Fabri, Honoré, Tractatus physicus de motu locali, 1646

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            <pb pagenum="290" xlink:href="026/01/324.jpg"/>
            <p id="N22494" type="main">
              <s id="N22496">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              54.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N224A2" type="main">
              <s id="N224A4">
                <emph type="italics"/>
              Hinc ſi tantùm habeatur ratio vectis, maior difficiliùs verſatur in plano
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              horizontali, quàm minor.
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              v.g. AE circa centrum E quam FE, producto
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              ſcilicet æquali motu in extremitate vtriuſque A & F; </s>
              <s id="N224B3">ſi enim A dato
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              tempore percurrit AK; </s>
              <s id="N224B9">certè F percurret FG; </s>
              <s id="N224BD">ſed quadrans FEG eſt
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              ſubduplus ſectoris AEK, vt conſtat; </s>
              <s id="N224C3">igitur faciliùs vertitur FE, quàm
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              AE in proportione AE, ad FE: </s>
              <s id="N224C9">ſi tamen non conſideretur pondus ſeu
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              reſiſtentia vectis, haud dubiè ſi pondus ſit in Q, faciliùs mouebitur ope­
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              ra maioris vectis AE, quàm minoris FE; </s>
              <s id="N224D1">quia opera maioris mouetur
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              motu vt QT; </s>
              <s id="N224D7">operâ verò minoris motu vt QY, igitur difficiliùs opera
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              minoris in proportione QY ad QT; </s>
              <s id="N224DD">denique ſi pondus ſit in F maioris
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              vectis, & in
                <foreign lang="grc">δ</foreign>
              minoris, ſitque AE ad AF, vt FE ad F
                <foreign lang="grc">δ</foreign>
              , æquale erit
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              momentum vtriuſque vectis ad mouendum pondus; </s>
              <s id="N224ED">quia arcus FV erit
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              æqualis arcui
                <foreign lang="grc">δ</foreign>
              Y; </s>
              <s id="N224F7">hîc autem nullomodo conſideratur vectis reſiſten­
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              tia; </s>
              <s id="N224FD">ſi verò producatur
                <expan abbr="tantũdem">tantundem</expan>
              impetus in toto vecte AE quamtum
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              in FE; </s>
              <s id="N22507">certè pro rata ſingulæ partes FE duplum habent; </s>
              <s id="N2250B">igitur tempo­
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              ra gyrorum erunt in ratione duplicata radiorum; </s>
              <s id="N22511">quia cum F habeat du­
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              plum impetum A, certè deſcribit orbem integrum eo tempore, quo A
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              quadrantem; </s>
              <s id="N22519">ergo F 4. orbes, dum A vnicum: ſed hæc ſunt facilia. </s>
            </p>
            <p id="N2251D" type="main">
              <s id="N2251F">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              55.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N2252B" type="main">
              <s id="N2252D">
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              Si vectis BH ita pellatur in B in plano horizontali, in quo liberè moueri
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              poſſit
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                <emph type="italics"/>
              v.g. dum aquæ ſupernatat, nulli centro immobili affixus, ſit que aqualis
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              denſitatis in omnibus ſuis partibus; mouebitur circa aliquod centrum, etiamſi
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              nulli centro affigatur.
                <emph.end type="italics"/>
              </s>
              <s id="N22543"> Probatur, quia punctum B velociùs mouebitur, quàm
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              A vel H, vt patet experientiâ: </s>
              <s id="N22549">ratio eſt, quia minùs impetus producitur
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              in toto cylindro BH, applicata potentia in B, quàm in A, quod eſt cen­
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              trum grauitatis cylindri BA, vt iam oſtendimus Th. 68. 69. BB; </s>
              <s id="N22551">porrò
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              ratio à priori eſt, quia cùm impetus producatur tantùm ad extra, vt tol­
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              latur impedimentum motus, vt fusè oſtendimus lib. 1. certè in tantùm
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              amouetur impedimentum, in quantum amouetur corpus impediens mo­
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              tum alterius; </s>
              <s id="N2255D">atqui amoueri tantùm poteſt per motum; </s>
              <s id="N22561">igitur eo motu
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              amouetur, quo faciliùs amoueri poteſt, & minore ſumptu, vt ita dicam,
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              id eſt minore impetu: </s>
              <s id="N22569">porrò cum potentia ſit determinata ad producen­
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              dum tabem impetum, immediatè ſcilicet, id eſt, in ea parte, cui immedia­
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              tè admouetur; </s>
              <s id="N22571">alioqui ſi poſſet minorem, & minorem in infinitum pro­
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              ducere poſſet etiam immediatè ſine operâ organi mechanici quodlibet
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              pondus mouere, quod eſt abſurdum, de quo iam ſuprà; </s>
              <s id="N22579">ſit igitur potentia
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              applicata in A, ſcilicet in centro grauitatis cylindri BH; </s>
              <s id="N2257F">certè producit
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              maximum impetum, quem poteſt producere in cylindro BH (ſuppono
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              enim eſſe cauſam neceſſariam, & producere perfectiſſimum impetum,
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              quem producere poſſit) producit inquam maximum ratione numeri; </s>
              <s id="N22589">
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              cùm in toto cylindro BH producat impetum eiuſdem perfectionis; </s>
              <s id="N2258E">igi­
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              tur mouetur motu recto; </s>
              <s id="N22594">igitur æquali in omnibus partibus; </s>
              <s id="N22598">igitur æqua­
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              lis eſt impetus in omnibus partibus, id eſt, æquè intenſus; </s>
              <s id="N2259E">ſit autem po-</s>
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