Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              quadrans ABG in quo ſint duæ chordæ GC, CB: </s>
              <s id="N1D9E1">Dico quòd per vtram­
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              que ex G breuiori tempore deſcendit, quàm per inferiorem CB; </s>
              <s id="N1D9E7">quia
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              per CB, & GB æquali tempore deſcendit per Th.27.ſed per GCB bre­
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              uiori tempore deſcendit, quàm per GB; </s>
              <s id="N1D9EF">ſit enim GD perpendicularis
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              parallela AB; </s>
              <s id="N1D9F5">ſit ED perpendicularis in CG, & per 3. puncta GCD
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              ducatur circulus: </s>
              <s id="N1D9FB">his poſitis, GH & GC eodem tempore percurrentur,
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              & in C idem erit motus, ſiue ex G per GE, ſiue ex E per EC deſcen­
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              dat mobile per Th.27.& 20. ſit autem EB ad EK vt EK ad EC, ſitque
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              BE v.g, dupla BE vel BA: </s>
              <s id="N1DA05">dico EK eſſe æqualem BG; </s>
              <s id="N1DA09">eſt autem BH
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              maior BC vel AB, vel HG minor CK; </s>
              <s id="N1DA0F">ſit etiam GH ad GI, ita GI
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              ad GB: </s>
              <s id="N1DA15">dico tempus, quo deſcendit per GCB eſſe ad tempus quo de­
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              ſcendit per GB vt GCK ad compoſitam ex GC, HI; </s>
              <s id="N1DA1B">ſed hæc eſt ma­
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              ior illa, vt patet ex Geometria, & analytica; </s>
              <s id="N1DA21">igitur breuiori tempore de­
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              ſcendit per GCB, quàm per GB; ſed de hoc aliàs. </s>
            </p>
            <p id="N1DA27" type="main">
              <s id="N1DA29">Sit enim EB 8. dupla ſcilicet AB; </s>
              <s id="N1DA2D">ſit autem EE ſubdupla EB ad
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              EK vt EK ad EB; </s>
              <s id="N1DA33">aſſumatur GE, ſitque tempus, quo continetur GC.
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              vt GC, & quo conficitur BC vt CK; </s>
              <s id="N1DA39">igitur quo conficitur GCB vt
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              GCK: </s>
              <s id="N1DA3F">ſimiliter ſit ſecunda linea GB, ſitque tempus, quo percurritur
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              GH vt GC, vel NO æqualis GC, ſitque vt GH ad GN, ita GN ad
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              GB certè ſi GH decurratur tempore GH, AB decurretur tempore
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              HN; </s>
              <s id="N1DA49">ſed HN maior eſt MB, vel CG, vt conſtat ex analytica; </s>
              <s id="N1DA4D">adde quod
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              in figura prima ſit GI ad GM vt GM ad GB; </s>
              <s id="N1DA53">certè ſi tempore GI
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              percurratur GI, percurretur GB tempore GM; </s>
              <s id="N1DA59">eſt autem GM æqua­
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              lis AB, vel EC; </s>
              <s id="N1DA5F">ſimiliter ſit EC ad EK vt EK ad EB, ſi percurratur
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              EC tempore EC, percurretur EB tempore EK; </s>
              <s id="N1DA65">ſed GC percurretur
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              tempore GC ſed GCK minor eſt GIM; </s>
              <s id="N1DA6B">ſit enim GM. 4. EK R.
                <expan abbr="q.">que</expan>
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              32. id eſt, 5 7/8 paulò minùs, quibus ſi ſubtrahas CE 4. & ſubſtituas CG
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              2. paulò plùs habebis 3 7/8; igitur GCK minor eſt GIM. </s>
              <s id="N1DA77">Ex his habes
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              omnes Galilei propoſitiones de motu in planis inclinatis numero 38. in
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              quo ſtudio, vt verum fatear, maximam ſibi laudem peperit; </s>
              <s id="N1DA7F">in quo ta­
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              men opere duo deſiderari videntur,
                <expan abbr="alterũ">alterum</expan>
              à Philoſophis, quod ita phyſi­
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              cæ partes omnes neglexerit, vt ferè vni Geometriæ ſatisfaceret; alterum
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              ab Geometris quod Geometriam equidem accuratè tractarit. </s>
              <s id="N1DA8D">Sed minùs
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              ad captum Tyronum: atque hæc de his ſint ſatis, vt tandem noſtrorum
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              Theorematum ſeriem interruptam repetamus. </s>
            </p>
            <p id="N1DA95" type="main">
              <s id="N1DA97">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              31.
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              </s>
            </p>
            <p id="N1DAA3" type="main">
              <s id="N1DAA5">
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              Ex dictis ſequitur pondus centum librarum poſſe habere tantùm grauitatio­
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              nem vnius libræ
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              ; </s>
              <s id="N1DAB0">ſit enim planum inclinatum centuplum horizontalis, id
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              eſt, ſecans centupla Tangentis; haud dubiè grauitatio in prædictum pla­
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              num erit tantùm ſubcentupla per Th.16. </s>
            </p>
            <p id="N1DAB9" type="main">
              <s id="N1DABB">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              32.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1DAC7" type="main">
              <s id="N1DAC9">
                <emph type="italics"/>
              Ex duobus ferentibus idem parallelipedum in ſitu inclinato poteſt alter fer­
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              re tantùm vnam libram, licèt pendat centum libras
                <emph.end type="italics"/>
              ; </s>
              <s id="N1DAD4">ſit enim ita inclina-</s>
            </p>
          </chap>
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    </archimedes>
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