Ceva, Giovanni, Geometria motus, 1692

Table of figures

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              do rectangulum IH in HO eſt imago velocitatum eiuſ­
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              dem motus per AGEA. </s>
              <s id="s.000527">Ducatur nunc ex quocun­
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              que momento Q linea QRMN ipſi IK æquidiſtans, & au­
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              ſpicato motu ex centro D momento I, vt nempe oriatur
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              ſpiralis, intelligatur momento Q ventum eſſe in B, quamo­
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              brem ductâ DBE, erit rectangulum, ſeu imago QIKR ad
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              imaginem rectangulum HIKL, ita DB ad DE, in qua ra­
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              tione, cum propter ſpiralem, ſit etiam circunferentia AGE
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              ad circunferentiam AGEA, erit rectangulum IQ in HO
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              imago velocitatis per AGE, eſtque velocitas iuxta tangen­
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              tem in E ad velocitatem iuxta tangentem circulum BC in
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              B vt ED ad DB, ſeu vt HO ad QM; ergo cum iuxta
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                tem</expan>
              in A, hoc eſt in E velocitas ſit HO, erit ſecundùm tan­
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              gentem circulum BC in B, ipſa QM velocitas; propterea­
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              que imago triangulum HIO, quæ in parabolæ deſcriptio­
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              ne erat per AG, nunc erit per omnes tangentes circulos ſu­
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              binde creſcentes ex D in E: ſcilicet momento I, erit mobi­
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              li puncto ſecundùm DA, velocitas IK; momento Q dum̨
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              adeſt in B, erit ſecundùm BE velocitas QR, & iuxta
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                tem</expan>
              in B circuli BC velocitas QM; quæ ambæ, hoc eſt ve­
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              locitates QR, QM cum ſint normaliter directæ, erit eidem
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              mobili in B iuxta ſpiralem velocitas QN potentia ipſis am­
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              babus æqualis. </s>
              <s id="s.000528">Similiterque momento H cum mobilę
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              fuerit in A, erit velocitas iuxta ſpiralem, ipſa HP æqualis
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              potentiâ duabus velocitatibus HL iuxta radium, et HO
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              iuxta tangentem; & ſic omnino liquet, ipſum quadrilineum
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              HIKP eſſe imaginem velocitatum tam in deſcriptione pa­
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              rabolæ AGF, quàm ſpiralis Archimedeæ DBA, & cum ſit
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              in ijſdem deſcriptionibus homogenea ſibi ipſi, conſtat ip­
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              ſas curuis æquales eſſe. </s>
              <s id="s.000529">Nam vt imago illa ad ſe ipſam ita
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              parabola ad ſpiralem prædictam. </s>
              <s id="s.000530">Quod &c. </s>
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