[ 28 o ] 
*LD, being perpendicular to AL, is given in pofition 
((by 30. dat.). But AL being given in magnitude, 
the proportion of AF to LD is given (by loga- 
rithms). And AF is given in magnitude. There- 
fore LD is given in magnitude. Therefore the 
point D is given, E. I. 
The conffru&ion is obvious. It is evident, that 
the points L and N are on the fame fide of A, if 
F be at the greater curve, as in fig. 3 and 4; but 
on different fides of A, if the curve to which F 
belongs be the lefs, as in fig. 5 and 6 
The calculation of the lengths AL, LD, by 
•means of the logarithmic canon, is very fimple. 
Putting B for the fubtangent of the Briggian 
fiyftem, L for the tabular logarithm of AC, and D 
for the difference of the tabular logarithms of x^C, 
AF, we (hall have, 
Firff, AL = 
A H x A K x l) 
B xKH * 
And again, L =j= - = tab. log. of L D. 
In this fecond exprefiion, the fecond term is nega- 
tive, if the greater of the given ordinates belong to 
the lefs curve, as in fig. 3 and 5 ; but pofitive if 
the greater ordinate belong to the greater curve, as 
in fig. 4. and 6. 
Both thefe theorems are fo eafily derived from 
the preceeding analyfis of the problem, that it is 
needlefs to add the fynthetic demonftration ; but 
they may be reduced to more commodious forms for 
practice by the following artifice. 
(*) By the greater and the left curve I mean that which hath 
•the greater or the lefs fubtangent. 
Firff, 
