( 2-04 ) 
perlbns, who make it their bufinefs to detrad from that little 
ihare of Reputation I have in chefe things. But to return 
to the matter in hand, Let us demonftiate the following 
.Propoftion. 
The Meridian Line is a Scale of Legarithmick 'Xangents of tht 
half Complements. of the Latitudes, 
For this Demonftration, it is requifite to premile thefefour 
Lemmata^ 
,f Lemma, I. In the Stereografhick ProjeBion of the Sphere upon 
the plain of the Equinodial, the diftances from the Center, 
which in this cafe is the Pole, are laid down by the Tan- 
,gents of half thofe diftances, that is, of half the Comple- 
ments of the Latitudes. This is evident from EucL ;.2o. 
Lem. IL In the Stereografhick ProjeBionj the Angles, under 
which the Circles interfed each other, are in all cafes equal 
to the Spherical Angles they reprefent: Which is perhaps as 
valuable a property of this ProjeBion, as that of all the Circles 
of the Sphere thereon appearing Circles : But this not being 
vulgarly known , muft not be affumcd without a Demonfira- 
tion. 
Let £ jB PL be any great circle of the Sphere, E the Eye 
placed in its Circumference, 
C its Center,? any point there- 
of, and let FC O be fiippofed 
a plain ereded at right Angles 
to the Circle EBP L,on which 
FCOWQ defign the Sphere to 
be projeded. Draw E P crot- 
fmg the Plain FC O in />, and 
p fhall be the point P projeded. 
To the point P draw the Tan- 
gent A P G, and on any point 
thereof^ as A, ered a perpen- 
dicular AD^ at right angles 
to the plain EBPLy and draw 
the lines PD, ACyDC : and the 
angle ^PD /hall be equal to 
the Spherical Angle contained 
between the plains APC, DPC. Draw alfo AE, PE, inter- 
feding 
