metrias Professoris Saviliani. Oxonii e Theatro Sheldoniano, 1676. 



Though this tract of Archimedes's Arenarius has been formerly twice printed 

 in Greek, and thrice in Latin, yet the learned Dr. Wallis saw reason for pub- 

 lishing another edition ; presenting us with many emendations in the original, 

 and with a new version in Latin, also adding some short explanatory strictures. 

 Indeed the book seemed to deserve these pains, being not only an elegant and 

 acute piece, worthy of Archimedes, but also an excellent monument preserving 

 both a piece of remote antiquity, as is that of the hypothesis of Aristarchus 

 Samius revived by Copernicus, and that of the Doric dialect in prose. Be- 

 sides, it exhibits the foundation laid of the art of numbering, or rather noting 

 of numbers, now in use amongst us, with Saracenic or rather Indian cyphers. 

 And it accommodates those numbers a, p, y, $, t, &c. not only to numbers pro- 

 portional in a decuple ratio ; but also to any others, in any ratio whatever, that 

 are in a continual proportion from the unit: and they are the same with what 

 is commonly called unit, root, quadrat, cube, biquadrat, viz. 

 a j3 y (J" £ ^ n, &C. 

 \ a aa c? a^ a" a^, &c. 



This book exhibits a number exceeding that which is equal to the number of 

 the sand, capable to fill up, not only the whole earth and its cavities, but also 

 the whole world. 



To this tract of the number of the sand, is added that other of the same 

 Archimedes, touching the dimension of a circle, because it is several times 

 quoted in the former, as the foundation of his calculus; nor did it want emenda- 

 tion. To it is annexed Eutocius's short commentary on the said dimension, 

 which exhibits a specimen of the form and manner, wherein the later Greeks 

 used to write their comments on the more ancient authors ; and it shows also 

 how laborious it was to make multiplications, divisions, and extractions of roots 

 before the use of the Indian cyphers was introduced, as well as in what manner 

 they were performed. 



