Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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in eadem linea; </
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<
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">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. </
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<
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">Quænam verò ſit huius æqualitatis ratio à
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priori, difficilè dictu eſt; </
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<
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">dico tamen petendam eſſe ab æqualitate glo
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borum; </
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<
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">cum enim determinatio noua ſit duplò maior à plano immobili
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& duro; </
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<
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">certè à plano mobili minor eſt, vt conſtat, quia cedit; </
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<
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quâ proportione plùs, vel minùs cedit, eſt minor dupla; </
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<
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bus minùs cedit, quàm æqualis; </
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<
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">quia ceſſio eſt minor impulſione; </
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<
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">igitur
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quando ceſſio eſt æqualis impulſioni, æquales ſunt determinationes; </
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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. </
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Theorema
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63.
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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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; </
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<
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">quod demonſtratur, quia ſemper eſt determinatio mixta; </
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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; </
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<
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">fit autem primò linea
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incidentiæ connectens centra FBA; </
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<
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">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; </
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<
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">ſit EB linea incidentiæ faciens angulum EBC cum Tangente
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NC; </
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<
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">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; </
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<
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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; </
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<
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">vides eſſe eandem viam proportio
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num quæ fuit ſuprà; </
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<
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">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. </
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<
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">determinatio prior per EB eſt ad
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nouam per BF, vt BE ad BG; </
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<
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">igitur ducantur EP PL; </
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">aſſumatur LI
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æqualis BG, & GI, BL æqualis BE; </
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lineam reflexionis ſeu determinationem mixtam ex BG BL per Th.
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137.lib.1.&c. </
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<
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">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. </
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<
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<
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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; </
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<
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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; </
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<
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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 </
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