222 PHILOSOPHICAL TRANSACTIONS. [aNNO 1763^ 



was as it had been stated. His friend, the physician, gave him for answer, that 

 the thing was true. 



Dr. Reghellini thereupon communicated the case to the physicians of the hos- 

 pital of Florence and Pisa, and desired them to make trial of it, the first oppor- 

 tunity that should offer, and acquaint him with the success. He likewise com- 

 municated it to his other friends, among which was Dr. Turton, an English 

 physician then at Venice; and to Dr. de la Fontaine, a physician, who attended 

 Lord Spencer. Dr. Reghellini judged, that so uncommon an event ought to be 

 published with all its circumstances; and having in his possession the history of 

 28 hydrophobous persons, though in different manners, and treated by different 

 physicians, 1 5 of whom were afterwards opened, and the bodies carefully 

 examined, he thought he might thence compose a rational and useful tract. He 

 therefore went to Padua, to have a personal interview with Count Leonissa, the 

 physician; but in this conference he discovered, that the man who was said to 

 have been cured with the use of vinegar, really never had the hydrophobia, 

 though he had been assured that Dr. Bertossi saw him in the hydrophobous 

 state. That man, it was true, did receive a very slight and superficial scratch on 

 his cheek from the same dog, who bit the other 2 persons, who became hydro- 

 phobous, and afterwards died; but the person of whom the account was pub- 

 lished, about the useful discovery of a cure by vinegar, was in reality never 

 arrived to the state of the hydrophobia ; that is, to such a degree of the malady 

 as most frequently follows the bite of a mad dog, and which, after some weeks, 

 discovers itself by an uneasiness in attempting to drink ; and after drinking, by 

 a fever, delirium, convulsions, vomiting, sweating, and death, within the 5th, 

 and sometimes within the 4th day. 



Dr. Reghellini, having thus found, that the account first given him, and the 

 confirmation of it from his friend at Padua, were doubtful, or rather a misappre- 

 hension, wrote again to Florence and Pisa, retracting his former account, and 

 relating the fact, as on a more strict examination he had found it truly to be, 

 and which was exactly agreeable to the preceding account. 



XXJI. Two Theorems, hy Edivard Waring, M.A., F.R.S., ^c. From the 



Latin, p. 143. 



Theor. 1 . — In a given ellipse inscribe 2 polygons of n sides, abcde &c, and 

 pqrst &c; at the respective points a, h, c, d, e, &c, p, q, r, s, t, &c, draw the 

 tangents ab, bc, cd, de, &c, and pq, aR, RS, st, &c, fig. 7, pi- 5; and let the 

 Z. ai'B = Z cZ)C; Z ^cc = Z den; /_ cdi> = ^ cdE; &c; and Z.pq<^ = Z. rqH; 

 ^qrR = Z. srs; Z "s = Z '*t; and so on. Then will the sum of the sides 

 ah + be + ed + de+ &cc = pq + qr -\- rs + st + &c. 



Corol. In the ellipse draw the polygon abcde &c, fig. 8, of n sides, in the 



