Fabri, Honoré, Tractatus physicus de motu locali, 1646

Table of figures

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              <s id="N28C61">Decimononò, ſi æqualis ſit ſecundus ictus. </s>
              <s id="N28C64">Primò, poteſt determina­
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              ri proportio iuxta quam defigitur palus, quod vt melius explicetur, ſit
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              cuneus BE, cuius ſolidum facilè demonſtratur; </s>
              <s id="N28C6C">eſt enim ſubduplum pa­
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              rallelipedi, cuius baſis ſit quadratum AC, & altitudo RE; </s>
              <s id="N28C72">ſi enim trian­
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              gulum ADE ducatur in latus AB vel EF habebitur ſolidum cunci, vt
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              conſtat, vnde cunei eiuſdem latitudinis ſunt, vt triangula, v.g. cuneus A
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              F ad eumdem YF; </s>
              <s id="N28C7E">vt triangulum ADE ad triangulum YHE: </s>
              <s id="N28C82">hoc po­
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              ſito ſit triangulum MKN æqualis ADF, & primo ictu tota EI vel N
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              Z ſecundo ictu defigitur, non quidem æquali altitudine, ſed æquali ſoli­
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              do; </s>
              <s id="N28C8C">cùm autem triangulum XZN ſit ſubquadruplum trianguli QON
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              ſit media proportionalis N inter NZNO, triangulum N
                <foreign lang="grc">β</foreign>
              Y eſt du­
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              plum NZX; </s>
              <s id="N28C98">igitur ſecundo ictu defigetur N
                <foreign lang="grc">β</foreign>
              : </s>
              <s id="N28CA0">ſimiliter ſi vt NZ ad N
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                <foreign lang="grc">β</foreign>
              , ita N
                <foreign lang="grc">β</foreign>
              ad N. Tertio, ita defigetur NT, & quarto NO dupla NI: ra­
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              tio eſt, quia æquales ictus æquales habent effectus. </s>
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              <s id="N28CB1">Vigeſimò, ſi æquales accipiantur altitudines ſingulis ictibus, ictus
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              ſunt in ratione duplicata altitudinum, ſuppoſitâ prædicta hypotheſi cunei
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              v.g.ſi dato ictu defigatur NZ, & altero NO, ſecundus eſt ictus quadruplus
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              primi; </s>
              <s id="N28CBB">ſi verò tertio ictu defigatur N
                <foreign lang="grc">θ</foreign>
              tripla NZ, ictus eſt ad primum
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              in ratione 9/1. ſi denique dato ictu defigatur NM, ictus eſt ad primum
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              in ratione 36/3, vt patet ex dictis; ſi verò primo ictu defigatur NZ, ſecundo
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              ZO, tertio O
                <foreign lang="grc">θ</foreign>
              , quarto
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              M, ictus ſunt, vt numeri impares 1.
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              3. 7. 9. </s>
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              <s id="N28CD7">Vigeſimoprimò, hinc ſi dentur duo ictus, & eorum proportio deter­
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              minari, vt poteſt proportio altitudinum, quæ defiguntur, quæ ſunt in
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              ratione ſubduplicata ictuum, ſuppoſito cuneo: </s>
              <s id="N28CDF">ſimiliter, ſi dentur alti­
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              tudines, carumque proportio, determinari poteſt proportio ictum; </s>
              <s id="N28CE5">ſunt
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              enim in ratione duplicata, vt patet ex dictis; porrò vtrumque poteſt
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              conſiderari duobus modis. </s>
              <s id="N28CED">Primò, coniunctim, ſi ſecundus ictus ſucce­
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              dat primo, & eius altitudinem augeat. </s>
              <s id="N28CF4">Secundò, ſi ſeorſim vterque
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              conſideretur, &c. </s>
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            <p id="N28CF9" type="main">
              <s id="N28CFB">Vigeſimoſecundò, in clauis, vel conis altitudines ſunt in ratione
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              ſubtriplicata
                <expan abbr="ictuũ">ictuum</expan>
              , & ictus in ratione triplicata altitudinum defixarum,
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              quòd manifeſtum eſt ex Geometria; </s>
              <s id="N28D07">ſit enim conus BAF, qui defigatur
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              vno ictu; </s>
              <s id="N28D0D">ſitque alter ictus, quo defigatur tantùm FD ſubdupla FA: </s>
              <s id="N28D11">
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              cùm ictus ſint vt defixa ſolida; </s>
              <s id="N28D16">certè conus FD eſt ad conum FA in
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              ratione triplicata, id eſt vt cubus FD ad cubum FA, id eſt vt 1. ad 8.
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              quæ omnia conſtant: </s>
              <s id="N28D1E">idem dico de pyramide, quod de cono: hinc vi­
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              detur differentia ictuum, quibus defigitur cuneus, & conus, </s>
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              <s id="N28D26">Vigeſimotertiò, poteſt explicari quomodo deprimatur cylindrus con­
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              ſtans ex molliori materia; </s>
              <s id="N28D2C">nam primò deprimitur prima ſuperficies
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              cylindri, & extenditur; quia cùm materia. </s>
              <s id="N28D32">ſit mollior, prematurque a
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              duobus corporibus duris vtrinque, ſcilicet ab vtraque baſi, cedit & di­
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              latatur propter humorem in cauitatibus contentum. </s>
              <s id="N28D39">Secundò, aliquan­
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              do totus cylindrus deprimitur ſeruatà ſemper cylindri licet craſſio­
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              ris figurâ, quod vt fiat, molliſſimam materiam eſſe neceſſe eſt. </s>
              <s id="N28D40">Ter-</s>
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