56 Mifcellanea Curio fa. 



In thefe three latter Cafes no ufe is made of 

 the Angle obferved between the two Obje&s, 

 as A and B, that are made the Bafe-line of the 

 Conftru&ion \ yet the fame is of ready ufe' for I 

 finding the third Diftance,. or laft fide fought, 

 as in the fourth Scheme, in the Triangle S A B 0 

 there is given the Diftance A B, its oppofite 

 Angle equal to the ftim of the two obferved 

 Angles, and the Angle SAB attained, as in 

 the fourth Cafe : Hence the third Side or laft 

 Diftance S B may be found. 



And here it may be noted, that the three 

 Angles C A 5, a 5 5, S B C\ are together equal 

 to the Angle A C £, for the two Angles c5B, 

 and c B S, are equal to E c 5, as being the 

 Complement of S c B to two right Angles:, and 

 the like in the Triangle on the other fide. 

 Ervo, &c. 



Cafe 6. If the three Objects be A, 5, C, and 

 the Station at S. } as before, it may happen, ac- 

 cording to the former Gonftru&ions, that the 

 Points c and D may fall clofe together, and 

 fo a right Line joining them may be produced 

 with uncertainty - 7 in fuch cafe the Circle may 

 be conceived to pafs through the place of Sta- 

 tion at 5, and any tw r o of the Objects ( as in 

 the fixth Scheme ) through B and c ; wherein 

 making the Arigle DBC equal to the obferved 

 Angle A S c, and BCD equal to the Comple- 

 ment to 180 degrees of both the obferved An- 

 gles in DSB thereby the Points is determi- 

 ned, through which, and the points c £, the 

 Circle is to be described, and joyning d A A 

 (produced, when need requireth) where it in- j 



terfe&s I 



