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

Marci of Kronland, Johannes Marcus, De proportione motus figurarum recti linearum et circuli quadratura ex motu, 1648

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1les FM, PA. Cùm itaque angulus OMF ſit grad. 33. prim. 30.
ſemiſſis nimirum anguli externi NOM grad. 67: & angulus
OMA grad: 78. prim: 30; quòd æquales ſint arcus AM. FC:
ablato angulo OMF ex OMA, erit angulus reliquus FMA,
hoc eſt illi æqualis FPA grad: 45. Cùm itaque angulus FIC ſit
quoque oſtenſus grad. 45, erit angulus FIC externus æqualis
angulo interno FPI: quod eſt abſurdum.

Lapſus grauium in ſegmento
Circuli minore, quàm grad: 90. eſt velocior per duas chordas, quàm per
unam chordam.

Moueatur graue ex B in F per arcum grad: 45. Dico veloci
ùs moueri per duas chordas BC. CF, quàm per unam chordam
BF. Supponatur BC æqualis CF: & ducatur FQ parallela BC:
in productâ verò BC ſumatur BT æqualis Fque erit itaque BT
partium 11111400, & BC partium 3901806. Quâ ablatâ ex
BT manet CT partium 7209594. Adde Logaritmum huius
logaritmo anguli CTH grad. 67. prim. 30; qui per lemma eſt
complementum anguli FCT grad: 22. prim. 30. eritque aggre
gatum logaritmus lateris CH partium 6659688. Eſt autem
CH maius latere BC, ſeu CF partium 3901806. Cùm itaque,
motus ex C in H ſit æqualis duratione motui ex C in T, per pri:
theorema huius; erit mot9 in CF minor duratione motu in CH:
additoque communi motu in BC, motus in BC, CF minor du
ratione motu in BT ſeu Fque hoc eſt per prop. 15. illi æquali
motu in BF.

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