[ 3 * 1 
REMARKS. 
r. If it fhould be thought that the reafoning ia 
Art. III. refts too much upon a metaphyfical princi- 
ple of Leibnitz, and requires, if not an apology., 
at lead: a more formal proof: the ground of luch 
reafoning,. and its extenlive ufe, may be more par- 
ticularly explained on fome other occafion. Suffice 
it at prefent to add to the note on that article.. 
That as the given factors ( Qjmd Qj_) in F and x, 
may be joined with M”, or with M 1 ” indifferent- 
ly* the cafe is fimilar to that of an equal chance at play,, 
for the flakes n and i —n, where the juft expecta- 
tion of each gamefter is JL, whatever be the value 
ofn. The fifth and fixth Propofitions of Element I. 
fcarce needed any other demonftration than, that it is 
manifeftly impoffible to affign any reafon of inequa- 
lity, of the angles in one of thefe theorems, and of 
the hides in the other. In the following Propolition, 
where it is proved, that two lines being extended 
from the extremities of a right line, A B, to a point 
C, there is no other point on the fame fide of A B, 
to which lines from A and B equal to the former 
can be drawn : he who holds the contrary is fup- 
pofed to fix upon that other point D; but why D? 
rather than d, d\ d'\ See. he is ft lent : and, there- 
fore, I conclude, there is no fuch point different 
from C. And the like may be laid of fome other 
fimple theorems, that are commonly demonftrated by, 
fhewing the abfurdity of after ting their contraries. 
5 2, The 
