quippe ad qnem cafLim noftra figura eft accommodata, 

 ynde iiidiciiim haiid difRculter inrtituetur, fi fecus euenerit. 



§. 19. Cum nt tang. ^ r= ^-i^^' erit 



-_/- y n c' — f n' 



COl. t, ^ ( ^3 j,/ _ e i,'j2 _^_ (a c' — c a'; = ) ' 



quo valore ia altera formula fubftituto prodibit 



cang. j/ _ siiV^^iri-s» ' 



praecedens vero formula vtique eft commodior, quoniam, 

 poftquam angulus ^ fuerit inuentus, inde faciiius angulus 

 •vj concluditur. 



§. 20. Vt autem indolem ipfius orbitae inuefti- 

 gemus, aequationibus ditferentio-ditferentialibus primo ex- 

 hibitis erit vtendum. Primam igitur per zdx, fecundam 

 per 2.dy ac tertiam per 2. d z multiplicando , fumma da- 

 bit hanc aequationem : 



■iixddx-^-idyidy-^-idzdd.z [xdx-it-ydy-V-^zdz ) 



J75 ■ — Z « V3 > 



Hinc igitur, quia 



fUV — xx-^-yy-^-zz, ideoque x dx-^y dy-\-zdz~v dv ^ 

 ob elementum dt conftans elicietur inregrando 



d ji' -H i y' -f- d z^ — _i_ 1_^ _i_ C 



Pro conftante igitur determinanda faciamus 



X fl, JK P, Z t, ^^ «, ^^ <7, ^^ I., 



tum vero fiat diftantia v — d^ ita vt fit 



d — Viaa-\-bb-^cc), 

 quo fado noftra aequatio fiet 



a' a' -j-b^bi-h- c' c' — '-^-^ C, vnde fit 



C = a'ai-\-b'b'-^c'c'--'-^. 



Sicque 



