Fabri, Honoré, Tractatus physicus de motu locali, 1646

Table of figures

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            <pb pagenum="210" xlink:href="026/01/242.jpg"/>
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              <s id="N1D652">
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              Theorema
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              28.
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            <p id="N1D65E" type="main">
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              Hinc per omnes chordas inſcriptas circulo ad alteram extremitatem,
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              diametri perpendicularis terminatas deſcendit mobile æquali tempore
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              ; </s>
              <s id="N1D66B">a ſit
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              enim circulus centro B; </s>
              <s id="N1D671">ſit diameter AE perpendicularis deorſum; </s>
              <s id="N1D675">du­
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              catur AC inclinata, tùm CE; </s>
              <s id="N1D67B">deſcendat haud dubiè æquali tempore
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              per AC.CE.AE. per Th.24.25.26. idem dico de omnibus aliis AD.D
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              E. AG.GE.AF.FE; </s>
              <s id="N1D683">eſt enim eadem omnibus ratio; hinc non poteſt da­
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              ri planum tam paruæ longitudinis, quo non poſſit dari minus, quod dato
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              tempore percurratur. </s>
              <s id="N1D68B">Hæc eſt illa propoſitio toties à Galileo enuncia­
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              ta; </s>
              <s id="N1D691">cum enim motus per BE ſit ad motum per GE vt GE ad BE, & tem­
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              pus per BE ad tempus per GE vt BE ad GE; </s>
              <s id="N1D697">cumque ſit vt BE ad GE
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              rita GE ad AE; </s>
              <s id="N1D69D">certè motus per AE eſt ad motum per GE vt AE ad G
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              E; </s>
              <s id="N1D6A3">igitur tantùm addit AE ſupra GE ratione ſpatij, quantum ratione
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              motus: igitur tempore æquali per AE. & GE fiet motus, idem dico de
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              aliis chordis. </s>
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            <p id="N1D6AB" type="main">
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                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              29.
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              </s>
            </p>
            <p id="N1D6B9" type="main">
              <s id="N1D6BB">
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              Hinc datis duabus inclinatis æqualibus poteſt determinari ratio tempo­
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              rum, in quibus percurruntur
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              ; </s>
              <s id="N1D6C6">ſint enim AG.AH æquales, ſed diuerſæ incli­
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              nationis; haud dubiè cum æquali tempore AG. AF percurrantur per
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              Th. 27. tempora quibus percurruntur AGAH erunt vt tempora quibus
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              percurruntur AF AH, & hæc vt tempora quibus percurruntur AE. A
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              K, & hæc vt radices quadratæ illorum ſpatiorum AE. AK, cum autem
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              ſpatia ſint vt quadrata temporum, vel in duplicata ratione, ſi inter AE
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              & AK ſit media proportionalis AN. v. g. tempus quo percurretur AE
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              erit ad tempus, quo percurretur AK vt AE ad AN, vel AN ad AK. </s>
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            <p id="N1D6DE" type="main">
              <s id="N1D6E0">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              30.
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              </s>
            </p>
            <p id="N1D6EC" type="main">
              <s id="N1D6EE">
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              Hinc cognito tempore quo percurritur data portio linea cognoſci potest
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              tempus, quo percurritur aliud ſpatium vel alia portio,
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              v. g. cognoſco tem­
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              pus quo percurritur AK, & volo cognoſcere tempus quo percurritur K
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              E, conſequenti motu ex AK, ſcio tempus quo percurritur ſola AE, quod
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              eſt ad tempus quo percurritur AK vt AE ad AN per Th. 28. igitur
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              tempus quo percurritur KE conſequenti motu ex AK eſt ad tempus,
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              quo percurritur AK vt EN ad NA, vel vt NK, ad NA. </s>
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            <p id="N1D706" type="main">
              <s id="N1D708">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              30.
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              </s>
            </p>
            <p id="N1D714" type="main">
              <s id="N1D716">
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              Hinc in planis inæqualibus tùm in longitudine, tùns in inclinatione,
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              poteſt ſciri ratio temporum, quibus percurruntur
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              ; </s>
              <s id="N1D721">ſint enim AC AR duo pla­
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              na; </s>
              <s id="N1D727">ſit autem AE perpendicularis indefinita; </s>
              <s id="N1D72B">diuidatur AC bifariam
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              in V ducta perpendiculari VB; </s>
              <s id="N1D731">ex B fiat circulus, ſecabit puncta
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              ACE; </s>
              <s id="N1D737">ſecat etiam AR; </s>
              <s id="N1D73B">in D igitur AC, & AD percurruntur æquali
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              tempore per Th. 27. ſimiliter fiat circulus ART eodem modos certè A
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              R & AT percurruntur æqualibus temporibus per Th. 27. igitur tempus,
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              quo per curritur AR, vel AD eſt ad tempus, quo percurritur AR vt
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              tempus, quo percurritur AE ad tempus, quo percurritur AT; </s>
              <s id="N1D747">ſed hæc </s>
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