relate as proj€(5led 5 and proceed icythe refoktion of the Prob- 
lem propoPd: And howto fit inthofe Seftions/eethey. books 
of Apelhnms^Mjd^rgius^ the jd, Volumcof Des Cartes* shttitx%^ 
Leotaudi Gecmetricd fracticdi Anderfonii ExereitAt. Geometric^, 
As to the Problem it felf , it is determin'd ©n the Sphere by 
the laterfcdions of the two leffer Circles of Diftancc;, whofe F^- 
are the known Starrs, Aad this Problem harh diwQi^sGeme-^ 
/r/V^ ways of refolucion. 
1. By Plain Geometry (in the fenfebefore- mentioned ^ J Sap-^^ 
pofing a Plain to touch theSphere at the North- f&le i if the Eye 
heat the South-pole^ projediing thofe Circles into the faid Plaio^ 
they are ftill Circle5(by reafon of the fub-contrary Seiftions of th© 
VifaalCones)whofc Centers fall in the fides of the Right-lin'd' 
Angle^made by the Projected Meridians, that pafs through th§ 
known Starrs^and thus the Problem is eafily folv'd in this manner^ 
2, Ifitbe required to be performed by in' 
one cafe it may be done, by placing the Ey at the Center of 
the Sphere, and projecfting as before > to wit, when thelon^ 
ger Axes.o( the figures being prodaced concur above the Vertex % 
Here the Problem is determined by the Incerfedions of two Co- 
nick Sections (whereof a Circle cannot be one , ualefs its Cen* 
ter be in the Axis of the other figure. ) And in this fecond Cafe 
tfiefe points of Inter feftion fallin the fame right \mzox projeiS:- 
ed Meridian^th^Y d^id before^ but at a more remote diftance from 
the Pde-point ^.towic, in the former Suppofition^ the Polajf 
diftance was meafur'd by a Right line, that was the double Tan- 
gent of half the Arch 5 here it is the Tangent of the^whole Arch^ 
Hence it is evident^ how one Pr^;^/7/V;^ may beget another 5 yea 
infinite others, altering the Scale 5 and how the leffer Circles 
mih^ Stereografhiek Projcdlion help,to defcribe the ConickSec-^ 
tionsiathc (7^w^;7/Vi: Proje£lion: But ( to reduce the matter 
to one common radius ) if we fuppofe two Spheres equal^ .an i fa 
placed about the fame Axk^ that the Pole-poinc of the one iliail 
pafs thraugh the Centrr of the other, and the Touch- plain to 
f^fs through the faid Cetu^r or Pole-point, and that a lelfer Cir^ 
cle hath the famep ficion in the one as in the other* T^ej^, if 
the Eye-be at theSouth-Poleoftheone^ it is at the* Center of 
theotKer 5 , and any pr^jeded MeridianAxmti from the projec- ' 
^d Pt)Ie-ppinttopafe through both the proj^flioos of thefe let 
