Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
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THEOREMA XVII.
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Fieri poteſt ut idem parallelogrammum mutato ſitu moueatur, &
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quieſcat in codem plano inclinato.
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<
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>Aſſumatur inclinatio plani æqualis angulo EDB: cadetq,
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linea hypomochlij DE in centrum figuræ. </
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>Et quia tum cen
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trum grauitatis hypomochlio occurrit, quieſcet
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parallelogrã-mum
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mum</
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in co ſitu, per theorema 6. </
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>Cùm verò angulus ECD ſit
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maior angulo inclinationis EDB; ſi ex C ducatur linea hypo.
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mochlij, cadet inter EC. DC: ac proinde centrum figuræ ex
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tra hypomochlium motum continuabit in eodem plano. </
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THEOREMA XIX.
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Motus circuli in eodom plano inclinato eſt velocior motufiguræ
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rectilineæ.
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>Moueatur in eodem plano AN circulus GCA, atq, penta
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gonum BILMN: Dico motum circuli eſſe velociorem. </
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>Aſſu
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matur radius EA æqualis ON & ducantur lineæ hypomochlij
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AC. NR ſecetur autem ſemidiameter figuræ motús OQ bifa
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riam & æqualiter in P: ut ſit OP æqualis
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Pq.
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per primum
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lemma: dico EF maioren rationem habere ad FG, quàm OP
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ad OQ Nam quia rectus eſt angulus DAE, & angulus BNO
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ſemiſſis anguli pentagoni minor recto: ſunt verò anguli DAC.
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BNP einſdem inclination is ex hypotheſi æquales: erit angu
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lus reliquus FAE maior angulo reltquo PNO. </
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<
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>Et quia OP
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per conſtructionem eſt æqua is PQ, ſi iungatur recta NQ, erit
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angulus PNQ æqualis angulo ONP, maior verò angulo BNP,
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hoc eſt illi æquali angulo DAF: ac proinde maior
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