±$6 D E M T V 



Ulo cafu erit fuccinclius p zz ^l±j^hi}^tJpi^!lzl±:^ 

 -;s(fin.£f rin.<) hoc vero p-O^-^- U^n.^-^ii n.^w-x^^): 



C o r o 1 1. I. 



ab. III. 42. Sit tubi briichium AB. horizontale et BC 



Fig. 43- verticale hincque g rz o et <^ 11190°. Vnde fit ce- 

 leritns in U-=:.=zY i^ (ff^ll- 2kx+ zlx-x x), 

 Ponamus initio totam vcnam tubum horizontalem 

 A B occupafle , ibique quieuifle , vt fit A B — /, 

 necefle ergo e(l , vt pofito B M zz x zz l celeritas 

 euanefcat , fumique debeat^^r:- 2kl; vnde cum ve- 

 na in fitum M B N peruencrit erit celeritas 

 — y —^ (/ — vV)(2 k — l -^ x) 'j et quando tota vtna 



in tubum verticalem peruenit , quod fit fi x =z Oy 

 eius celeritas qua afcendere perget erit adhuc 

 zn V '-M. {2 k — l). Dum ergo longitudo venae mi- 

 nor fit quam 2 ^, tota vena in tubum verticalem; 

 afcendit , fiquidem fuerit altior quam 2 k, 



O o r o 1 1- o 



4-!^. Sumto i^utem ff-=z2kl et X — V iA , 

 aequatio bis integrata fit: xzn — k + I-^-kcotCKt-^^y). 

 Vnde cum initio fuerit x zz I, angulus conftans yt 

 euanefcit , vt fit a' 3: /— ^ (i — cof X t), Tempus 

 ergo quo tota vena in tubum verticaiem intrat , 

 hinc definiri debet i — cof >> t zz ~- feu 'h t =z Ang.. 



cof. (1 -l). Quare fi /z= i^ erit t zz: -^ zz -^" ^^- ' 



Scho- 



fin autem ij^ ,l:zzzh fit ifn^P^-. 



