Fabri, Honoré, Tractatus physicus de motu locali, 1646

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            <p id="N20386" type="main">
              <s id="N203E0">
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              in eadem linea; </s>
              <s id="N203E9">ſi noua, igitur debet tantillùm reflecti; igitur cum nec
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              vlteriùs producatur motus, nec retrò agatur mobile, vtraque determi­
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              natio neceſſariò æqualis eſt. </s>
              <s id="N203F1">Quænam verò ſit huius æqualitatis ratio à
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              priori, difficilè dictu eſt; </s>
              <s id="N203F7">dico tamen petendam eſſe ab æqualitate glo­
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              borum; </s>
              <s id="N203FD">cum enim determinatio noua ſit duplò maior à plano immobili
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              & duro; </s>
              <s id="N20403">certè à plano mobili minor eſt, vt conſtat, quia cedit; </s>
              <s id="N20407">igitur
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              quâ proportione plùs, vel minùs cedit, eſt minor dupla; </s>
              <s id="N2040D">ſed maior glo­
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              bus minùs cedit, quàm æqualis; </s>
              <s id="N20413">quia ceſſio eſt minor impulſione; </s>
              <s id="N20417">igitur
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              quando ceſſio eſt æqualis impulſioni, æquales ſunt determinationes; </s>
              <s id="N2041D">at­
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              qui cum producitur æqualis impetus, & imprimitur æqualis motus,
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              æqualis eſt ceſſiò impulſioni, id eſt æquè cedit, ac impellitur; cum tamen,
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              ſi maior ſit globus, non æquè citò cedat, quia tardior motus imprimitur,
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              & hæc eſt, ni fallor, vera ratio huius æqualitatis determinationum, &
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              hæc vera cauſa quietis globi impacti, de qua iam ſuprà Th. 40. </s>
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            <p id="N2042B" type="main">
              <s id="N2042D">
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              Theorema
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              63.
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              </s>
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            <p id="N20439" type="main">
              <s id="N2043B">
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              Cum verò globus impellitur in globum æqualem per lineam obliquam, num­
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              quam quieſcit
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              ; </s>
              <s id="N20446">quod demonſtratur, quia ſemper eſt determinatio mixta; </s>
              <s id="N2044A">
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              quod vt meliùs intelligatur, opus eſt nouâ figurâ ſit ergo punctum con­
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              tactus duorum globorum B, & ipſa CBN ſit Tangens communis, ſeu
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              ſectio plani, quæ gerit vicem plani reflectentis; </s>
              <s id="N20453">fit autem primò linea
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              incidentiæ connectens centra FBA; </s>
              <s id="N20459">nulla fit in ea reflexio per Th. 61.
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              quia ſcilicet determinatio noua per lineam BF eſt æqualis priori per
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              FB; </s>
              <s id="N20461">ſit EB linea incidentiæ faciens angulum EBC cum Tangente
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              NC; </s>
              <s id="N20467">determinatio noua eſt ad determinationem priorem vt BG vel
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              ER ad BE, & ſi ſit linea incidentiæ DB vt BH, vel SD ad BD; </s>
              <s id="N2046D">deni­
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              que ſi ſit BV vt TV ad BV, donec tandem linea incidentiæ ſit CB, quâ
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              poſitâ nulla eſt determinatio noua; </s>
              <s id="N20475">vides eſſe eandem viam proportio­
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              num quæ fuit ſuprà; </s>
              <s id="N2047B">licèt non ſit futura eadem angulorum reflexionis
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              proportio, quia determinationum nouarum rationes non ſunt eædem;
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              producatur enim EBL DBM &c. </s>
              <s id="N20483">determinatio prior per EB eſt ad
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              nouam per BF, vt BE ad BG; </s>
              <s id="N20489">igitur ducantur EP PL; </s>
              <s id="N2048D">aſſumatur LI
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              æqualis BG, & GI, BL æqualis BE; </s>
              <s id="N20493">denique ducatur BI: dico BI eſſe
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              lineam reflexionis ſeu determinationem mixtam ex BG BL per Th.
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              137.lib.1.&c. </s>
              <s id="N2049D">Similiter ſi ſit linea incidentiæ DBN, ducanturque DO.
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              OM, & aſſumatur MK æqualis BH, vel SD, dico lineam BK eſſe de­
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              terminationem mixtam ex BH BM, ex quibus etiam longitudo omnium
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              reflexarum facilè determinari poteſt; quippe longitudo eſt vt linea de­
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              terminationis mixtæ. </s>
              <s id="N204A9">v.g. BI, BK; </s>
              <s id="N204AF">demonſtratur autem hæc determi­
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              nationum progreſſio, quia determinatio per EB eſt ad determinationem
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              per FB vt ictus per EB ad ictum per FB, vt iam ſæpè dictum eſt; </s>
              <s id="N204B7">ſed
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              ictus per EB in CN eſt ad ictum per FB vt ER ad FB vel EB, id eſt, vt
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              ſinus rectus anguli incidentiæ ad ſinum totum; </s>
              <s id="N204BF">ſed determinatio noua
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              in perpendiculo FB eſt ad priorem, vt FB ad BF per Th.62. igitur noua
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              determinatio per EB eſt ad priorem vt ER ſeu ſinus rectus anguli EBC </s>
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