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

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1quia rationem habet hypomochlij; ſecabitur impulſus eâ rati
one, quâ grauitas verticalis ſecatur à plano inclinato, in par
tem motam & quieſcentem: ac proinde per propoſitionem
11. motus interciſus à plano, erit| æqualis duratione reliquo
motui: qvorum terminos connectit linea recta, perpendicu
laris ad motum interciſum.

LEMMA.

Si in ſegmento Circuli ducantur duæ chordæ, angulus
ab his contentus, erit complementum dimidij anguli eiuſ
dem arcus ad duos rectos.

In ſegmento BF ducantur duæ chordæ BC. CF: dico angu
lum BCF ab his contentum eſſe complementum dimidij an
guli BOF ad duos rectos. Nam duo anguli OFC. OCF ſunt
complementum anguli FOC: duo verò anguli OCB, OBC
complementum anguli COB. Cùm igitur FCB ſit ſemiſſis
illorum angulorum; erit complementum dimidij anguli FOB.

Corollarium.

Sequitur angulum externum FCT eſſe æqualem ſemiſſi an
guli FOB: propterea quòd utriuſque complementum ad duos
rectos ſit angulus FCB.

THEOREMA II.

Lapſus grauium in quædrante Circuli, per duas chordas
æquatur lapſui per unæm chordam.

Secetur primùm AF quadrans circuli æqualiter in B: &

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