100 jDE TRAIECTORIIS 



mo tertiam varlabilem ^, et inueftigabo , quomodo.v ct 

 j in ^ , determinari debeant, vt traiedoria reciproca re- 

 fultet , pono itaque dx:=rdt ^ et dyzzpdt. Efficiendum 

 ergo eft , Yt pofito t negatiuo , et dx in negatiuum a- 

 beat. Quare loco r ponatur oportet fundlio ipfius t par, 

 quae fit N-, txitdxzzkdtj et abeunte t in ncgatiuum , e- 

 rit dxz=i-lkdt. Confequenter ob d dzzz-dx'^ , pofito 

 in cafu — /, loco p, ^, vt ante, habebitur /j^hiNN. 



XXIII. Ponaturp=(P-l-Q)'' denotante P fundio- 

 ne parc et Q impare ipfms t , erit ^zz(P-Qf adeoque 



( pp_QQ. ) ^ =zN^ ergo PP—N"^ -+-QQ,ct Vzn 



V/(N^-^QQ)eritergojr>i=:(Q-i-i/(N^+ QQ ))".Nihil 



contradicfloriihic latct in nequatione Pn^^(N^H-QQ ) 

 etenim P , quae fundio par effe debet,talLS etiam in aequatio- 



ne exhibetur. Atfi Q erueretur,inueniretui QzzV^^N^-PP ) 

 id quod contradictionem inuoluif,nam Q,quae fundionem 

 imparemdenotat, aequatur hic fundioni pari.Vtfradio- 

 nes in exponentibus euitem , fcribo loco N^N"" et erit 

 dx— NV/,et dy-dt (Q-f-V^N'-4-Q'))" poteil hie lo- 

 coQ,fcribiNQ , ('.ip^et dein loco N^vt ante, Nj 

 habebitur dx—^t, et ^^r=zNVAQ-V-V(i-hQQ) ^. 



XXIV. Vt nouae tormulae refultent,tollo irratio- 

 nalitatem,ponendoy(N--4-Q')i=:N4-RQeritQz=:.i^^^^ 



vnde Rfundio impar fitipfius /^neceife efl: , ob Q im- 

 parem,erit ergoQ-4-V(N'-4-Q')=='^*-^^:!-R -(fcripto io- 



coR, 



