Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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ad ſinum totum EB, & per DB vt DS ad DB: idem dico de aliis. </
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<
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<
s
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">Hinc colligo primò, omnes determinationes nouas in hypotheſi glo
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borum æqualium eſſe ſubduplas in eiſdem angulis priorum determina
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tionum in hypotheſi corporis reflectentis immobilis. </
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<
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<
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id
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">Colligo ſecundò, omnes reflexiones fieri neceſſariò per eandem li
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neam, quæ ſcilicet eſt Tangens puncti contactus globi reflectentis, quod
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valdè mirificum eſt, & facilè obſeruabunt, qui Tudicula minore ludunt. </
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<
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Colligo ſexto, cum angulus incidentiæ eſt 60. lineam reflexam eſſe ſub
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duplam directæ quæ vlteriùs produceretur; infrà verò ſexto eſſe maio
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rem, ſuprà verò eſſe minorem, eſt autem longitudo lineæ ſinus comple
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menti anguli incidentiæ. </
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<
s
id
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">v.g. ſi linea incidentiæ ſit EB eſt EG, ſi DB
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eſt DH, ſi VB eſt VX. </
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Theorema
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64.
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Si globus minor in maiorem impingatur, qui ab eo tamen moueatur per li
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neam connectentem centra vtriuſque impactus, reflectitur
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; </
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<
s
id
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N2050B
">ratio eſt, quia ma
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ior globus eſt maius impedimentum, vt iam diximus Th. 131.lib.1.id
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eſt, vt clariùs hic explicetur, quæ ibidem tantùm obiter indicauimus,
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noua determinatio maior eſt priore, quia ceſsio eſt minor impulſione; ſit
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autem. </
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<
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">v.g. globus reflectens duplus impacto; </
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<
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">igitur motus eſt ſubduplus,
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quia ſcilicet impetus diſtribuitur pluribus partibus ſubjecti; </
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<
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id
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N20523
">igitur ſin
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gulæ minùs habent; </
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<
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id
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N20529
">igitur impetus eſt remiſsior; </
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<
s
id
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N2052D
">igitur motus tardior; </
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>
<
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N20531
">
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igitur ceſsio minor ſubduplo; </
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<
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id
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N20536
">igitur determinatio noua eſt maior æqua
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li 1/2 hinc debet neceſſariò reflecti, quia quotieſcunque ad lineas op
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poſitas ex diametro determinatur impetus, maior determinatio præua
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let pro rata per Th.134.lib.1. nam perinde ſe habet, atque ſi eſſet duplex
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impetus; </
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<
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id
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N20542
">quanta porrò eſſe debeat linea reflexa, determinari poteſt; </
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>
<
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id
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">ſi
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enim determinatio noua eſſet ſolilaria mobile cum eo impetu, quem ha
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bet
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expan
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v.g. BA vel BF; </
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<
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id
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">diuidatur BF in duas partes æquales in
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>
,
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determinatio noua eſt ad priorem vt 3. ad 2. aſſumatur F
<
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>
æqualis B
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; </
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igitur propter determinationem priorem oppoſitam ſcilicet BA detra
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hi debent duæ partes toti B
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">β</
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ſcilicet
<
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">βυ</
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æqualis BA; </
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<
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id
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N20575
">igitur linea re
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flexa erit B
<
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grc
">υ</
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>
dupla totius BF; </
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>
<
s
id
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N2057F
">ſit etiam globus reflectens, qui mouetur
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ab impacto, quadruplus, determinatio noua erit ad priorem vt 7. ad 4.
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fit B
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grc
">δ</
foreign
>
ad BA vt 7. ad 4. ex B
<
foreign
lang
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grc
">δ</
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>
detrahatur DH æqualis BA, ſupereſt
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HB id eſt 3/4 totius BF; non poteſt autem eſſe maior determinatio no
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ua priore quàm in ratione dupla, vt diximus ſuprà. </
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<
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">Ratio eſt, quia eò mi
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nor eſt determinatio noua, quò maior eſt motus impreſſus globo maiori
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reflectenti; </
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<
s
id
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N2059B
">igitur tantum detrahitur duplæ, quantum additur motus; </
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<
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id
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N2059F
">ſi
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motus eſt æqualis, detrahitur duplæ æqualis priori; </
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<
s
id
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N205A5
">igitur ſupereſt æqua
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lis; </
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<
s
id
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">ſi motus eſt ſubduplus, detrahitur duplæ ſubdupla prioris; </
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<
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id
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">igitur ſu
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pereſt 1/2 ſi ſubquadruplus detrahitur duplæ ſubquadrupla prioris, igitur
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ſupereſt 1 3/4 ſi ſit duplus motus, determinatio noua eſt ſubdupla; </
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<
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">igitur
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priori detrahitur 1/2 de quo infrà; </
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>
<
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id
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">quod autem ſpectat ad longitudi
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nes linearum non eſt difficultas; quippe determinatio minor detrahi
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deber maiori. </
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