-44^ ) i<Js ( r?i<- 



Propofitio 2. 



f. 12. Maximum impulfionis momentum in Fof* 

 Tab. IV. ^'^^^ femicirculari, in omni arcus puntlo aequaliter gra- 

 Fig. 5, vato, definire. 



Redla BS tangat femicircnlum GBMD in B,, 

 atque e fulcro F Pilae G F ducatur ad B S normalis re- 

 da F S , ordinataque ad diametrum Circuli D G redla 

 BC, quae produda occurrat re(^ae S F produdae in Q, 

 agantur BA, FE diametro DG paralielae, ducaturque 

 iemidiameter P B. Efto itaque radius circuli =z i 



MA=:x, AB — ?C=:jy erit 

 AP— CB=:i-a:, CG=i-jrzFE, 

 altitudo Pilae GF = a. Ob parallelas B P , Q S anguli 

 PBC, FQE inter fe aequantur; vterque vero angulus 

 P C B, F E Q redus eft. Ergo et reliqui E F Q, B P C 

 erunt aequales. Quare Triangula P B C , F E Q func fi- 

 milia , ideoque PC:CB=:FE:EQ, hoc eft 



j:i-x-i-jiEQ, Ergo E Q zz ^' -y)('-*)^ 



cft autem 



PC:PB=rFE:QF, vel j : i r= i -j' : QF, 



atque ideo QF— i^=-2^. Erit itaque 



BQ = i ~x-\-a-{- (■ ->)(■- x)^ 



y 



Verum eft P B : B C =r B Q : Q S , hoc cft 

 I ; I - A- — B Q : Q S. 



Ergo 



(lS = (i-x){i -^^+fl + il-^U-^-l), 



atque 



FS=: 



