Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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Theorema
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54.
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Hinc ſi tantùm habeatur ratio vectis, maior difficiliùs verſatur in plano
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horizontali, quàm minor.
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v.g. AE circa centrum E quam FE, producto
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ſcilicet æquali motu in extremitate vtriuſque A & F; </
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<
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">ſi enim A dato
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tempore percurrit AK; </
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">certè F percurret FG; </
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<
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ſubduplus ſectoris AEK, vt conſtat; </
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<
s
id
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">igitur faciliùs vertitur FE, quàm
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AE in proportione AE, ad FE: </
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<
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id
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">ſi tamen non conſideretur pondus ſeu
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reſiſtentia vectis, haud dubiè ſi pondus ſit in Q, faciliùs mouebitur ope
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ra maioris vectis AE, quàm minoris FE; </
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<
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">quia opera maioris mouetur
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motu vt QT; </
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<
s
id
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N224D7
">operâ verò minoris motu vt QY, igitur difficiliùs opera
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minoris in proportione QY ad QT; </
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<
s
id
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N224DD
">denique ſi pondus ſit in F maioris
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vectis, & in
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minoris, ſitque AE ad AF, vt FE ad F
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, æquale erit
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momentum vtriuſque vectis ad mouendum pondus; </
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<
s
id
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">quia arcus FV erit
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æqualis arcui
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Y; </
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<
s
id
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">hîc autem nullomodo conſideratur vectis reſiſten
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tia; </
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<
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id
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N224FD
">ſi verò producatur
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abbr
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tantũdem
">tantundem</
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>
impetus in toto vecte AE quamtum
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in FE; </
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<
s
id
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">certè pro rata ſingulæ partes FE duplum habent; </
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<
s
id
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">igitur tempo
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ra gyrorum erunt in ratione duplicata radiorum; </
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<
s
id
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N22511
">quia cum F habeat du
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plum impetum A, certè deſcribit orbem integrum eo tempore, quo A
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quadrantem; </
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>
<
s
id
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">ergo F 4. orbes, dum A vnicum: ſed hæc ſunt facilia. </
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Theorema
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55.
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Si vectis BH ita pellatur in B in plano horizontali, in quo liberè moueri
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poſſit
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v.g. dum aquæ ſupernatat, nulli centro immobili affixus, ſit que aqualis
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denſitatis in omnibus ſuis partibus; mouebitur circa aliquod centrum, etiamſi
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nulli centro affigatur.
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</
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<
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id
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"> Probatur, quia punctum B velociùs mouebitur, quàm
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A vel H, vt patet experientiâ: </
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<
s
id
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N22549
">ratio eſt, quia minùs impetus producitur
<
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in toto cylindro BH, applicata potentia in B, quàm in A, quod eſt cen
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/>
trum grauitatis cylindri BA, vt iam oſtendimus Th. 68. 69. BB; </
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>
<
s
id
="
N22551
">porrò
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ratio à priori eſt, quia cùm impetus producatur tantùm ad extra, vt tol
<
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latur impedimentum motus, vt fusè oſtendimus lib. 1. certè in tantùm
<
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amouetur impedimentum, in quantum amouetur corpus impediens mo
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tum alterius; </
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>
<
s
id
="
N2255D
">atqui amoueri tantùm poteſt per motum; </
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>
<
s
id
="
N22561
">igitur eo motu
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amouetur, quo faciliùs amoueri poteſt, & minore ſumptu, vt ita dicam,
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id eſt minore impetu: </
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>
<
s
id
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N22569
">porrò cum potentia ſit determinata ad producen
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dum tabem impetum, immediatè ſcilicet, id eſt, in ea parte, cui immedia
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tè admouetur; </
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>
<
s
id
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N22571
">alioqui ſi poſſet minorem, & minorem in infinitum pro
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ducere poſſet etiam immediatè ſine operâ organi mechanici quodlibet
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pondus mouere, quod eſt abſurdum, de quo iam ſuprà; </
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>
<
s
id
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N22579
">ſit igitur potentia
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applicata in A, ſcilicet in centro grauitatis cylindri BH; </
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<
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id
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">certè producit
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maximum impetum, quem poteſt producere in cylindro BH (ſuppono
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enim eſſe cauſam neceſſariam, & producere perfectiſſimum impetum,
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quem producere poſſit) producit inquam maximum ratione numeri; </
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<
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cùm in toto cylindro BH producat impetum eiuſdem perfectionis; </
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<
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">igi
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tur mouetur motu recto; </
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<
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">igitur æquali in omnibus partibus; </
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<
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id
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">igitur æqua
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lis eſt impetus in omnibus partibus, id eſt, æquè intenſus; </
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<
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