ctum Mperpetuo tangit lineam Rectam. Ergo duæ ſectiones Co
nicæ tranſibunt per eadem quinque puncta, contra Corol. 3. Lem.
xx. Igitur punctum Mverſari in linea Curva abſurdum eſt. Q.E.D.
nicæ tranſibunt per eadem quinque puncta, contra Corol. 3. Lem.
xx. Igitur punctum Mverſari in linea Curva abſurdum eſt. Q.E.D.
DE MOTU
CORPORUM
CORPORUM
PROPOSITIO XXII. PROBLEMA. XIV.
Trajectoriam per data quinque puncta deſcribere.
Dentur puncta quinque A, B, C, P, D.Ab eorum aliquo Aad
alia duo quævis B, C,quæ poli nominentur, age rectas AB, AC,
48[Figure 48]
hiſque parallelas TPS, PRQper punctum quartum P.De
inde a polis duobus B, Cage per punctum quintum DinfiNI
tas duas BDT, CRD,noviſſime ductis TPS, PRQ(prio
rem priori & poſteriorem poſteriori) occurrentes in T& R.De
niQ.E.D. rectis PT, PR,acta recta tripſi TRparallela, ab
ſcinde quaſvis Pt, Pripſis PT, PRproportionales; & ſi per
earum terminos t, r& polos B, Cactæ Bt, Crconcurrant in
d,locabitur punctum illud din Trajectoria quæſita. Nam punc
tum illud d(per Lemma xx) verſatur in Conica Sectione per
puncta quatuor A, B, C, Ptranſeunte; &, lineis Rr, Ttevane
ſcentibus, coit punctum dcum puncto D.Tranſit ergo ſectio Co
nica per puncta quinque A, B, C, P, D. Q.E.D.
alia duo quævis B, C,quæ poli nominentur, age rectas AB, AC,
48[Figure 48]hiſque parallelas TPS, PRQper punctum quartum P.De
inde a polis duobus B, Cage per punctum quintum DinfiNI
tas duas BDT, CRD,noviſſime ductis TPS, PRQ(prio
rem priori & poſteriorem poſteriori) occurrentes in T& R.De
niQ.E.D. rectis PT, PR,acta recta tripſi TRparallela, ab
ſcinde quaſvis Pt, Pripſis PT, PRproportionales; & ſi per
earum terminos t, r& polos B, Cactæ Bt, Crconcurrant in
d,locabitur punctum illud din Trajectoria quæſita. Nam punc
tum illud d(per Lemma xx) verſatur in Conica Sectione per
puncta quatuor A, B, C, Ptranſeunte; &, lineis Rr, Ttevane
ſcentibus, coit punctum dcum puncto D.Tranſit ergo ſectio Co
nica per puncta quinque A, B, C, P, D. Q.E.D.