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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<
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">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; </
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">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; </
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<
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">ducantur BC.BR.BM. dico BC breuiore tempore quàm B
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R, BM, percurri, quod breuiter demonſtro: </
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ris in BC, ſitque vt BH ad BI, ita BI ad BC; </
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">certè BH & AC æquali
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tempore percurruntur; ſit autem tempus quo percurritur BH, vel AC
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vt. </
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">BH; </
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">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; </
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">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; </
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">igitur BR & YR perpendicularis eodem tem
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pore percurruntur; </
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">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; </
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">igitur QM eſt dupla QB,
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igitur maior EC; </
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">igitur maiore tempore percurritur; </
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<
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æquali tempore decurruntur; igitur BM maiore tempore, quam BC
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quod erat demonſtrandum. </
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<
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">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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</
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<
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">& angulus ABM addit angulum CBM 15.grad. </
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M fient æqualibus temporibus, vt conſtat ex dictis. </
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<
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">Obſeruabis tertiò rationem à priori inde eſſe ducendam; </
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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; </
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<
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">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; </
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<
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">ſed collectum ex extremis inæqualibus, eſt ſemper maius
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collecto ex æqualibus, poſita ſcilicet eadem media proportionali; </
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ſunt æqualia, media proportionalis eſt ſemidiameter circuli cuius dia
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meter eſt æqualis collecto; </
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<
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">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. </
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<
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<
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