Marci of Kronland, Johannes Marcus - De proportione motus figurarum recti linearum et circuli quadratura ex motu

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21[Figure 21]

THEOREMA XVII.

Fieri poteſt ut idem parallelogrammum mutato ſitu moueatur, &
quieſcat in codem plano inclinato.

Aſſumatur inclinatio plani æqualis angulo EDB: cadetq,
linea hypomochlij DE in centrum figuræ. Et quia tum cen
trum grauitatis hypomochlio occurrit, quieſcet parallelogran
mum in co ſitu, per theorema 6. Cùm verò angulus ECD ſit
maior angulo inclinationis EDB; ſi ex C ducatur linea hypo.
mochlij, cadet inter EC. DC: ac proinde centrum figuræ ex
tra hypomochlium motum continuabit in eodem plano.

THEOREMA XIX.

Motus circuli in eodom plano inclinato eſt velocior motufiguræ
rectilineæ.

Moueatur in eodem plano AN circulus GCA, atq, penta
gonum BILMN: Dico motum circuli eſſe velociorem. Aſſu
matur radius EA æqualis ON & ducantur lineæ hypomochlij
AC. NR ſecetur autem ſemidiameter figuræ motús OQ bifa
riam & æqualiter in P: ut ſit OP æqualis Pque per primum
lemma: dico EF maioren rationem habere ad FG, quàm OP
ad OQ Nam quia rectus eſt angulus DAE, & angulus BNO
ſemiſſis anguli pentagoni minor recto: ſunt verò anguli DAC.
BNP einſdem inclination is ex hypotheſi æquales: erit angu
lus reliquus FAE maior angulo reltquo PNO. Et quia OP
per conſtructionem eſt æqua is PQ, ſi iungatur recta NQ, erit
angulus PNQ æqualis angulo ONP, maior verò angulo BNP,
hoc eſt illi æquali angulo DAF: ac proinde maior quoque

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