Miscellanea Curio fa. 5 9 



beyond the view of the naked Eye, with a 

 TelefcopkkQvadrant) to find the diftanccs or 

 lines AB, AC, AE, EC. 



ConftruBion. 

 In each of the Triangles BAE, CAE y 

 two Angles at A, E, being known, the third 

 is alfo known: then take any line at plea- 

 fure, on which conftitute the Triangles 

 Aty refpe&ively equiangular to the Triangles 

 B AE, A EC-, join 0 y. Then upon BC con- 

 ftitute the Triangles BCA,BCE, equiangu- 

 lar to the correfpondent triangles 0 y *, £ y^ 

 join AE, and the thing is manifeftly done. 



Tm Calculation. 

 AfTuming^« of any number of parts, in 

 triangles * £ s, the angles being given, 



the fides A 7,^?>, 0 -y may be found by 

 Trignometry : Then in the Triangle p a y 7 

 having the angle and the legs 



we may find ' Then £>. BC: : £*. : 

 3 J. Z? £ : : > : : y g . CF. 



7V /k<wd Problem (Fig. $ and tfj 



Three Objedls .5, C, D, are given, or f which 

 is the fame ) the fides, and confequently an- 

 gles of the triangle BCD are given \ alfo 

 there are two points or ftations A, E, fuch, 

 that at A may be feen the three points B C E, 

 but not D ; and at the ftation E may be 

 feen ^, D, but not B, that is the angles 

 BAC, BAE, A EC, A ED, f and confe- 

 quently E A C, A EC, are known by obferva- 

 tion : to find the lines A B^ AC, A E E C 7 

 E V. Con- 



