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54 Miscellanea Curio fa. 



Cafe 2. If the Station be in one of the Sides 

 of the Triangle, as in the ioth Figure at S, 

 then having the three fides AC, CB,BA given, 

 fmd the Angle CA B'-, then again in the Tri- 

 angle 5 A B, all the Angles, and the fide AB, 

 are known ; whence may be found either AS, 

 or S B, Geometrically, if you make the Angle 

 C AD equal to the obferved Angle C S B, and 

 draw B S parallel to D A, you determine the 

 Point of Station S. 



Cafe 3. If the three Obje&slie in a right Line* 

 as A C B (fuppofe it done) and that a Circle 

 pafleth through the Station S, and thetwo ex- 

 terior Objeds A B, then is the Angle A B D 

 equal to the obferved Angle ASc (by 21 of 

 the 3d Book of Euclid) as infilling on the fame 

 Arch AD: And the Angle BAD in like 

 manner equal to the obferved Angle c SB: 

 By this means, the point D is determined. 

 Join DC, and produce the fame, thn a Circle 

 pafTing through Points A B D, interfe&s D C, 

 ' produced at 5, the place of Station. 



Calculation. 



In the Triangle ABD, all the Angles and 

 the fide A B are known, whence may be found 

 the fide A D. 



Then in the Triangle C A D thetwo fides 

 C A and A D are known and their contained 

 Angle c A D is known *, whence may be found 

 the Angles CD A' and A CD, the comple- 

 ment whereof to a Semicircle is the Angle 5 

 cA : in which Triangle the Angles are now 

 all known and the fide AC: whence may be] 

 found either of the Diftances, Sc or S A. 

 >; Cafe 4. 



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