Fabri, Honoré, Tractatus physicus de motu locali, 1646

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              <s id="N204BF">
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              ad ſinum totum EB, & per DB vt DS ad DB: idem dico de aliis. </s>
            </p>
            <p id="N204CC" type="main">
              <s id="N204CE">Hinc colligo primò, omnes determinationes nouas in hypotheſi glo­
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              borum æqualium eſſe ſubduplas in eiſdem angulis priorum determina­
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              tionum in hypotheſi corporis reflectentis immobilis. </s>
            </p>
            <p id="N204D5" type="main">
              <s id="N204D7">Colligo ſecundò, omnes reflexiones fieri neceſſariò per eandem li­
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              neam, quæ ſcilicet eſt Tangens puncti contactus globi reflectentis, quod
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              valdè mirificum eſt, & facilè obſeruabunt, qui Tudicula minore ludunt. </s>
              <s id="N204DE">
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              Colligo ſexto, cum angulus incidentiæ eſt 60. lineam reflexam eſſe ſub­
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              duplam directæ quæ vlteriùs produceretur; infrà verò ſexto eſſe maio­
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              rem, ſuprà verò eſſe minorem, eſt autem longitudo lineæ ſinus comple­
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              menti anguli incidentiæ. </s>
              <s id="N204E9">v.g. ſi linea incidentiæ ſit EB eſt EG, ſi DB
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              eſt DH, ſi VB eſt VX. </s>
            </p>
            <p id="N204F0" type="main">
              <s id="N204F2">
                <emph type="center"/>
                <emph type="italics"/>
              Theorema
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              64.
                <emph.end type="center"/>
              </s>
            </p>
            <p id="N204FE" type="main">
              <s id="N20500">
                <emph type="italics"/>
              Si globus minor in maiorem impingatur, qui ab eo tamen moueatur per li­
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              neam connectentem centra vtriuſque impactus, reflectitur
                <emph.end type="italics"/>
              ; </s>
              <s id="N2050B">ratio eſt, quia ma­
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              ior globus eſt maius impedimentum, vt iam diximus Th. 131.lib.1.id
                <lb/>
              eſt, vt clariùs hic explicetur, quæ ibidem tantùm obiter indicauimus,
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              noua determinatio maior eſt priore, quia ceſsio eſt minor impulſione; ſit
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              autem. </s>
              <s id="N20517">v.g. globus reflectens duplus impacto; </s>
              <s id="N2051D">igitur motus eſt ſubduplus,
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              quia ſcilicet impetus diſtribuitur pluribus partibus ſubjecti; </s>
              <s id="N20523">igitur ſin­
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              gulæ minùs habent; </s>
              <s id="N20529">igitur impetus eſt remiſsior; </s>
              <s id="N2052D">igitur motus tardior; </s>
              <s id="N20531">
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              igitur ceſsio minor ſubduplo; </s>
              <s id="N20536">igitur determinatio noua eſt maior æqua­
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              li 1/2 hinc debet neceſſariò reflecti, quia quotieſcunque ad lineas op­
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              poſitas ex diametro determinatur impetus, maior determinatio præua­
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              let pro rata per Th.134.lib.1. nam perinde ſe habet, atque ſi eſſet duplex
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              impetus; </s>
              <s id="N20542">quanta porrò eſſe debeat linea reflexa, determinari poteſt; </s>
              <s id="N20546">ſi
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              enim determinatio noua eſſet ſolilaria mobile cum eo impetu, quem ha­
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              bet
                <expan abbr="cõficeret">conficeret</expan>
              v.g. BA vel BF; </s>
              <s id="N20554">diuidatur BF in duas partes æquales in
                <foreign lang="grc">υ</foreign>
              ,
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              determinatio noua eſt ad priorem vt 3. ad 2. aſſumatur F
                <foreign lang="grc">β</foreign>
              æqualis B
                <foreign lang="grc">υ</foreign>
              ; </s>
              <s id="N20566">
                <lb/>
              igitur propter determinationem priorem oppoſitam ſcilicet BA detra­
                <lb/>
              hi debent duæ partes toti B
                <foreign lang="grc">β</foreign>
              ſcilicet
                <foreign lang="grc">βυ</foreign>
              æqualis BA; </s>
              <s id="N20575">igitur linea re­
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              flexa erit B
                <foreign lang="grc">υ</foreign>
              dupla totius BF; </s>
              <s id="N2057F">ſit etiam globus reflectens, qui mouetur
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              ab impacto, quadruplus, determinatio noua erit ad priorem vt 7. ad 4.
                <lb/>
              fit B
                <foreign lang="grc">δ</foreign>
              ad BA vt 7. ad 4. ex B
                <foreign lang="grc">δ</foreign>
              detrahatur DH æqualis BA, ſupereſt
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              HB id eſt 3/4 totius BF; non poteſt autem eſſe maior determinatio no­
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              ua priore quàm in ratione dupla, vt diximus ſuprà. </s>
              <s id="N20593">Ratio eſt, quia eò mi­
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              nor eſt determinatio noua, quò maior eſt motus impreſſus globo maiori
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              reflectenti; </s>
              <s id="N2059B">igitur tantum detrahitur duplæ, quantum additur motus; </s>
              <s id="N2059F">ſi
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              motus eſt æqualis, detrahitur duplæ æqualis priori; </s>
              <s id="N205A5">igitur ſupereſt æqua­
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              lis; </s>
              <s id="N205AB">ſi motus eſt ſubduplus, detrahitur duplæ ſubdupla prioris; </s>
              <s id="N205AF">igitur ſu­
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              pereſt 1/2 ſi ſubquadruplus detrahitur duplæ ſubquadrupla prioris, igitur
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              ſupereſt 1 3/4 ſi ſit duplus motus, determinatio noua eſt ſubdupla; </s>
              <s id="N205B7">igitur
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              priori detrahitur 1/2 de quo infrà; </s>
              <s id="N205BD">quod autem ſpectat ad longitudi­
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              nes linearum non eſt difficultas; quippe determinatio minor detrahi
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              deber maiori. </s>
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