Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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Scholium.
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<
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">Obſeruabis, quod aliquando in mentem venerat; </
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<
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">ſcilicet, verſus cen
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trum produci maiorem numerum in ratione diſtantiarum permutando; </
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& imperfectiorem in ratione duplicata earumdem diſtantiarum, etiam
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permutando, v. g. ſit idem vectis AC ſectus bifariam in B; </
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<
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">in puncto
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B producitur numerus duplus producti in A; </
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<
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id
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">at verò perfectio impetus
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in B eſt ad perfectionem impetus in A, vt quadratum BC ad quadra
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tum AC; </
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<
s
id
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">vel in ratione ſubquadrupla, licèt tota collectio impetus B
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ſit tantùm ſubdupla perfectione collectionis impetus A; </
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<
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">ſed hoc profe
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ctò dici non poteſt; </
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<
s
id
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">nam ſint in A 4. partes impetus; igitur in B erunt
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8. applicetur autem pondus in B. </
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<
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">Primò producentur in eo partes 8.
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impetus perfectionis ſubquadruplæ; </
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<
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">ſi comparentur cum partibus A,
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tum producentur 16. quæ æquiualent 4 A; </
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<
s
id
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">igitur 24. at verò in A pro
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ducentur primò 4. tum deinde 2. quæ æquiualent 8. productis in B; igitur
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6. igitur pondus, quod leuari poteſt in B, eſt ad pondus, quod leuari poteſt
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in A, vt 24. ad 6.id eſt, in ratione quadrupla quod omninò falſum eſt. </
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Theorema
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108.
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Iam facilè explicatur ex dictis, quomodo, & cuius rationis pondera attol
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lantur ex diuerſis punctis vectis
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; ſit enim idem vectis AC, & producan
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tur.v.g. </
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<
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id
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">in ſingulis punctis vectis ſingula puncta impetus, ſed diuerſæ
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perfectionis; </
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>
<
s
id
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">haud dubiè plures partes impetus imperfecti poſſunt face
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re impetum æqualem in perfectione alteri, qui conſtat paucioribus, ſed
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perfectioribus; </
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>
<
s
id
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N14C5E
">igitur cum impetus B ſit imperfectior duplò quàm im
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petus in A, duplò plures partes impetus producentur in B, quàm in A, er
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go duplò maius pondus mouebitur; atque ita deinceps; </
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>
<
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id
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">eum enim ap
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ponitur pondus in B, producuntur in eo partes impetus omnes eiuſdem
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perfectionis; </
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<
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id
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">quæ ſcilicet reſpondet B, id eſt, quæ eſt ſubdupla perfectio
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nis impetus A; </
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<
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id
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">igitur plures partes producuntur, quàm ſi eſſent perfe
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ctionis A; </
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<
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id
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">ſed pauciores quàm ſi eſſent perfectionis O, quæ minor eſt;
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quippe eadem potentia, ſeu cauſa, quæ agit quantum poteſt (quod ſup
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pono modò) producit æqualem effectum in perfectione, per Ax. 13. n. </
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4. ſed æqualis perfectio poteſt conſtare pluribus, vel paucioribus parti
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bus perfectionis, nam 4. pattes perfectionis vt 4. faciunt æqualem effe
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ctum alteri qui conſtat 8. partibus perfectionis vt 2. quod certum eſt; ſed
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de his plura aliàs. </
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Theorema
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109.
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Perfectio decreſcit verſus centrum iuxta diuerſam rationem longitudinum
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vectis, ſeu distantiarum.
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v.g.ſit idem vectis AC, ita decreſcit ab A verſus
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centrum C; </
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<
s
id
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">vt impetus puncti B ſit ſubduplus in perfectione, puncti R
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ſubtriplus: </
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<
s
id
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">iam verò ſit vectis ſubduplus prioris BC, ſectus bifariam in
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Z; </
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<
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id
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">ſi impetus productus in B, quę eſt extremitas minoris vectis B ſit æqua
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lis perfectionis cum impetu producto in A (& reuera ſunt æquales) ſi
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æquali tempore percurrant arcus æquales, ſcilicet AV, & BD) certè im-</
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