MOTUS MEDII Pl.ANETAR.UM. I 5 



YdX — X d Y— — v v d $ cof. a , feu 

 X d Y — Y d X = v v d <p cof a>. 



XVIII. 



Simili modo habebimus 

 X d Z — Z d X = v d <p (X cof. % fin. + Z 



(fin. £ cof. 4 -t- cof. I cof. a> fin. 4 ) ) > 



& pro X & Z in membro pofteriori fubftitutis valo 

 ribus 



XdZ - ZdX-v vdqfin.as \cof. £ (cof. £ cofi-^-fin.% cof.a>fm.\) 

 -^ fin. £ {fin. £ cof. 4 -+- cof. | cof a fin. 4 )) > 



quae maniflfto in hanc fimpliceni contrahitur, 

 XdZ — Z d X = v v d ip Jin. a cof. -\>. 



Denique eodem veftigio infiftentes colligimus: 



Y d Z — Z d Y= v d <p ( Y cof. I fin. a -¥■ Z 

 (fin. £ fin. 4 — co/i £ co/m co/I 4 ) )» 



& pro F & Z & valoribus fubftitucis 



T </Z -ZdY-vvd<pfin. a>(cof.% (cof ZJin.-\>+Jin£,cof.a> cof.-\) 



-¥-fin. £ (fin. £ fin. 4 — "?/. £ co/ a co/i 4) ) ' 

 qua; fponte in hanc fimpliceni formulam abic : 

 Y dZ — Z dY -=vv d tpjin. a fin. 4- 



XIX. 



Deniqne cum ex dementis dX, dY &c d Z fit ele- 

 mcntum revera dcfcriptum Z^=V(dX 1 -*- d F l -*- d Z-) 

 ob AZ = v&.AZ = v->rdv fi centra A arculus 

 Z v defcribatur erit { v = dv 6c cum poficus fit an- 



