Marci of Kronland, Johannes Marcus, De proportione motus figurarum recti linearum et circuli quadratura ex motu, 1648
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              Sit iam ſi fieri poteſt, hyperbole. aſſumatur verò huius diame­
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              ter partium 8, qualium AC eſt 10, & AV 2. </s>
              <s>Igitur triangu­
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              lum rectangulum contentum AV, & latere compoſito ex AV
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                <expan abbr="atq;">atque</expan>
              diametro figuræ erit partium 20:
                <expan abbr="triangulũ">triangulum</expan>
              verò
                <expan abbr="contentũ">contentum</expan>
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              AC
                <expan abbr="atq;">atque</expan>
              latere compoſito ex AC & diametro eiuſdem figuræ,
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              partium 180: huius verò ratio ad illud noncupla. eſt autem
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              quadratum
                <expan abbr="quoq;">quoque</expan>
              ſemiordinatæ CG ad quadratum alterius
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              ſemiordinatæ VE in eadem ratione. propterea quòd latus CG
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              ſit triplium lateris VE. </s>
              <s>Cùm
                <expan abbr="itaq;">itaque</expan>
              eandem rationem ad ſe
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              habeant rectangula ſubſegmentis axis hyperbolæ, quam habent
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              quadrata ſemiordinatarum; erit permutando eadem
                <expan abbr="quoq;">quoque</expan>
              ra­
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              tio rectangulorum ſub ſegmentis axis ad quadrata ſuarum ſe­
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              miordinatarum: ac proinde puncta EG in eadem hyperbole. </s>
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              <s>Rurſum verò quoniam AOS. AKF ſunt triangula ſimilia;
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              & AO
                <expan abbr="quadruplũm">quadruplumm</expan>
              OS; erit
                <expan abbr="quoq;">quoque</expan>
              KF quadruplum AK:
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              & AK partium 5, qualium KF eſt 20. triangulum ergo
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              rectangulum contentum AK
                <expan abbr="atq;">atque</expan>
              latere compoſito ex AK
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              & diametro figuræ erit partium 65: rectangulum verò conten­
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              tum AV, & latere compoſito ex AV
                <expan abbr="atq;">atque</expan>
              diametro eiuſdem
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              figuræ, partium 20. eſt autem ratio 65 ad 20 minor, quàm ſit
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              quadrati KF ad quadratum VE: Igitur permutando non ea­
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              dem eſt ratio rectangulorum ſub ſegmentis axis ad quadrata
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              ſemiordinatarum: ac proinde puncta EF non continentur in
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              lineâ hyperbolæ. </s>
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              <s>Demum
                <expan abbr="neq;">neque</expan>
              ellipſin eſſe hanc lineam motûs, ita oſtendo. </s>
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              <s>Producatur AC in Z: quam ſecetperpendicularis IZ. </s>
              <s>Cùm
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                <expan abbr="itaq;">itaque</expan>
              in I gravitas fiat æqualis impulſui; erit IZ maior omni­
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              bus rectis, quæ ex lineâ motûs cadunt perpendiculariter ad dia­
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              metrum AZ: ac proinde erit ſemidiameter figuræ. </s>
              <s>At ve­
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              rò IZ æquatur ſemidiametro AZ: oportebat verò eſſe in­
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              æqualem: non igitur puncta AEFGHI in ellipſi continentur. </s>
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