REMIS PROTVLSARVM IN PLWIIS 29 



Corollarium 1. Tangens anguli AMP, quem curua 

 a cymba defcripta cnm curfu fluminis PM conftituit efl 

 — \ x y ~ ^Zn- Vbi ergo celeritas fluuii u euanefcit , ibi 

 fpinae diredio curuam tangit. 



Corollanum 3. Si C fiierit pun&um in oppofita flu- 

 uii ripa , in quo cymba appellit , erit B C — ^m.Ai r^ 



- m AB. Quare fi fuerit area A QB A = n A. B. A D, 

 tum cymba in ipfo puncto B appellet. 



Corollarium 4. Si ponatur AB — a\ area AQBA 

 ~ab, atque BCizf, erit /= ~ c — ™. Ex qua aequa- 

 tione erit m cf^na b—n a c. atqne tn c*j 2 =^' V * — n * c*f*znalf' 



2, , 2 2 2 1 . a 2 &->-/V(a 2 c 2 -4-c 2 / 2 — a 2 2> 2 ) 



— ina bc-\-n a c , vnde ontur« — — (a 2 -Km c — ^^ 



-,<._„_ .„ q&/^IaV( a 2 c 2 -4-c 2 j- 2 -a 2 & 2 ) , m ac 2 /±a5Va 2 c 2 - ( -c 2 / 2 -a 2 ^) 



acque;/Z — (a 2 -^-/ 2 ^ l dL n a 2 b 2 -c-p 



Corolhirium 5. Si ergo cymba debeat appellere ad 

 punctum datum C j tangens anguli P M B , qnem cymba 

 cum direclione curfiis fluuii conftanter tenere debet , erit- — 



cc 2 /-4-a&Vfa ?c2 -+-c 2 / 2 -a 2 & 2 ) ^- r Ci . ../ , 2 , ^ . 



— ^— ;*&*-?v* Nifi ergofit<;V(tf -\-f)^ab 



hoc eft nifi fuerit AD> - arg ac — " > fi er * nequit vt cym- 

 ba ad pundhim C appellat. 



Corollarium 6. Quia 7/z negatiuum valorem habere 

 nequit , alias enim cymba non ad ripam oppofitam acce- 

 deret ; vnica directione cymbae ad pundhim C perueniri 

 poterit , fi fuerit bj<^V (a* c* -f- c*f* — afr) feu b <^ c . 



Corollarium 7 • At fi fiierit bj>~V (a*c*-\-c*f*-a*b*) 

 feu b)>c. tum duplici modo cymba ad punctum C per- 

 tingere poterit , ob dnplicem valorem ipfms m affirmati- 

 uum. Oportet autem praetera effe /£> ~ V(bb—cc) • ne 

 m prodeat imaginarium. 



D 3 Cflu 



