On determim'ng INNUMERABLE PORTIONS of a SPHERE, the 

 SOLIDITIES and SPHERICAL SUPERFICIES of which 

 PORTIONS are at the fame Time algebraically ajfignable. By the 

 Rev. J. BRINKLEY A. M. ANDREWS Profejfor of Aftrommy 

 in the Univerjity of Dublin. 



IN the year 1692, Viviani, a Florentine, who had been the pupil Read, Nov.2, 

 of Galileo, propofed to the mathematicians of the age a prob- 

 lem, in which it was required to aflign a portion of the fur- 

 face of a fpherp exadly quadrible. This problem, truly in- 

 determinate, and known by the name of the Florentine prob- 

 lem, was readily folved by feveral in various ways*. The con- 

 ftrudion, however, of Viviani, which was afterwards publifhed 

 by himfelf, without demonftration, exceeded the others in fim- 

 plicity and elegance. It cannot now be known in what manner 



Viviani 



,*Wallis's "Works, vol. ii. p. 478, and the LeipCc Ads, 1692. 



Vol. VIIL 3T 



