Fabri, Honoré, Tractatus physicus de motu locali, 1646

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            <p id="N1FC20" type="main">
              <s id="N1FC99">
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              determinatio noua in linea incidentiæ GD eſt ad nouam in linea inci­
                <lb/>
              dentiæ KD, vt GD vel KD ad K
                <foreign lang="grc">β</foreign>
              , & in linea incidentiæ AD vt AD
                <lb/>
              ad AB; </s>
              <s id="N1FCAA">igitur vt ſinus totus ad ſinum rectum dati anguli incidentiæ; </s>
              <s id="N1FCAE">ſed
                <lb/>
              in linea incidentiæ perpendiculari GD, determinatio noua eſt ad pri o­
                <lb/>
              rem in ratione dupla; </s>
              <s id="N1FCB6">igitur vt G
                <foreign lang="grc">δ</foreign>
              ad GD; </s>
              <s id="N1FCBE">ergo noua per KD eſt
                <lb/>
              ad nouam per DG, vt K
                <foreign lang="grc">θ</foreign>
              , ad G
                <foreign lang="grc">δ</foreign>
              ; </s>
              <s id="N1FCCC">nam vt eſt K
                <foreign lang="grc">β</foreign>
              ad GD ita K
                <foreign lang="grc">θ</foreign>
              ad
                <lb/>
              G
                <foreign lang="grc">δ</foreign>
              ; </s>
              <s id="N1FCDE">ergo noua per KD eſt ad priorem vt K
                <foreign lang="grc">θ</foreign>
              ad KD, & noua per
                <lb/>
              AD, vt AC ad AD, atque ita deinceps; ergo determinatio noua per
                <lb/>
              lineam incidentiæ obliquam eſt ad priorem, vt duplum ſinus recti an­
                <lb/>
              guli incidentiæ ad ſinum totum, quod erat demonſtrandum. </s>
            </p>
            <p id="N1FCEC" type="main">
              <s id="N1FCEE">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              42.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1FCFA" type="main">
              <s id="N1FCFC">
                <emph type="italics"/>
              Hinc in ipſo angulo
                <emph.end type="italics"/>
              60.
                <emph type="italics"/>
              determinatio noua eſt æqualis priori, id eſt in an­
                <lb/>
              gulo incidentiæ
                <emph.end type="italics"/>
              30. ſit enim prædictus angulus IDR; </s>
              <s id="N1FD0D">certè RI eſt ſubdu­
                <lb/>
              pla ID, vt conſtat; </s>
              <s id="N1FD13">ſed determinatio noua per ID eſt ad priorem, vt
                <lb/>
              dupla IR ad ID; ergo vt æqualis ad æqualem. </s>
            </p>
            <p id="N1FD19" type="main">
              <s id="N1FD1B">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              43.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1FD27" type="main">
              <s id="N1FD29">
                <emph type="italics"/>
              Hinc ſupra angulum
                <emph.end type="italics"/>
              30.
                <emph type="italics"/>
              vſque ad
                <emph.end type="italics"/>
              90.
                <emph type="italics"/>
              noua determinatio eſt maior priore,
                <emph.end type="italics"/>
                <lb/>
              donec tandem in ipſa GD vel in ipſo angulo GDR 90. ſit dupla prio­
                <lb/>
              ris, infrà verò angulum 30. eſt minor priore, donec tandem in ipſa ſe­
                <lb/>
              ctione plani FDB nulla ſit noua. </s>
            </p>
            <p id="N1FD42" type="main">
              <s id="N1FD44">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              44.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1FD50" type="main">
              <s id="N1FD52">
                <emph type="italics"/>
              Ex his demonstratur acuratiſſimè æqualitas anguli reflexionis cum ſuo an­
                <lb/>
              gulo incidentiæ
                <emph.end type="italics"/>
              ; </s>
              <s id="N1FD5D">ſit enim linea incidentiæ KD v. g. determinatio noua
                <lb/>
              per DG eſt ad priorem per DQ, vt K
                <foreign lang="grc">θ</foreign>
              vel XQ æqualis ad DQ; igi­
                <lb/>
              tur vt DZ æqualis QX ad DX; </s>
              <s id="N1FD71">ſed quotieſcumque ſunt duæ determi­
                <lb/>
              nationes, fit mixta per diagonalem Parallelo grammatis; </s>
              <s id="N1FD77">ſed QZ eſt pa­
                <lb/>
              rallelogramma, & DX diagonalis; </s>
              <s id="N1FD7D">igitur determinatio mixta ex vtra­
                <lb/>
              que eſt per DX; </s>
              <s id="N1FD83">ſed angulus XDG eſt æqualis KDG, vt patet, nam
                <lb/>
              XDG eſt æqualis DXQ, & hic DQX, & hic QD
                <foreign lang="grc">δ</foreign>
              , & hic QDK; </s>
              <s id="N1FD8D">
                <lb/>
              igitur KDR, qui eſt angulus incidentiæ eſt æqualis angulo XDF, qui
                <lb/>
              eſt angulus reflexionis: idem dico de omni alio. </s>
            </p>
            <p id="N1FD94" type="main">
              <s id="N1FD96">Obſeruaſti iam ni fallor primò determinationes nouas eſſe vt chor­
                <lb/>
              das arcus ſubdupli incidentiæ. </s>
              <s id="N1FD9B">Secundò planum reflectens quaſi repelle­
                <lb/>
              re omnes ictus per DG, id eſt per lineam, quæ à puncto contactus duci­
                <lb/>
              tur per centrum grauitatis, vt demonſtratum eſt lib.1. Th.120.121. </s>
            </p>
            <p id="N1FDA2" type="main">
              <s id="N1FDA4">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              45.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1FDB0" type="main">
              <s id="N1FDB2">
                <emph type="italics"/>
              Nullus impetus deſtruitur per ſe in pura reflexione
                <emph.end type="italics"/>
              ; </s>
              <s id="N1FDBB">nam per accidens vt
                <lb/>
              plurimùm deſtruitur, vt dicemus infrà: </s>
              <s id="N1FDC1">dixi in pura reflexione; </s>
              <s id="N1FDC5">quia cum
                <lb/>
              fit aliqua compreſſio, vel repellitur corpus impactus niſu poſitiuo, etiam
                <lb/>
              deſtruitur impetus; </s>
              <s id="N1FDCD">demonſtratur Th. quia nihil impetus eſt fruſtrà; </s>
              <s id="N1FDD1">
                <lb/>
              igitur nihil deſtruitur: </s>
              <s id="N1FDD6">conſequentia patet ex dictis; probatur antece­
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              dens, quia linea determinationis mixtæ eſt ſemper æqualis lineæ prioris
                <lb/>
              determinationis, ſi remoto obice fuiſſet propagata. </s>
              <s id="N1FDDE">v.g. ſit linea inciden-</s>
            </p>
          </chap>
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