Fabri, Honoré
,
Tractatus physicus de motu locali
,
1646
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026/01/172.jpg
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<
s
id
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N197A3
">Hinc inuertenda eſt progreſſionis linea; </
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<
s
id
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N197A7
">quippe linea AE repræſen
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tat nobis progreſſionem motus accelerati, quæ fit in inſtantibus, & li
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nea FK progreſſionem motus, quæ fit in partibus temporis ſenſibilibus; </
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<
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N197AF
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in illa primo inſtanti decurritur primum ſpatium AB, ſecundo tempore
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æquali BC, tertio CD, quarto DE: </
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<
s
id
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N197B6
">in hac vero prima parte acquiritur
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ſpatium FG ſecunda æquali primæ GH, tertia HI, quarta IK; </
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<
s
id
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N197BC
">igitur ſi ac
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cipiatur linea AE, progrediendo ab A verſus E, vel linea FK progre
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diendo ab F verſus K habebitur progreſſio motus naturaliter accelerati; </
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<
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N197C4
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ſi verò accipiatur EA, vel KF, progrediendo ſcilicet ab E verſus A, vel à
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K verſus F, erit progreſſio motus violenti naturaliter retardati; </
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<
s
id
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N197CB
">vt con
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ſtat ex præcedèntibus Theorematis; & quemadmodum progreſſio acce
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lerationis in inſtantibus finitis fit iuxta ſeriem iſtorum numerorum 1.2.
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3.4. in partibus verò temporis ſenſibilibus iuxta ſeriem iſtorum 1.3.5.7.
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ita fit omninò progreſſio retardationis in inſtantibus iuxta hos nume
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ros 4.3.2.1. in partibus temporis ſenſibilibus iuxta hos 7.5. 3. 1. </
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<
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Theorema
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type
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italics
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28.
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type
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</
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</
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type
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<
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N197EA
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<
emph
type
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italics
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Motus violentus durat tot inſtantibus ſcilicet æquiualentibus quot ſunt ij
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gradus impetus quibus violentus ſuperat innatum,
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emph.end
type
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italics
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v.g. ſit vnus gradus im
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petus innati; </
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>
<
s
id
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N197F9
">producantur 5. gradus violenti, quorum ſinguli ſint æqua
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les innato etiam
<
expan
abbr
="
æquiualẽter
">æquiualenter</
expan
>
, motus durabit 4. inſtantibus etiam æqui
<
lb
/>
ualenter id eſt 4. temporibus, quorum ſingula erunt æqualia primo in
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ſtanti motus naturalis, probatur, cum ſingulis inſtantibus æqualibus de
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/>
ſtruatur vnus gradus; certè 4. inſtantibus durat motus. </
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>
</
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<
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id
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N19809
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type
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<
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id
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N1980B
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<
emph
type
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center
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<
emph
type
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italics
"/>
Theorema
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emph.end
type
="
italics
"/>
29.
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type
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</
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<
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N19819
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Si accipiantur ſpatia æqualia in hac progreſſione retardationis, eſt inuerſa
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illius, quàm tribuimus ſuprà accelerationi, aſſumptis ſcilicet ſpatiis æqualibus; </
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>
<
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id
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N19821
">
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tum ſi accipiantur ſpatia æqualia prime ſpatie quod decurritur prime inſtan
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ti metus naturalis, tum ſi accipiantur ſpatia æqualia date ſpatie quod in par
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te temporis ſenſibili percurritur
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emph.end
type
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italics
"/>
; </
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>
<
s
id
="
N1982D
">quippe quemadmodum in progreſſione
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lb
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accelerationis decreſcunt tempora; </
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>
<
s
id
="
N19833
">ſic in progreſſione retardationis
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lb
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creſcunt, aſſumptis ſcilicet ſpatiis æqualibus; quare ne iam dicta hic re
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/>
petam, conſule quæ diximus lib.2. de hac progreſſione. </
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>
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<
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id
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type
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main
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<
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id
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emph
type
="
center
"/>
<
emph
type
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italics
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Theorema
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emph.end
type
="
italics
"/>
30.
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type
="
center
"/>
</
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>
</
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<
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N19849
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type
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">
<
s
id
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N1984B
">
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emph
type
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italics
"/>
Hinc instantia initio huius metus ſunt minora ſicut initio motus naturalis
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ſunt maiora; </
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>
<
s
id
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N19853
">& ſub finem in motu violente ſunt maiora, in naturali ſunt mi
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nora
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emph.end
type
="
italics
"/>
; </
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>
<
s
id
="
N1985C
">quia ſcilicet hic acceleratur, ille retardatur: </
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>
<
s
id
="
N19860
">igitur velo
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lb
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citas accelerati creſcit; </
s
>
<
s
id
="
N19866
">igitur ſi accipiantur ſpatia æqualia, decreſcit tem
<
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/>
pus; </
s
>
<
s
id
="
N1986C
">at verò velocitas retardati decreſcit, igitur aſſumptis ſpatiis æquali
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bus, creſcit tempus; </
s
>
<
s
id
="
N19872
">igitur ſi accipiatur ſpatium, quod percurritur primo
<
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inſtanti huius motus, & deinde alia huic æqualia; </
s
>
<
s
id
="
N19878
">haud dubiè, cum ſe
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/>
cundo inſtanti motus ſit tardior, ſitque aſſumptum æquale ſpatium; haud
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dubiè inquam inſtans ſecundum erit maius primo, & tertium ſecundo,
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atque ita deinceps. </
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>
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