Fabri, Honoré, Tractatus physicus de motu locali, 1646

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    <archimedes>
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        <body>
          <chap id="N1EE3A">
            <p id="N1F947" type="main">
              <s id="N1F95C">
                <pb pagenum="246" xlink:href="026/01/278.jpg"/>
              tùm ID producatur in O, denique ducatur NG: </s>
              <s id="N1F964">prima determinatio
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              lineæ incidentiæ ID, eſt per DO, determinatio plani eſt per DG; </s>
              <s id="N1F96A">ſed
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              DO eſt æqualis DG; </s>
              <s id="N1F970">nam DON, DNG ſunt æquilatera æqualia; </s>
              <s id="N1F974">
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              hinc determinatio mixta eſt per DN, diuidens angulum GDO bifa­
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              riam; </s>
              <s id="N1F97B">igitur ſi ſit linea incidentiæ ID & angulus ID B. 30. graduum,
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              æqualis eſt determinatio plani determinationi prioris lineæ; </s>
              <s id="N1F981">hinc angu­
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              lus diuiditur æqualiter bifariam; </s>
              <s id="N1F987">ſit verò linea incidentiæ AD produ­
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              cta vſque ad E, linea reflexionis DH; </s>
              <s id="N1F98D">ducatur HE; </s>
              <s id="N1F991">aſſumatur DT
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              æqualis EH: </s>
              <s id="N1F997">dico determinationem plani eſſe ad determinationem
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              prioris lineæ AD vel DE, vt DT ad DE; </s>
              <s id="N1F99D">cum enim determinatio mix­
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              ta ſit per DH; </s>
              <s id="N1F9A3">certè DH accedit propiùs ADDG, quàm ad DE; </s>
              <s id="N1F9A7">igi­
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              tur determinatio per DG eſt ad determinationem, per DE vt DT
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              æqualis HE ad DE; nam perinde ſe habent, atque ſi eſſent duo impe­
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              tus determinati ad duas lineas, de quibus hoc ipſum demonſtrauimus
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              tùm libro 1. Th.137. 138. 139. &c. </s>
              <s id="N1F9B3">tùm lib.4. à Th. 1. ad Th.14.quippe
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              linea determinationis mixtæ eſt diagonalis, vt ſæpè probauimus: </s>
              <s id="N1F9B9">deinde
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              ſit linea incidentiæ per KD; </s>
              <s id="N1F9BF">ſit DX linea reflexionis; </s>
              <s id="N1F9C3">ſit XQ, ipſique
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              æqualis DZ, dico determinationem per DG eſſe ad determinationem
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              per DQ vt DZ ad DQ, ſed XQ eſt minor GS, vt conſtat; </s>
              <s id="N1F9CB">igitur quò
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              linea incidentiæ accedit propiùs ad perpendicularem GD, determinatio
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              plani eſt maior, eſtque vt chordæ NO, HE,
                <expan abbr="Xq;">Xque</expan>
              igitur ſi tandem li­
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              nea incidentiæ ſit perpendicularis GD, determinatio plani eſt ad deter­
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              minationem lineæ incidentiæ, vt DY æqualis GS ad DG: </s>
              <s id="N1F9DB">ſed cum ex
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              Th.4. multa lux reliquis conſequentibus immò & antecedentibus afful­
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              gere poſſit, paulò fuſiùs explicandum, & demonſtrandum eſſe videtur: </s>
              <s id="N1F9E3">
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              itaque duobus modis, primò ex hypotheſi anguli reflexionis æqualis an­
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              gulo incidentiæ, quod iam reuerâ præſtitum eſt; ſed cum ex hoc Theo­
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              remate prædicta æqualitas angulorum reflexionis tanquam per princi­
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              pium immediatum poſitiuum demonſtrari poſſit, ne ſit aliqua circuli
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              ſpecies, quo determinatio noua dupla prioris poſita linea incidentiæ
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              perpendiculari per æqualitatem anguli reflexionis, & hæc æqualitas per
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              illam eandem determinationem duplam demonſtretur, aliam viam inire
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              oportet, vnde intima totius reflexionis principia eruantur, quod vt
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              fiat. </s>
            </p>
            <p id="N1F9F8" type="main">
              <s id="N1F9FA">Primò certum eſt, corpus reflectens in perpendiculari, (quæ eſt cum
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              linea incidentiæ terminata ad punctum contactus ducitur per centrum
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              grauitatis globi reflexi) certum eſt inquam corpus reflectens in prædi­
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              cta linea aliquando cedere, aliquando non cedere; </s>
              <s id="N1FA04">cedere autem dici­
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              tur cùm vel amouetur à corpore impacto, vel ſaltem concutitur:
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              tunc autem nullo modo cedere dicitur, cum ab ictu nullo modo mo­
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              uetur. </s>
            </p>
            <p id="N1FA0E" type="main">
              <s id="N1FA10">Secundò, ceſſio, & reſiſtentia ita poſſunt comparari, vt vel ceſſio ſit
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              æqualis reſiſtentiæ, vel ceſſio ſine reſiſtentia, vel reſiſtentia ſine ceſſione: </s>
              <s id="N1FA16">
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              porrò tunc eſt ceſſio tota, cum nulla eſt reſiſtentia, quod tantum accide­
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              ret, ſi corpus moueretur in vacuo; </s>
              <s id="N1FA1D">quippe nullum eſt medium quamtum-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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