Fabri, Honoré, Tractatus physicus de motu locali, 1646

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    <archimedes>
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          <chap id="N22A20">
            <p id="N234DF" type="main">
              <s id="N234F3">
                <pb pagenum="308" xlink:href="026/01/342.jpg"/>
              pus per NG, vt BG ad NG, & ad tempus per GF, vt BG ad 24951. &
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              ad tempus per BGF, vt BG id eſt, 100000. ad 124951. porrò tempus
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              per B 3. eſt BG; </s>
              <s id="N23500">ergo vt quadratum temporis per BG ad quadratum
                <lb/>
              temporis per BGF, ſcilicet vt 10000000000. ad 1561475241. ita B 3.
                <lb/>
              ſcilicet 81655. ad aliam, hæc erit 123496. igitur in BF, quæ eſt partium
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              141422. percurruntur partes 123496. eo tempore, quo percurruntur
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              BGF; </s>
              <s id="N2350C">at verò eo tempore, quo percurruntur BHF; </s>
              <s id="N23510">percurruntur in
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              BF 122702. igitur pauciores; </s>
              <s id="N23516">igitur minore tempore; igitur duæ BHF
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              percurruntur minore tempore, quàm duæ BGF, quod erat demon­
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              ſtrandum. </s>
            </p>
            <p id="N2351E" type="main">
              <s id="N23520">Similiter deſcendet citiùs per duas BHF, quàm per duas BZF: </s>
              <s id="N23524">immò
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              quod mirabile eſt, patetque ex analytica, citiùs per duas BGF, quàm per
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              duas BZF; </s>
              <s id="N2352C">(ſuppono enim BZ eſſe arcum grad. 45.) ſit enim Z
                <foreign lang="grc">υ</foreign>
              per­
                <lb/>
              pendicularis, itemque Z
                <foreign lang="grc">δ, δ</foreign>
              B eſt æqualis BR. igitur 70711. Z
                <foreign lang="grc">δ</foreign>
              eſt
                <lb/>
              29289. igitur
                <foreign lang="grc">δ υ</foreign>
              1223. igitur B
                <foreign lang="grc">υ</foreign>
              71924. igitur B
                <foreign lang="grc">β</foreign>
              51858. iam tempus
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              per BZ eſt ad tempus per YZ vt BZ ad YZ. id eſt, vt 76536. ad 184777.
                <lb/>
              ſit autem vt AYF 261313. ad aliam 219737.ita hæc ad YZ; </s>
              <s id="N23552">certè tem­
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              pus per BZ eſt ad tempus per BZF, vt BZ ad 111496. igitur B
                <foreign lang="grc">β</foreign>
              fit
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              tempore BZ; ergo vt quadratum BZ ad quadratum 111496. id eſt, vt
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              4857759296. ad 12431358016. ita ſit B
                <foreign lang="grc">β</foreign>
              , id eſt 51858.ad 132708.igitur
                <lb/>
              eo tempore, quo percurruntur BZF, percurruntur in BF 132708.earum
                <lb/>
              partium, quarum BF eſt 141422. ſed pauciores percurruntur eo tempo­
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              re, quo fit deſcenſus per BHF, vel BGF. </s>
            </p>
            <p id="N2356A" type="main">
              <s id="N2356C">
                <emph type="center"/>
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              16.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N23578" type="main">
              <s id="N2357A">
                <emph type="italics"/>
              Citiùs percurruntur duæ inferiores.v.g. </s>
              <s id="N2357F">HGF, quàm duæ BHF
                <emph.end type="italics"/>
              ; </s>
              <s id="N23586">eſt enim
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              PF ſubdupla ſecantis NF; </s>
              <s id="N2358C">igitur 193185. FG eſt 51764. GP 141421.
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              ſit autem PG ad 165285.vt hæc ad PF; </s>
              <s id="N23592">certè tempus per HG eſt ad
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              tempus per PG, vt HG ad PG; </s>
              <s id="N23598">igitur tempus per HG eſt ad tempus
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              per HGF, vt 51764. ad 75628. ſed BX eſt æqualis, eiuſdemque incli­
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              nationis cum HG; </s>
              <s id="N235A0">igitur tempus, quo percurritur BX eſt BX. vel HG; </s>
              <s id="N235A4">
                <lb/>
              ſit autem vt BX ad 75628. ita hæc ad aliam 111092. igitur eo tempore,
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              quo percurruntur HGF, percurruntur in BF 111092. minor BF; igitur
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              citiùs percurruntur HGF quàm BHF, vel BZF, &c. </s>
              <s id="N235AD">igitur duæ infe­
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              riores citiùs, quàm duæ ſuperiores. </s>
            </p>
            <p id="N235B2" type="main">
              <s id="N235B4">Ex his manifeſtum eſt, quænam ſint quaſi termini progreſſionis in aſ­
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              ſumptis duabus chordis; ſi enim diuidatur arcus BF in 6.arcus æquales,
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              BF tardiſſimè, BHF velociſſimè, &c. </s>
              <s id="N235BC">poſt BHF, BGF, tùm ſingulæ ab
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              H verſus Z & verſus V reſpondent ſingulæ immediatè AG verſus Z, &
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              verſus
                <foreign lang="grc">θ. </foreign>
              </s>
            </p>
            <p id="N235C6" type="main">
              <s id="N235C8">
                <emph type="center"/>
                <emph type="italics"/>
              Lemma
                <emph.end type="italics"/>
              17.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N235D4" type="main">
              <s id="N235D6">
                <emph type="italics"/>
              Si ſint duo pendula inæqualia, tempora deſcenſuum per chordas ſimiles,
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              ſunt in ratione ſubduplicat a earumdem; </s>
              <s id="N235DE">hæ verò ſunt vt radij
                <emph.end type="italics"/>
              ; </s>
              <s id="N235E5">ſit enim qua­
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              drans A
                <foreign lang="grc">α ρ</foreign>
              , cuius radius A
                <foreign lang="grc">α</foreign>
              ſit ſubquadruplus radij AB; </s>
              <s id="N235F3">ſint chordæ
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              ſimiles
                <foreign lang="grc">α ρ</foreign>
              , BF; </s>
              <s id="N235FD">hæc eſt quadrupla illius; </s>
              <s id="N23601">igitur cum ſit eadem vtriuſ-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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