Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              <s id="N2370C">
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              ſu BF eſſe ad acquiſitam in deſcenſu HP, vt vecta AF ad rectam OF,
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              quod facilè probatur; </s>
              <s id="N23717">quia ex B in F æqualis acquiritur velocitas ſiue
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              per rectam BF
                <expan abbr="deſcẽdat">deſcendat</expan>
              mobile, ſiue per duas BHF, ſiue per tres BHGF,
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              ſiue per totum quadrantem BHF; </s>
              <s id="N23723">ſed æqualis eſt acquiſita per BF ac­
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              quiſitæ per AF, vel BE; </s>
              <s id="N23729">quæ omnia conſtant per Lemm.10.& 11.ſimili­
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              ter acquiſita in recta HF eſt æqualis acquiſitæ in recta OF in duabus
                <lb/>
              HGF; </s>
              <s id="N23731">immò & in arcu HZF; </s>
              <s id="N23735">igitur acquiſita in arcu BHF eſt ad
                <lb/>
              acquiſitam in arcu HZF, vt acquiſita in AF ad acquiſitam in OF; </s>
              <s id="N2373B">ſed
                <lb/>
              illa eſt ad hanc vt AF ad OF, vt conſtat; igitur ſunt vt altitudines, quod
                <lb/>
              erat probandum. </s>
            </p>
            <p id="N23743" type="main">
              <s id="N23745">Hinc non ſunt vt chordæ, neque vt arcus; </s>
              <s id="N23749">hinc acquiſita in arcu
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              BHF eſt dupla acquiſitæ in arcu HZF; </s>
              <s id="N2374F">cùm tamen arcus BF non ſit
                <lb/>
              duplus; ſed ſeſquialter arcus HZF. </s>
            </p>
            <p id="N23755" type="main">
              <s id="N23757">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              7.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23763" type="main">
              <s id="N23765">
                <emph type="italics"/>
              Hinc ſunt diuerſi ictus inæqualium vibrationum in eadem altitudinum ra­
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              tione
                <emph.end type="italics"/>
              ; </s>
              <s id="N23770">quia eadem eſt ratio ictuum, quæ velocitatum acquiſitarum in
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              puncto percuſsionis; </s>
              <s id="N23776">ſed ratio velocitatum eſt eadem quæ altitudinum,
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              ſeu perpendicularium per Th.7. igitur eadem ratio ictuum, quæ altitu­
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              dinum; </s>
              <s id="N2377E">ſed inæqualium vibrationum eiuſdem funependuli diuerſæ ſunt
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              altitudines; igitur diuerſi ictus, quod erat demonſtrandum. </s>
            </p>
            <p id="N23784" type="main">
              <s id="N23786">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              8.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23792" type="main">
              <s id="N23794">
                <emph type="italics"/>
              In diuerſis funependulis ſimilium vibrationum velocitates ſunt vt chordæ
                <emph.end type="italics"/>
              ; </s>
              <s id="N2379D">
                <lb/>
              ſint enim duo funependula inæqualis A
                <foreign lang="grc">ρ</foreign>
              , AF; </s>
              <s id="N237A6">certè ſit vibratio maio­
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              ris BF, & minoris vibratio ſimilis
                <foreign lang="grc">α ρ</foreign>
              , velocitas vibrationis BF eſt vt al­
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              titudo AF & minoris
                <foreign lang="grc">α ρ</foreign>
              , vt altitudo A
                <foreign lang="grc">ρ</foreign>
              ; </s>
              <s id="N237BA">ſed vt AF eſt ad A
                <foreign lang="grc">ρ</foreign>
              , ita BF
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              ad
                <foreign lang="grc">α ρ</foreign>
              ; </s>
              <s id="N237C8">ſunt enim triangula proportionalia; </s>
              <s id="N237CC">idem dico de aliis.v.g ZF
                <lb/>
              & X
                <foreign lang="grc">ρ</foreign>
              , iu quo non eſt difficultas: hinc percuſsiones vtriuſque erunt etiam
                <lb/>
              vt chordæ, quia ſunt vt altitudines. </s>
            </p>
            <p id="N237D8" type="main">
              <s id="N237DA">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              9.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N237E6" type="main">
              <s id="N237E8">
                <emph type="italics"/>
              Tempora, quibus peraguntur vibrationes ſimiles funependulorum inæqua­
                <lb/>
              lium ſunt ferè in ratione ſubduplicata longitudinum, ſeu radiorum
                <emph.end type="italics"/>
              : </s>
              <s id="N237F3">Probatur,
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              quia tempora deſcenſuum per chordas ſimiles ſunt in ratione ſubdupli­
                <lb/>
              cata earumdem chordarum, ſiue ſint 2.ſiue ſint tres, & per Lemma 17.
                <lb/>
              ſed ſi accipiantur plures chordæ, tandem habebitur arcus; </s>
              <s id="N237FD">igitur vibra­
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              tio per arcum eſt veluti deſcenſus per infinitas ferè chordas æquales; </s>
              <s id="N23803">ſed
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              tempora horum deſcenſuum ſunt in ratione ſubduplicata chordarum; </s>
              <s id="N23809">&
                <lb/>
              hæc eſt eadem ratio cum ſubduplicata radiorum; igitur tempora vibra­
                <lb/>
              tionum ſimilium ſunt ferè in ratione ſubduplicata radiorum. </s>
            </p>
            <p id="N23811" type="main">
              <s id="N23813">Obſeruabis rem
                <expan abbr="iſtã">iſtam</expan>
              accuratè, & analyticè diſcuti poſſe, ſit enim qua­
                <lb/>
              drans ADH maioris vibrationis, & quadrans CED minoris; </s>
              <s id="N2381D">ſitque
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              CD ſubquadrupla AD, & arcus DE ſubquadruplus DKH; </s>
              <s id="N23823">aſſumatur
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              DN ſubquadruplus DH; </s>
              <s id="N23829">ſitque DN æqualis DE; </s>
              <s id="N2382D">certè eo tempore, </s>
            </p>
          </chap>
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