Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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<
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retineret pondus in L; </
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<
s
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">ducatur autem KLG Tangens parallela CT; </
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<
s
id
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">certè
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eadem potentia in L per LG retinebit pondus in L; </
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<
s
id
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">quæ idem retine
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ret applicata in C per CT; </
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<
s
id
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N1CCD9
">cum enim RC & RL ſint æquales ſi ſint ap
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plicatæ duæ potentiæ æquales in C quidem per CT, & in L per LG; </
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<
s
id
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">
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haud dubiè erit perfectum æquilibrium; </
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<
s
id
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N1CCE4
">igitur ſi pondus A pendeat in
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H fune LGH, retinebit pondus L in plano inclinato GLK; </
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>
<
s
id
="
N1CCEA
">eſt autem
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pondus H ad pondus LN SR ad RL; </
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>
<
s
id
="
N1CCF0
">ſed triangula RSL, & GKI
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lb
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ſunt proportionalia; </
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>
<
s
id
="
N1CCF6
">igitur pondus in H eſt ad pondus L, vt GI ad G
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K; </
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>
<
s
id
="
N1CCFC
">igitur ſi vires, quæ retinent pondus in plano inclinato GK ſunt ad vi
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lb
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res, quæ retinent pondus in perpendiculari GI, vt GI ad GK; igitur im
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petus ſeu motus mobilis in plano GK eſt ad impetum, ſeu motum eiuſ
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dem in perpendiculo GI, vt GI ad GK. </
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</
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<
p
id
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type
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">
<
s
id
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N1CD08
">Hæc omnia veriſſima ſunt, ſemper tamen deſiderari videtur ratio phy
<
lb
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ſica, cur idem pondus pendulum ex C in O, ſit eiuſdem momenti cum
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pondere affixo puncto P, ſeu brachio libræ horizontalis PS. quod certè
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Mechanica Axiomatis, vel hypotheſeos loco iure aſſumere poteſt; </
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>
<
s
id
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N1CD12
">at ve
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rò phyſica non ſatis habet de re cognoſcere quod ſit, niſi ſciat propter
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quid ſit; igitur nos aliquam afferre conabimur. </
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<
s
id
="
N1CD1A
">Suppono tantùm tunc
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eſſe æquilibrium perfectum duorum ponderum æqualium cum
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abbr
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vtrimq;
">vtrimque</
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>
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æqualia illa pondera ita ſunt appenſa, vt linea directionis vnius æqua
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lis ſit lineæ directionis alterius, cur enim alterum præualeret ſi ſint æ
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qualia? </
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<
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id
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">hoc poſito. </
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</
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type
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<
s
id
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">Dico pondus affixum P æquale ponderi L facere æquilibrium; cum
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enim linea directionis ſit PO, ſi deſcenderet liberè per PO. </
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>
<
s
id
="
N1CD34
">L eodem
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tempore attolleretur per LS, quod certè applicatis planis SL PO facilè
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fieri poſſet; </
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>
<
s
id
="
N1CD3C
">ſed eodem modo P grauitat, quo ſi deſcenderet per PO; </
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>
<
s
id
="
N1CD40
">eſt
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enim eius linea directionis; </
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<
s
id
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N1CD46
">atqui tunc faceret æquilibrium, quod oſten
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do; </
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>
<
s
id
="
N1CD4C
">æquale ſpatium conficeret L, per LS aſcendendo, quod P per PO
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deſcendendo; </
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>
<
s
id
="
N1CD52
">igitur ſi attolleret L in S, ſimiliter pondus L æquale P in S
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/>
attolleret pondus P ex O in P, igitur neutrum præualere poteſt; ſed quia
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hæc fuſiùs explicabimus cum de libra, nunc tantùm indicaſſe ſufficiat. </
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<
s
id
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">Supereſt vt breuiter oſtendamus accipi non poſſe hanc proportio
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nem imminutionis motus in plano inclinato à Tangente BE tùm
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quia; </
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>
<
s
id
="
N1CD64
">iam à ſecante accipi oſtendimus, tùm quia ſit Tangens BD æqualis
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ſumi toti ſeu perpendiculari AB; </
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>
<
s
id
="
N1CD6A
">ſequeretur motum per AD æqualem
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eſſe motui per AB; </
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>
<
s
id
="
N1CD70
">Equidem in maxima diſtantia accedit Tangens ad
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ſecantem; igitur eò plùs impeditur motus, quò maius ſpatium conficien
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dum eſt, &c. </
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Theorema
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6.
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Ex hoc ſequitur neceſſariò motum in plano inclinato eſſe ad motum in per
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pendiculari, vt ipſa perpendicularis ad ipſum planum inclinatum,
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emph.end
type
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italics
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v.g. velo
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citas motus per AE eſt ad velocitatem motus per AB, vt ipſa AB eſt
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ad ipſam AE, ſit enim AE dupla AB, velocitas per AB eſt dupla veloci
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tatis per AE. </
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