Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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<
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203
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026/01/235.jpg
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cubans F; </
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<
s
id
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N1D046
">dico grauitationem ponderis F in inclinatam GD eſſe ad gra
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uitationem in horizontalem CD vt CD ad GD; </
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<
s
id
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">quia pondus F pellit
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planum per lineam FE ſeu GB Tangentem; </
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<
s
id
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N1D052
">quia determinari non po
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teſt ſeu percuſſio, ſeu impreſſio ex alio capite quàm ex linea ducta à
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centro grauitatis perpendiculariter in planum, vt demonſtrauimus
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in Th. 120. l. 1. atqui libræ extremitas G initio deſcendit per Tangen
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tem GB, id eſt per minimum arcum, qui ferè concurrit cum Tangente; </
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<
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ſed ideò deſcendit in AB, quia pellitur deorſum à pondere; </
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<
s
id
="
N1D065
">igitur men
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ſura grauitationis eſt deſcenſus libræ, ſed libra faciliùs deſcendit ex A
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deorſum quàm ex G in proportione AD ad CD vel GD ad CD; </
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>
<
s
id
="
N1D06D
">igitur
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grauitatio ponderis in A eſt ad grauitationem eiuſdem in G, vt GD ad
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CD; quia rationes cauſarum ſunt eædem cum rationibus effectuum. </
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>
</
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<
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type
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<
s
id
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">Præterea ſit planum inclinatum GD, ſit IF parallela GD; </
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<
s
id
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">ſint IK, I
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M & quadrans KFR; </
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<
s
id
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N1D081
">punctum I ſit centrum libræ immobile; </
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<
s
id
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N1D085
">certè ſi ſit
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alterum brachium libræ æquale IF inſtructum æquali pondere F, erit æ
<
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quilibrium; ſed pondus illud in F eſt ad idem in R, vt IM ad IF, ſeu vt
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CD ad GD, quod erat dem. </
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</
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<
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Scholium.
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<
s
id
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">Obſeruabis poſſe facilè ex dictis explicari diuerſas potentias applica
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tas ponderi F in eodem plano GD, primò ſi accipiatur IHF parallela
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GH cum centro immobili I pondus retinebitur, ſi potentia in I ſit ad
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globum vt GC ad GD, vt demonſtratum eſt; ſi verò pellat potentia per
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lineam IF, globus deſcendet, vt patet. </
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>
</
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type
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<
s
id
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">Hinc ſecundò ſuſtinens MF totum pondus F ſuſtinet, patet, quia ſi
<
lb
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ue planum inclinatum pondus ipſum tangat, ſiue perpendiculare, totum
<
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ſuſtinet pondus; ſubſtracto enim plano pondus immobile manet, adde
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quod non poteſt pondus F ſuſtineri in brachio IM, niſi æquale pondus
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ex æquali brachio oppoſito pendeat. </
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</
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<
s
id
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">Tertiò ex puncto T lineâ TFE non poteſt ſuſtineri pondus licèt po
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tentia in T eſſet infinita, quia ex TE deſcendet in TV, patet; idem
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dico de omnibus aliis lineis ductis ab F ad aliquod punctum inter
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TM. </
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</
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<
s
id
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">Quartò ex puncto X linea XF ſuſtinebitur pondus dum potentia ap
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plicetur in X, maior quidem potentia applicata in I, ſed minor applica
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ta in M; </
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>
<
s
id
="
N1D0CF
">nam potentia M eſt ad potentiam I vt IF ad MF; </
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>
<
s
id
="
N1D0D3
">igitur poten
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tia X eſt ad potentiam M vt MF ad XF; ad potentiam verò I vt IF
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ad XF. </
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>
</
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<
s
id
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">Quintò, cùm triangula IF M.HF 4. ſint proportionalia, potentia M
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eſt ad potentiam I vt HF ad 4. F. </
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>
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<
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id
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<
s
id
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">Sextò, ſi applicetur potentia, vel in T pellendo per lineam TFE, quæ
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cadit perpendiculariter in planum GD, vel ſi applicetur in A per lineam
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AE trahendo, non poterit retineri globus, quæcunque tandem poten
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tia applicetur; </
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<
s
id
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">quia ſemper per GD globus rotari poterit nullo cor
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pore impediente; </
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<
s
id
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N1D0F6
">ſuppono enim tùm planum tùm globum eſſe perfectè </
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