192 On the ORIGIN and 
and to remark that, in one of them, it became indeterminate ; 
and that, by a curious coincidence, this happened in the 
only cafe which could be fuppofed applicable to the aftronomi- 
cal problem above mentioned ; in other words, he found, that 
in the ftate of the data, which mutt there always take place, 
innumerable lines might be drawn, that would be all cut 
in the fame ratio, by the four lines given in pofition. This 
he demonftrated in a differtation publifhed at Rome in 1749, 
and fince that time in the third volume of his Opu/cula. A 
demonttration of it, by the fame author, is alfo inferted at the 
end of CasTILLoNn’s Commentary on the drithmetica Univer- 
__falis, where it is deduced from a conftruction of the general 
problem, given by Mr TuomAs Simpson, at the end of his Ele- 
ments of Geometry*. The propofition, in Boscovicn’s words, is 
this: ‘ Problema quo queritur recta linea quz quatuor rectas po- 
“* fitione datas ita fecet, ut tria ejus fegmenta fint invicem in ra- 
*€ tione data, evadit aliquando indeterminatum, ita ut per quod- 
“ vis punctum cujufvis ex iis quatuor rectis duci poflit recta. 
“ linea, que ei conditioni faciat fatis f.”’ 
Ir is needlefs, I believe, to remark, that the propofition thus 
enunciated is a Porifm, and that it was difcovered by Bosco- 
vicu, in the fame way, in which I have fuppofed Porifms to 
have been firft difcovered by the geometers of antiquity. I 
fhall add here a new analyfis of it, conducted according to 
the method of the preceding examples, and to which the fol- 
lowing /emma is fubfervient. 
LEMMA 
* Elements, p. 243. Edit. 3. Srmpson’s folution is remarkably elegant, but no men- 
tion is made in it, of the indetermmaie cafe, 
+ Jos. Boscovicu Opera, Baflani. tom. 3. p. 33% 
