Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
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angulo interno
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hei,
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æqualis autem angulo
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ifh;
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propterea
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quòd
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aſſumpto angulo communi
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ihf
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facit rectum:
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& angulo
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ifh
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eſt æqualis angulus
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kfm;
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erit
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æqualis an
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gulo
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ahi,
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ac proinde maior angulo interno
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hei,
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angulo inci
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dentiæ. </
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Obijcies. </
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>Si vectis continet gr auitatem mobilis, totus totam, pars ve
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rò partem proportionalem per 2 Axioma; et impulſus centri grauitatis
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totus mouet, cùm huius interuallum ab hypomochlio eidem eſt æquale per
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7 theorema 2 partis; neceßè in figurâ 3 theor: 2 huius, cùm tota ſemidia
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meter figuræ motûs ſit extra hypomochlium, & non niſi in puncto tan
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gat planum AZ; aut nullam, aut inſenſibilem inferre plagam: non igi
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tur rectè aſſumebatur ratio plagæ ad reliquum impulſum, quam habet
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quadratum ED ad quadratum EA: ſiquidem totum impulſum metitur
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quadratum eiuſdem ED.
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<
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>Reſpondeo noſtram aſſertionem veram eſſe, cùm ſemidia
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meter figuræ motûs eâ ratione ſecatur ab hypomochlio, ut re
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liquus impulſus ab illatâ plaga non prohibeatur à ſuo mo
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tu: at verò hic impulſus cogitur ab hypomochlio ad
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motũ
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incli
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natum
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di,
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per tangentem circuli centro
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a
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deſcripti. </
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<
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>Erit
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impulſus reliquus in eâratione ad totum impulſum, quam ha
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bet motus in eiuſmodi plano inclinato ad motum verticalem. </
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>Ducatur enim
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el
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parallela ipſi
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di:
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motus verticalis in
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ea
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ad motum inclinatum in
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el,
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ut quadratum
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ea
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ad quadratum
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el,
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hoc eſt ut quadratum
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da
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ad quadratum
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de:
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quòd ſimilia
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ſunt triangula
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ael. aed.
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Et quia quadratum
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ad
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hoc eſt totus
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impulſus æquatur duobus quadratis
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de. ae;
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eſt autem quadra
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tum
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de
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impulſus movens, erit quadratum
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ae
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impulſus qui
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eſcens, hoc eſt plaga; quam infert eidem plano
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az.
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Magis er
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go univerſalis eſt hæc ratio, quàm à ſemidiametro figuræ </
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