6l:^ FHILOSOPHICAL TRANSACTIONS. [anNO l6g3'4. 



double the Florentine sail, that is to double the square of the diameter. And 

 this appears from hence, that the Florentine sail is equal to 4 figures of the 

 sines of the quadrant, and the perforating furface is also equal to the same, be- 

 cause it is congruous with it if inflection be made as above. 

 ^^Further, I shall only add, that the consideration of the figure of the sines 

 (the parts also of which are easily changed into squares) is sufficient for the de- 

 monstration of all those things, which are delivered concerning the other solids 

 wrought by the turning-lathe, or perforated by a cylinder, and of their surfaces, 

 by the very acute geometrician V. V. (Vincent Viviani, if I am not mistaken) the 

 very worthy disciple of Galileo, when he treats of the construction and mea- 

 surement of vaults or cupolas ; particularly that the surface of the Roman boat- 

 like cupola consists of 8 figures of the sines of the quadrantal arc, and there- 

 fore is equal to the Florentine veliform cupola. Hence it appears how two 

 cupolas may be constituted on equal squares, one of which is inclosed on all 

 sides, the other perforated by windows, each of which is double the square of 

 the base. 



9ft 



j^n Anatomical Observation respecting a Stone in the [/e/i] Kidney. By Dr. 

 Jfittie, F. R. S. N° 207, p- 30. An abridged Translation from the Latin. 



A lady 31 years of age, had long laboured under loss of appetite and bad 

 health. She not only loathed her food, but whenever she swallowed any, it was 

 immediately returned by vomiting ; while at the same time there was a copious 

 discharge of green bile by stooU Some relief was procured from tonic medi- 

 cines, so that the patient was enabled to take an airing every day for several 

 months ; after which she relapsed into her former sufferings, and moreover con- 

 ceived a strong aversion for all those remedies from which she had before ex- 

 perienced relief; so that the disease was now left to take its course without any 

 assistance from medicine. Indeed 1 was aware that the abovementioned symp- 

 toms were occasioned by a stone in the left kidney, and accordingly I predicted 

 what would happen. In July she went to Epsom for change of air, and to 

 drink the waters there ; but after she had been there 2 months, all her symp- 

 toms grew worse ; insomuch that she could not be recruited either by cordials 

 or food, and was unable to lie on either side, on account of the pain. She died 

 on the 28th of Jan. l680. 



On opening the body the next day, the lungs were found in a state which 

 indicated an approaching phthisis. The stomach was distended to an unusual 

 degree, resembling a blown up bladder; whence the vomiting might be ac- 

 counted for. The heart was remarkably small, and flaccid or collapsed, like an 

 empty purse ; its substance having been softened and worn away (absorbed) by 



