Wright's Mathematical Papers. 77 
From the sum of the products in the column N W, SE, subtract 
the product in the column NE, SW, and divide the remainder by 
2 according to the rule, and we obtain, 
DEKI-+ HAtg — GHgr+FGrm=ACFGH. 
Demonstration. 
lk xkm=2DEAI. 
(2m¥F — Fn)nG=2FGrm. 
(2rG+0H)Go=2GH oar. 
(2qgH—Hp)pA=2H Aig. 
Hence, ae 2GHqr, and eae by 2, we — 
Ekl+-HAig— GHqr+FGrm=EDIAiAHG 
For EF m substitute its equal CDi, aa for BCk pa its equal 
ABi, and we have, DEAI--HAig — GHqr+FGrm=ACFGH. 
No. II.—The propositions contained in this paper are obvious, 
and may, perhaps, be found in many treatises on surveying. J] have 
chosen, notwithstanding, to send it for insertion in the Journal of 
Science, for the purpose of bringing the methods contained in the 
first and third —_ side by side, that their connexion and relation 
may readily be seen. _ 
A method of finding the contained angles of a field, having the 
courses and sides given. 
The courses of the two sides, that form the ait when compared 
together, admit of the four following variations. 
Var. 1. Unlike, like; when letters are 4 or G and on or sg 
The contained angle is the sum of the points of compass. 
Var. 2. Unlike, unlike; when they are MY or = and a orp 
The contained angle is the difference of the points of 
compass. 
Var. 3. Like, unlike; when they are i. or Be and 4 or af 
The angle is their sum subtracted from 180°. 
V; . : z N - Ss. E. Ww. 
ar. 4. Like, like; when they are 1 org and E. 7 w. 
The angle is their difference subtracted from 180°. 
The following rule may be of use to the surveyor, in ascertaining 
the accuracy with which the courses have been taken. 
t 
