Marci of Kronland, Johannes Marcus
,
De proportione motus figurarum recti linearum et circuli quadratura ex motu
,
1648
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Had ABCD. </
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<
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>Hoc eſt permutando ut AF ad H, ita FE ad
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ABCD. </
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<
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>Quòd ſi
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fiat ut FE ad AF, ita ABCD ad aliud
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quadratum: inventum erit circulo H æquale quadratum. </
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<
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>Quòd ſi ex illâ plagâ moveatur E per lineam parallelam GK:
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erit per Lemma 2. minor proportio AF ad H, quàm FE ad
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ABCD:
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huius motus velocior motu circuli. eandem er
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gò plagam recipit quadratum ABCD, quam infert circulo:
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ac proinde illius impulſus à percuſſione erit æqualis AE: com
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poſitus nimirum ex plagâ reciprocâ AF & impulſu reſiduo FE. </
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<
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>Supponamus verò AE ad AF eſſe ut 6 ad 2, hoc eſt in ratione
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triplâ: ſpatium verò decurſum ab E ad ſpatium decurſum ab H
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ut 3 ad 2. </
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<
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>Quòd ſi
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circulus H accipiat impulſum ut 3. hoc
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eſt additâ ſemiſſe, movebitur ad idem intervallum cumquadra
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to ABCD. </
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<
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>Et ſi fiat ut 6 ad 3, ita ABCD ad aliud, inventum
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erit quadratum circulo H æquale. </
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<
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>Demum ſi motus quadrati E à percuſſione fiat parallelus li
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neæ mediæ inter tangentem GB, & perpen dicularem GH; erit
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per Lemma 3 maior proportio AF ad H, quàm FE ad ABCD:
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& motus H velocior motu ABCD. </
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<
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interval
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lum motûs Had interuallum motûs ABCD in ſeſqui alterâ
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ratione, hoc eſt ut 3 ad 2: FE autem ad AF ut 4 ad 2. </
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<
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>Quòdſi
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quadratum ABCD accipiat impulſum ut 6; movebitur
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eadem velocitate, & ad idem intervallum cum circulo H per
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poſit. 5. propterea quòd impulſus eandem rationem habeat ad
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ſuum mobile, per corollarium 2. 1 Axiomatis. </
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<
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>Et ſi fiat ut 6
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ad 2, ita quadratum ABCD ad aliud quadratum, inventum
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erit circulo H æquale quadratum. </
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