Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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ſecet arcum CFG ad angulos rectos; idem prorſus fiat in aliis punctis
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peripheriæ, aſſumptis ſcilicet lineis æqualibus ſubtenſis arcuum, v.g. in
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puncto D, aſſumpta linea æquali AD, in puncto C, aſſumpta æquali AC,
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&c. </
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<
s
id
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N29FD3
">hoc poſito habetur ſolidum, quod facilè vocauerim Elliptico cylin
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dricum, cuius conſtructio talis eſt, ſit cylindrus RI, cuius diameter
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baſis ſit KI, æqualis diametro AF circuli prioris; </
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<
s
id
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">ſit etiam altitudo KR,
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æqualis prædictæ diametro KI, ſit KR diuiſa bifariam in L, ſitque pla
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num IL ſecans cylindrum, itemque alterum LP, vtraque ſectio Ellipſis
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eſt, vt patet; </
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<
s
id
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">ac proinde habetur ſolidum quæſitum LIP conſtans gemi
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na baſi LI. & LP Elliptica, & reliqua circumferentià cylindricâ, cuius
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centrum grauitatis eſt in N, id eſt in puncto decuſſationis rectarum PM,
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IS, quæ diuidunt ILPL bifariam æqualiter, eſt autem NO 1/3 totius
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LO, per Sch. Th.2. hoc poſito ſit XF 1/3 totius AF: dico eſſe centrum
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percuſſionis quæſitum circuli ACFG rotati circa A, quia perinde ſe
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habet, atque ſi puncto X incubaret prædictum ſolidum ellipticocylindri
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cum, cuius X eſſet centrum grauitatis. </
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Scholium.
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<
s
id
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">Obſeruabis primò, in plano ACFG, vt punctum X ſit centrum per
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cuſſionis, incidendam eſſe ſtriam quamdam, ſeu rimam, quæ termi
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netur in X. </
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<
s
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">Secundò, idem eſſe centrum percuſſionis rectæ AF, quæ voluitur
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circa A, ſiue ſit ſimplex linea, ſiue diameter circuli. </
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Theorema
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23.
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Si voluatur rectangulum parallelum orbi in quo voluitur determinari
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po
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test centrum percuſſionis
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; </
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<
s
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">ſit enim rectangulum AD, quod voluatur circa
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centrum A, eo modo, quo dictum eſt ſit ducta AD, inueniatur centrum
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I, trianguli ABD; </
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<
s
id
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">itemque centrum H, trianguli ADF, per Th. 17.
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tùm ducta IH, diuidatur bifariam in K; </
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<
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id
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">ducatur AK, tùm GK perpen
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dicularis in AK: dico G eſſe centrum percuſſionis, per poſ.7.& Theo
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rema 17. </
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Corollarium.
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figuris planis; quia diuidi poſſunt in plura triangula. </
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Theorema
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24.
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Poteſt determinari centrum percuſſionis ſolidi
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trium facierum ABDE
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; </
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vt demonſtretur centrum percuſſionis pyramidis, & priſmatis, præmitti
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debuit hoc ſolidum; </
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<
s
id
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">ſit enim ſolidum priori ſimile, A.M. G.C. motus
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puncti M, eſt ad motum puncti G, vt recta BM ad rectam BG; </
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<
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NK ad OH, vt BM ad BG; </
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<
s
id
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">certè perinde ſe habet punctum M, atque
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ſi NMK incubaret, non quidem per MG, ſed per lineam perpendicu
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larem ductam in BM, vt patet ex dictis: </
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<
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perinde ſe habet, atque ſi incubaret OGH; </
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<
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centrum grauitatis ſolidi ACHKNOA, quod vt fiat, aſſumatur IP </
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