i^d DE MOTV RECTILINEO 



4. Ciim igitur foliitio fit perduda ad duas 

 aequiit oiies differentio - diffcrei.tial>-s inter p, q et i ; 

 infigne Uicrum obtineri eft cenfendum , fi has ae- 

 quat^ones ad duas al as primi tantum gradus diffe- 

 rentialts reuocare liceret. Hoc autem fingulari ar- 

 tificio fequentem in n'0dum praeftari poffe comperi, 

 Statuo q~piiy et binae aequationes d-fferentio-diffe-' 

 xendales; itai repraelentcntur r. 



^- al ^ p'p(~^~^~~ {V^T]i -^ u u) 



udp-i- pdu dj_f . A B — C > 



«•■ dt — ■ f fl^ (u -+- O^ " " /• 



lam artificium ia hac fubftitutione confiftit , vt po- 



d p r ^ dq udt-i-p d u s 



nam rt - vp ^' at^-di = v? i ^^^ ^^^'^ 

 patebit his fubftitutionibus binas variab les p et g e^.i 



calculo elidi poffe ita \t tantum hae tres r, s et u 



rehnquantur, per prima differentiaUa determinandae. 



Statim vero aequatio illa integralis fupra inuenta 



, - f. ■ j-.. u B(Arr-+-Csj^-f-AC(rH-s)* 



adeo ad formam nnitam rcdit hanc A-+rB^c~^~' 



z=:Gp-\-2. A.R-i- ^^ ■+- ~ quae infignem vfum. 

 afferre poterit.. 



5. Cum fit j-f = ^ erit dt — ^P, vnde 

 noftrae aequationes differentio-differentiales praebent; 



dr rjt_±p_, . T. _C ^. 



•<lp~~tpit — pr-^p^'*^ -t» ~ (a_^i)» "T^ uu^ 



d_s sdp ^t_ /A A B — C x 



Vf) 2 p VJ> — f r Vp v'^ ""(uH-i)» uu J 



tnde fit: 



**^ — 2p ^ pr^ ■" •" luH-')' ^ UM/ 



^j. -. »^ P . 'LP / A _ — c i-=-C V 



Praeterea 



