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

Table of figures

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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
                <expan abbr="uterq;">uterque</expan>
              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
                <expan abbr="quoq;">quoque</expan>
              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. </s>
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              Obijcies. </s>
              <s>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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              <s>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
                <expan abbr="motũ">motum</expan>
              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. </s>
              <s>Erit
                <expan abbr="itaq;">itaque</expan>
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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. </s>
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              <s>Ducatur enim
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              el
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              parallela ipſi
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              di:
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                <expan abbr="eritq;">eritque</expan>
              motus verticalis in
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                <emph type="italics"/>
              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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                <emph type="italics"/>
              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 </s>
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