VOL. XXI.3 PHILOSOPHICAL TRANSACTIONS. 445 



tion, nothing but to begin from the end of the analysis, and proceed to the 

 beginning of it ; observing that where the analysis argues by alternate or 

 inverted propositions, the synthesis argues by the same ; and that where the 

 analysis compound^, the synthesis divides, and vice versa. Take the following 

 example out of a great variety which the book, contains. 



Problem. — The line ac being divided at pleasure in b ; to divide it again in x, 



between b and c, so that ax, xc, bx be proportional. 



I 1 1 1 1 



a b 



Jnalysis. — Let therefore 



and componendo 

 and alternando 

 Let eq be made = be 

 and componendo 

 Therefore the problem is solved. 

 Construction. — Let the construction be made as before. 



Demonstration. — For since, by the construction, aq is to cq as be to bx, 

 therefore dividendo ac is to cq, that is to be, as xc to bx ; and alternando ac is 

 to xc, as be to bx. Therefore dividendo ax is to xc, as xc to bx, which was 

 to be done. 



Account of tivo Glands and their Excretory Ducts, lately discovered in Human 

 Bodies. By Mr. IfiUiam Coivper. F. R. S. N° 258, p. 364. 



About a quarter of an inch below the prostrate glands e, fig. 1, pi. 10, I 

 found two other small glands gg, placed on each side the urethra, F, a little 

 above the bulb of its cavernous body i. These glands are of a depressed 

 oval figure, not exceeding the size of a small French bean. After those 

 parts of the musculus accelerator ll are removed, which pass over these 

 glands, you may feel them placed like two hard bodies on each side the 

 urethra. They incline to a yellowish colour, like that of the prostates. Their 

 excretory ducts appear on their internal surface, fig. 1. a, b, next the inner 

 membrane of the urethra c, whence they descend about half an inch in length 

 before they grow less, and pierce that membrane obliquely, at their opening 

 into the urethra d, in which they discharge their separated liquor. After 

 opening the upper part of the urethra towards the dorsum penis, and ex- 

 panding its inner membrane, if you compress these glands, you may see their 

 liquor issue from two distinct orifices, which is very transparent and tenacious : 

 these two orifices open into the urethra, just below its bending, under the ossa 

 pubis in the perinaeum. 



The artifice of nature is very extraordinary in thus placing these glands 



