Fabri, Honoré, Tractatus physicus de motu locali, 1646

List of thumbnails

< >
141
141 		142
142
143
143 		144
144
145
145 		146
146
147
147 		148
148
149
149 		150
150
< >
page |< < of 491 > >|
    <archimedes>
      <text>
        <body>
          <chap id="N1C940">
            <p id="N1D8E0" type="main">
              <s id="N1D8F4">
                <pb pagenum="213" xlink:href="026/01/245.jpg"/>
              nec tandem perueniat ad horizontalem KY, quæ eſt dupla AK, quia in
                <lb/>
              horizontali non acceleratur motus; </s>
              <s id="N1D8FF">igitur cum impetu acquiſito in deſ­
                <lb/>
              cenſu AK, conficiet motu æquabili KY duplum AK per Th.42.l.3. poſito
                <lb/>
              quòd non deſtruatur; atque ex his ſatis facilè intelligentur, quæcumque
                <lb/>
              habes apud Galileum in dialog.3.à propoſitione 3.ad 23. </s>
            </p>
            <p id="N1D909" type="main">
              <s id="N1D90B">Sextò non probat Galileus, ſed tantùm ſupponit mobile ad
                <expan abbr="eãdem">eandem</expan>
                <expan abbr="alti-tudinẽ">alti­
                  <lb/>
                tudinem</expan>
              aſcendere poſſe motu reflexo ex qua deſcendit, quod examinabi­
                <lb/>
              mus lib.
                <expan abbr="ſequẽti">ſequenti</expan>
              , hinc non laborabimus in
                <expan abbr="examinãdis">examinandis</expan>
              prop. 24.25.26.27. </s>
            </p>
            <p id="N1D923" type="main">
              <s id="N1D925">Septimò, cognito tempore, quo percurrit mobile perpendiculum EC
                <lb/>
              quod ſit diameter circuli; </s>
              <s id="N1D92B">ſciri poteſt quo tempore percurrat duas chor­
                <lb/>
              das ſimul EGGC; </s>
              <s id="N1D931">ſit enim Tangens EF, ſitque vt FG ad FD, ita FD ad
                <lb/>
              FC; </s>
              <s id="N1D937">cum EG & EC deſcendat æquali tempore per Th.27. cum in G ſit
                <lb/>
              idem motus, ſiue ex E, ſiue ex F deſcendat per Th.20. certè ſi deſcendit
                <lb/>
              per EG dato tempore, quod ſit vt EG, deſcendit per GC tempore, quod
                <lb/>
              eſt vt GD; igitur tempus, quo deſcendit per EC eſt ad tempus, quo deſ­
                <lb/>
              cendit per EGC, vt EG ad EGD. </s>
            </p>
            <p id="N1D943" type="main">
              <s id="N1D945">Obſeruabis autem GF eſſe ad EF vt EF ad FC; </s>
              <s id="N1D949">igitur FD eſt media
                <lb/>
              inter FC GF, & eſt æqualis FE, igitur anguli FDE.FED æquales; </s>
              <s id="N1D94F">ſed FD
                <lb/>
              E eſt æqualis duobus DCE.DEC, & FEG, eſt æqualis DCE; igitur duo G
                <lb/>
              DE DEC ſunt æquales. </s>
            </p>
            <p id="N1D957" type="main">
              <s id="N1D959">Octauò, ſi accipiantur æquales horizontalis, & perpendicularis, v.g.
                <lb/>
              BA AC, ducaturque BC: </s>
              <s id="N1D960">Dico nullum duci poſſe planum inclinatum à
                <lb/>
              puncto B ad perpendiculum AEM, quod breuiori tempore percurratur,
                <lb/>
              quàm BC, nec intra angulum vt BR, nec extra vt BM; </s>
              <s id="N1D968">ſit enim vt BC ad
                <lb/>
              BI ita BI ad BH, eſt autem BI æqualis BA, igitur ſi BA, ſit 4.BC eſt v.g.
                <lb/>
              32. & BH radix q.8.igitur HI eſt ferè I paulò plùs; igitur cum BH percur­
                <lb/>
              ratur æquali tempore cum AC, eſt tempus, quo percurritur BH ad tem­
                <lb/>
              pus quo percurritur HC vt BH ad HI. </s>
            </p>
            <p id="N1D976" type="main">
              <s id="N1D978">Sit autem BR dupla AR, ſitque perpendicularis AK in BR; </s>
              <s id="N1D97C">certè KR
                <lb/>
              eſt ſubquadrupla BR; </s>
              <s id="N1D982">igitur percurritur BL æqualis KR eo tempore quo
                <lb/>
              percurritur AR; </s>
              <s id="N1D988">igitur BL ſit ad BV vt BV ad BR; </s>
              <s id="N1D98C">igitur temporibus æ­
                <lb/>
              qualibus percurruntur BL LR; </s>
              <s id="N1D992">igitur ſi tempus quo percurritur BL ſit vt
                <lb/>
              BH, tempus quo percurretur LR erit etiam vt BH; </s>
              <s id="N1D998">igitur totum tempus
                <lb/>
              quo percurritur tota BR erit vt tota BE, ſed tempus quo percurritur tota
                <lb/>
              BC eſt tantum vt BI quę eſt minor BC; </s>
              <s id="N1D9A0">igitur BC breuiori tempore per­
                <lb/>
              curritur quàm BR; ſit
                <expan abbr="etiã">etiam</expan>
              vt BP ad BX ita BX ad BM, ſi BO eſt 4. OP 2.
                <lb/>
              certè BP eſt rad.q. </s>
              <s id="N1D9AC">12.id eſt ferè 3.1/2 paulò minùs, BM verò eſt dupla BA
                <lb/>
              vel BO; </s>
              <s id="N1D9B2">igitur eſt 8. ducatur ergo 8. in 4. 1/3 productum erit 28. cuius radix
                <lb/>
              eſt ferè 5.1/3 paulò minùs; </s>
              <s id="N1D9B8">igitur BX eſt 5.1/3 paulò minùs; </s>
              <s id="N1D9BC">cum autem BH
                <lb/>
              ſit 2.q.8.eſt ferè 2.5/6, paulò minùs; </s>
              <s id="N1D9C2">igitur ſit vt BP 3.1/2 ad BX 5.1/3, ita BH
                <lb/>
              2.5/6 ad aliam; </s>
              <s id="N1D9C8">certè erit 144. id eſt 4.(26/63), licèt minùs acceptum ſit; </s>
              <s id="N1D9CC">igitur
                <lb/>
              126.eſt maior BI, quæ eſt tantùm 4; igitur BE breuiori tempore percur­
                <lb/>
              ritur, quàm BM. </s>
            </p>
            <p id="N1D9D4" type="main">
              <s id="N1D9D6">Nonò, per duas chordas quadrantis deſcendit breuiori tempore mo­
                <lb/>
              bile, quàm per alteram tantùm inferiorem ſcilicet ſit enim tantùm </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum