Mifcettanea Curio fa, 65 



Bemonflration. 

 Join AV^c, E D, EF, then is the L MAB 

 t=s& BC M ( by 21 . 3. Eucl.)^ fupplement of 

 the obferv'd L B A E by conilrution, therefore 

 the conftru&ed L D a £, is equal to that which 

 was obferved. Alio the LB AC of the feg- 

 ment is the'conftru&ion of the Segment, e- 

 qual to the obferv'd Lb AC. In like manner 

 the conftru&ed angles a E and B E F, are 

 equal to the correipondeflt obferved angles 

 A e F, B E F, therefore ^ £ are the points re- 

 quired. 



The Calculation. 

 In the Triangle B c M, the L B c M ( sup- 

 plement of2M£) and LBMC (^BaC) are 

 given, with the fide BC ? thence Mc may be 

 found ; in like manner B N in the ad i\TF 

 may be found. But the L Mc D)^ c D — 

 BCM) is known,with its legs Mc-, C there- 

 fore its Bafe MB, and L M DC, may be 

 known. Therefore the L MO N f r=j c D F— 

 CDM—FdN) is known, with its legs Af^ 

 D thence MN with the angles B M Kf 7 

 Dnm, will be known Then the L c M A( 

 (Z- BMC -\-D M N) is known, with the L MAC 

 —MAB+-BAC) and MC before found j there- 

 fore M y4 and a c will be known. In like 

 manner in the triangle E DN, the angles F, n, 

 with the fide D n being known, the fides £ AT, 

 £ D, will be known'-, therefore A E (^=5 MN — 

 MA— En) is known Alfo in the triangle A 

 2?C, the LA with its fides BC, being 

 known, the fide A z?, will be known, with the 

 L B c a ; lb in the triangle E Fz>, the X £ with 

 the fides, £ D, d F being known, £F will be 

 found, with the LedF. Laftly, in the trian- 

 gle 



