[ 9 2 7 ] 
This laft proportion was firft delivered by Gelli- 
brand, and the other two not long after by Oughtred, 
in their refpedtive treatifes of Trigonometry. 
But it may farther here be noted, that from two 
fides of a plain triangle, as AC, CB, with the angle 
between them A C B, the third ftde A B may be 
found either by the firft or fecond of the foregoing 
proportions y for by the firft may be found EG x G b , 
that is, AF q — A G q , and by the fecond EDxD F, 
or AD’ — A F q j whence by a table of fquares A F 
f — AB) may be readily found, for AG is equal to 
AC — BC, andAD- AC + CB. 
In like manner in the fphe- 
rical triangle from the fides 
AC, CB, and the angle ACB, 
may the third fide be expedi- 
tioufiy found with the aid of a 
table of natural fines, by the 
axiom referred to in the be- 
ginning of this difeourfe, as modelled for this pur- 
pofe by Napeir, in the propofition, which has been 
already referred to (h), whereby the axiom is re- 
duced to this analogy, 
Rad. q : fin. A C x fin . CB : ; tin. 
verf. f. A B — verf. f. AC w C B .... 
; rad. x - 4 ~ CO* 
May 
(h) Mirif. Canon. Conftr. p. 59. . 
(/) An example of this method has been given above m the tri- 
angle A B C in p. 920. And in default of a table of natural fines, 
the bafe A B might have been found thus. The fum of twice the 
logarithmic fine of £ AC B, added to the logarithmic fines of A C 
*=> and 
