Fabri, Honoré, Tractatus physicus de motu locali, 1646

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                <pb pagenum="230" xlink:href="026/01/262.jpg"/>
              vt ſi conficiat ſemicirculum BIIR; hæc ita clara ſunt, vt oculis tantùm
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              indigeant. </s>
            </p>
            <p id="N1E9E6" type="main">
              <s id="N1E9E8">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              59.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1E9F4" type="main">
              <s id="N1E9F6">
                <emph type="italics"/>
              Hinc poteſt eſſe mons per quem aliquis aſcendat, licèt ſub planum horizon­
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              tale deſcendat.
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              v.g. ſit Tangens in puncto B; </s>
              <s id="N1EA03">haud dubiè qui ex B verſus
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              H procederet per arcum BH, haud dubiè aſcenderet, quia recederet
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              ſemper à centro mundi A; </s>
              <s id="N1EA0B">deſcenderet tamen infra Tangentem in B; </s>
              <s id="N1EA0F">igi­
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              tur mons eſſet infra horizontale planum; montem enim appello tractum
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              arduum, in quo dum aliquis ambulat, aſcendit, hoc eſt recedit à terræ
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              centro. </s>
            </p>
            <p id="N1EA19" type="main">
              <s id="N1EA1B">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              96.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1EA27" type="main">
              <s id="N1EA29">
                <emph type="italics"/>
              Diuerſæ eſſent rationes motus in deſcenſu per ſemicirculum QLA
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              ; </s>
              <s id="N1EA32">ſcilicet
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              in iis punctis, quæ propiùs accedunt ad A motus eſſet velocior initio
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              ſcilicet; </s>
              <s id="N1EA3A">poteſt autem haberi hæc proportio ductis Tangentibus, vt ſæpè
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              iam dixi; </s>
              <s id="N1EA40">at verò in ſemicirculo ROB in puncto T eſſet velociſſimus mo­
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              tus initio, quia angulus ITA eſt maximus eorum omnium, qui poſſunt
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              fieri ductis duabus rectis ab A & I coëuntibus in ſemicirculo ROB, igi­
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              tur & illi oppoſitus; </s>
              <s id="N1EA4A">igitur perpendiculum AT accedit propiùs ad Tan­
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              gentem; </s>
              <s id="N1EA50">igitur planum inclinatius eſt; </s>
              <s id="N1EA54">igitur in puncto T eſt velocior mo­
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              tus initio quàm in aliis; igitur acceleratur motus ab R in T per cre­
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              menta ſemper maiora, & ab ipſo T ad B per crementa minora. </s>
            </p>
            <p id="N1EA5C" type="main">
              <s id="N1EA5E">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
                <emph.end type="italics"/>
              97.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N1EA6A" type="main">
              <s id="N1EA6C">
                <emph type="italics"/>
              Poteſt deſcendere corpus graue v.g. globus vſque ad centrum terræ per He­
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              licem
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              ; </s>
              <s id="N1EA79">ſit enim globus terræ AEQO, centrum K; </s>
              <s id="N1EA7D">diuidatur QK in 4.
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              partes æquales QR.RP.PS.SK; </s>
              <s id="N1EA83">aſſumatur EH æqualis QR, & AC æqua­
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              lis QP, & OM æqualis QS; </s>
              <s id="N1EA89">tùm per ſignata puncta deſcribatur helix Q
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              HCZMK: </s>
              <s id="N1EA8F">dico quod per eius conuexum globus deſcenderet ex Q, ad
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              centrum terræ; </s>
              <s id="N1EA95">quia ſemper accedit propiùs ad centrum; </s>
              <s id="N1EA99">immò per plura
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              volumina deſcendere poteſt; ſit enim QK diuiſa in 8. partes æquales Q
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              TTR, &c. </s>
              <s id="N1EAA1">tùm aſſumatur EF æqualis QT, AB æqualis QR, ON æqualis
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              QV tùm QR in ipſa QK, & æqualis QY, ED, a qualis QS, & OL æqualis
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              QX; & per puncta aſſignata deſcribatur Helix QFBNPIDLK, per cam
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              deſcenderet globus ad centrum terræ K poſt duas circumuolutiones. </s>
            </p>
            <p id="N1EAAB" type="main">
              <s id="N1EAAD">Per aliam quoque ſpiralem compoſitam ex ſemicirculis deſcendere
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              poteſt ad centrum terræ B; </s>
              <s id="N1EAB3">ſit enim centrum terræ F & globus terræ A
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              CMD; </s>
              <s id="N1EAB9">accipiantur duo puncta hinc inde HK ad libitum; </s>
              <s id="N1EABD">tunc ex H
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              fiat ſemicirculus MB; </s>
              <s id="N1EAC3">haud dubiè globus poſitus in M deſcendet in B per
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              conuexum ſemicirculi in B; </s>
              <s id="N1EAC9">quia B inter omnia illius puncta accedit pro­
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              ximè ad F; </s>
              <s id="N1EACF">tùm ex K ducatur ſemicirculus BI; </s>
              <s id="N1EAD3">certè ex B deſcenderet in I
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              propter
                <expan abbr="eãdem">eandem</expan>
              rationem, tùm ex H deſcribatur ſemicirculus IF; </s>
              <s id="N1EADD">certè
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              ex I deſcendet in F, quæ omnia patent ex dictis; </s>
              <s id="N1EAE3">poſſunt autem multipli­
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              cari iſtæ ſpiræ in infinitum: Hinc licèt globus ſingulis horis 100000. leu­
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              cas conficeret in deſcenſu, non tamen attingeret centrum niſi poſt 1000.
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              annos, immò plures ſecundùm numerum ſpirarum. </s>
            </p>
          </chap>
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