34 Abplication of Napier’s rules. 
The method of applying these solutions to the various cases of 
Right-Angled Spheric Trigonometry is very simple, and is explained 
in several treatises of Trigonometry. . 
To apply this method to Oblique- Angled - Siew Trigonometry 
it is necessary to divide the triangle into two right-angled spheric tr- 
angles by means of a perpendicular AP (Fig. 3) let fall from the point 
A upon the opposite side BC : the perpendicular being so chosen as to 
make two of the given things fall i in one of the right-angled triangles.* 
Each triangle thus formed contains, as above, five circular parts, | 
the perpendicular being counted and bearing the same name in each 
of them: consequently the parts of each triangle similarly situated with 
ees to sae Be Soa must have the same name. In every 
Jblig eric ea rigonomery there are three parts 
v care two of these parts 
ini ee the pare ACP, ABP, eRe 4 situated with reapecctte each 
other. To each of these must be joined the perpendicular AP, and there 
will be three parts in each triangle, which are to be named middle, adja- 
cent, or opposite, according to the above directions. Then the equations 
for solving all the cases <a fught: Sage 3 and most of the cases of Ob- 
a rn i. ae a Se ———- 
PPh oe he ts of the a a Be ae 
‘Sine m ait sep of the opposite parts. : 
~ These Sissies when spend to Right- Angled Spheric Triangles 
. Or in other words the perpendicula’ 
ought to be let fall from the end of o 
given side and opposite to a given caieels. When this can be done in two different: 
ways, that one is to be rejected, whieh makes the perpendicular a middle part. 
Thus in Example 3 the perpendicular ought not to be let fall from the point B. 
+ The cases excepted are where three sides or three angles are given; oF 
where the question relates to two angles and their LS cages mete: It ened be prop a 
er to observe, that it will be of considerable assistance in the above 
rules to take notice of the circumstance, that the second intiart of mn words fan 7 
“gent and cosine ave the same as the first letters of adjacent and opposite. 
