506 BHILOSOPHICAL TRANSACTIONS. [aNNO 1700. 



V ; the solid generated by the conversion of the portion onvt, about the axis 

 BA, is equal to a prism whose base is iotl, and height the circumference of a 

 circle whose diameter is ba. 



Having bisected ba in r, and drawn or meeting the quadrant in g, the sur- 

 face generated by the conversion of the arc ox about ba, is equal to ; X 

 CG X iL — cu X or. 



Bisect DE in y, fig. 15, through the centre r draw so parallel to bc, meet- 

 ing the circumference bka in s, bk parallel to ac in v, and the lines dh, em in 

 n and o ; the solid generated by the conversion of the portion fgmh about the 

 axis AC, is ' X 4 mo^ — -i- nh' -|- pc X nomh -}- cy X dnoe — ^ eg^ -\- jdf'; 

 and the solid generated by the segment kbs, is ; X t vk' + pc X bvks. 

 Therefore the solid generated by the semicircle bka about ac, is ; X 

 PC X vqak -f PC X BCQv — ^ ac' -j- -§■ vk' -1- PC X bvks ; which by due re- 

 duction will be found equal to the solid generated by the conversion of the same 

 semicircle about the axis bc 



The solid generated by the portion onvt about the axis cd, is equal to ; X 

 ^LV' — -i-iN' — ^ qt' + 4- po' -|- cs X PQII" 



From the points m, h, drop the two perpendiculars mz, hw, upon ca, pro- 

 longed if need be ; the surface generated by the conversion of the arc hm about 

 the axis ca, is equal to • X pc X hm — ra X wz, when the point z is next to 

 c, or J X PC X H -|- MRA X wz when the point w is next to it. 



Those who may think it worth their while to bestow some little pains to find 

 the demonstration of this, may solve the following problem : 



Any two conic sections being given, forming a lunula by their intersection, 

 and a right line being given by position, about which, as an axis, this lunula is 

 imagined to turn, to find the solids generated by tiie conversion of any of its 

 parts, cut ofi^ by lines perpendicular to that axis, or parallel to it, or making 

 any given angle with it ; as also the surfaces made by that conversion. 



Concerning the State of Learning, and several other Observations in Italij. By 

 Dr. Peter Silvestre, F.R.S. N° 2()5, p. ()27. 



I wrote to you that I had seen at Bononia Signor Sbaragli. There is a second 

 letter of iiis De Recentiorum Medicorum Studio, and De Generatione Vivipara 

 Scepsis, &c. both printed at Vienna. He is certainly a man of wit and learning; 

 but I found at Rome and in other places, most physicians angry with him, for 

 having abused the deservedly famous Malpighi. 



I had a very particular acquaintance witli a learned Benedictine monk, D. 

 Bernard de Montfaucon. He had been sent from France into Italy by the Con- 

 gregation of St. Maur, to search into all the libraries, and gather all the works 



