Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              Schol. pag.
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              217.
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              num.
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              8.
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            <p id="N2ABCA" type="main">
              <s id="N2ABCC">Obſeruabis primò, fœdatam eſſe pulcherrimam demonſtrationem quæ
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              habetur loco citato innumeris propemodum mendis, qua ſcilicet pro­
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              batur omnium inclinatarum, quæ ab eodem horizontalis puncto ad
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              idem perpendiculum ducuntur, cam quæ eſt ad angulum 45. grad. bre­
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              uiſſimo tempore decurri; </s>
              <s id="N2ABDA">ſit enim Fig.49. Tab.2. in qua ſit EC diuiſa
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              bifariam in A, ex quo ducatur circulus radio AC, ſit AB perpendicula­
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              ris in AC; </s>
              <s id="N2ABE4">ducantur BC.BR.BM. dico BC breuiore tempore quàm B
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              R, BM, percurri, quod breuiter demonſtro: </s>
              <s id="N2ABEA">ducatur AH perpendicula­
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              ris in BC, ſitque vt BH ad BI, ita BI ad BC; </s>
              <s id="N2ABF0">certè BH & AC æquali
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              tempore percurruntur; ſit autem tempus quo percurritur BH, vel AC
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              vt. </s>
              <s id="N2ABF8">BH; </s>
              <s id="N2ABFB">haud dubiè tempus quo percurretur BC erit vt BI, eſt autem B
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              I æqualis AC,, quæ eſt media proportionalis inter BC & BH, vt con­
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              ſtat; </s>
              <s id="N2AC03">ſit autem BR dupla AR, & angulus ABR 30. grad. ducatur BY
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              perpendicularis in BR, certè RY eſt dupla BR, ſunt enim triangula RB
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              A, RBY proportionalia; </s>
              <s id="N2AC0D">igitur BR & YR perpendicularis eodem tem­
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              pore percurruntur; </s>
              <s id="N2AC13">ſed YR eſt maior EC, nam EC eſt dupla AB, & R
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              Y dupla RB, quæ eſt maior AB, ergo YR maiore tempore percurritur
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              quam CE, igitur BR quam BC, ſimiliter ducatur BM ad angulum ABM
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              60. grad. ſit QB perpendicularis in BM; </s>
              <s id="N2AC1F">igitur QM eſt dupla QB,
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              igitur maior EC; </s>
              <s id="N2AC25">igitur maiore tempore percurritur; </s>
              <s id="N2AC29">ſed BM & QM
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              æquali tempore decurruntur; igitur BM maiore tempore, quam BC
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              quod erat demonſtrandum. </s>
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            <p id="N2AC31" type="main">
              <s id="N2AC33">Obſeruabis ſecundò BM & BR æquali tempore decurri, vnde quod
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              ſanè mirificum eſt, ſi pariter vtrimque creſcat, & decreſcat angulus in
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              puncto B, ſupra & infra BC, æquali tempore percurrentur duo plana in­
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              clinata; v.g.angulus RBA detrahit angulo ABC angulum CBR 15.grad.
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              </s>
              <s id="N2AC3E">& angulus ABM addit angulum CBM 15.grad. </s>
              <s id="N2AC41">motus per BR & B
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              M fient æqualibus temporibus, vt conſtat ex dictis. </s>
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            <p id="N2AC46" type="main">
              <s id="N2AC48">Obſeruabis tertiò rationem à priori inde eſſe ducendam; </s>
              <s id="N2AC4C">quod cum
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              perpendiculum ſeu diagonalis quæ ſuſtinet angulum rectum ſit regula
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              temporis quo decurritur omnis inclinata, diagonalis quadrati ſit om­
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              nium aliarum minima in rectangulis quorum minus latus ſit maius ſe­
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              midiagonali quadrati, in eodem ſcilicet perpendiculo; </s>
              <s id="N2AC58">v.g. ſit diagona­
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              lis EC, ſint latera quadrati EBC, ducatur infra BA quælibet recta, v.g.
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              BR, & in BR ducatur perpendicularis BY, certè YR eſt maior EC,
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              quia vt eſt RA ad AB, ita AB ad AY, igitur AB eſt media proportionalis
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              communis; </s>
              <s id="N2AC67">ſed collectum ex extremis inæqualibus, eſt ſemper maius
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              collecto ex æqualibus, poſita ſcilicet eadem media proportionali; </s>
              <s id="N2AC6D">ſi enim
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              ſunt æqualia, media proportionalis eſt ſemidiameter circuli cuius dia­
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              meter eſt æqualis collecto; </s>
              <s id="N2AC75">ſi verò ſunt inæqualia, media proportiona­
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              lis eſt ſunicorda circuli, cuius diameter eſt æqualis collecto; igitur col­
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              lectum iſtud eſt maius priore, ſed hæc ſunt ſatis clara. </s>
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              <s id="N2AC7F">Quod ſpectat ad demonſtrationem num. </s>
              <s id="N2AC82">9. ibidem poſitam, & peni-</s>
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