of several Places in Denmark. 
45 
the meridian GDE of a place G, whose longitude and latitude 
are to be calculated. For the first series of triangles may be 
taken the parallel, divided into small parts AB = BC = CD ; 
and for the second series may be taken the meridian GD ; be- 
cause the arches of those circles are known by the triangles, 
and computed from the trigonometrical operations. FAGD 
in the ist. fig. is laid down in fig. 2 upon a plane. The angles 
a, b, c, d, are equal to the angles A, B, C, D. The lines af bf 
cf gdf, are equal to AF, BF, CF, GDF, touching the meri- 
dians AE, BE, CE, GDE in A, B, C, D. The angle dfa = 
DFA = AFB -j- BFC + CFD. For the place g, or G, are 
given the distance from the meridian of Copenhagen = gk, 
and the distance from the perpendicular = ak, and af — AF 
= AV x tang. V. In the case that g is more southerly than 
an, th enfk = af -f ak. If the place is northerly, then fk = 
af — ak. Hence tang, dfa — yp The complement to the 
angle dfa is the angle fna =fgk, which the meridian gdf 
makes with the perpendicular to the meridian of Copenhagen. 
Now DEA : DFA == AF : AM = tang. V : sin. V ; therefore 
the longitude of the place G from the meridian of Copenhagen = 
DEA = DFA 
tang. V 
DFA 
sin. V 
gk _ 
cos. V 
Again, gf= If the place g is more south- 
erly than the perpendicular an, then dg=gf — fd — gf— 
af ; if more northerly than an, in that case dg = af~fg. 
From hence the latitude of the place g may be found. 
The following Table contains the latitudes of towns and 
places, with their longitudes from the royal observatory at 
Copenhagen, calculated from our trigonometrical operations. 
