Varro, Michael
,
De motv tractatvs
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<
expan
abbr
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partiũ
">partium</
expan
>
<
expan
abbr
="
illarũ
">illarum</
expan
>
<
expan
abbr
="
proportionẽ
">proportionem</
expan
>
<
expan
abbr
="
ſeruabũt
">ſeruabunt</
expan
>
. </
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>
<
s
>Sit
<
expan
abbr
="
exẽpli
">exempli</
expan
>
gratia
<
lb
/>
linea AB, quæ in puncto C in datam rationem ſecta
<
lb
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ſit, puta vt pars AC quadrupla ſit ad partem CB, mo
<
lb
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ueatúrque circa centrum C, punctum A deſcribet cir
<
lb
/>
culum
<
expan
abbr
="
quadruplũ
">quadruplum</
expan
>
ad illum quem B
<
lb
/>
deſcribet. </
s
>
<
s
>Eſt enim
<
expan
abbr
="
eadẽ
">eadem</
expan
>
ratio in cir
<
lb
/>
culo diametri ad
<
expan
abbr
="
diametrũ
">diametrum</
expan
>
, quæ eſt
<
lb
/>
circunferentiæ ad
<
expan
abbr
="
circunferentiã
">circunferentiam</
expan
>
(vt
<
lb
/>
alibi demonſtrauimus.) Hac igitur
<
lb
/>
ratione A puncti motus quadruplus
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lb
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figure
id
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id.044.01.035.1.jpg
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number
="
3
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<
lb
/>
erit ad puncti B
<
expan
abbr
="
motũ
">motum</
expan
>
. </
s
>
<
s
>Si verò ponamus AD
<
expan
abbr
="
perpen-dicularẽ
">perpen
<
lb
/>
dicularem</
expan
>
eſſe, & linea AB illi primùm
<
expan
abbr
="
coincidẽs
">coincidens</
expan
>
circa
<
lb
/>
punctum C, moueatur donec A ad D perueniat: tum
<
lb
/>
<
expan
abbr
="
eodẽ
">eodem</
expan
>
momento B perueniet ad E: motum igitur erit
<
lb
/>
A in linea
<
expan
abbr
="
perpẽdiculari
">perpendiculari</
expan
>
tota circuli maioris diame
<
lb
/>
tro, quæ eſt AD:B verò in
<
expan
abbr
="
eadẽ
">eadem</
expan
>
linea, minoris
<
expan
abbr
="
tãtùm
">tantùm</
expan
>
<
lb
/>
circuli diametro
<
expan
abbr
="
motũ
">motum</
expan
>
erit, quę eſt BE. </
s
>
<
s
>Atqui diame
<
lb
/>
ter AD quadrupla eſt ad BE, quia ex hypotheſi
<
expan
abbr
="
ſemi-diametrorũ
">ſemi
<
lb
/>
diametrorum</
expan
>
<
expan
abbr
="
illorũ
">illorum</
expan
>
<
expan
abbr
="
circulorũ
">circulorum</
expan
>
proportio eſt, vt 4 ad 1.
<
lb
/>
Motus igitur
<
expan
abbr
="
pũcti
">puncti</
expan
>
in linea A
<
expan
abbr
="
perpẽdiculari
">perpendiculari</
expan
>
ad
<
expan
abbr
="
motũ
">motum</
expan
>
<
lb
/>
<
expan
abbr
="
pũcti
">puncti</
expan
>
B quadruplus erit:
<
expan
abbr
="
Idẽ
">Idem</
expan
>
dicetur ſi in data aliqua
<
lb
/>
alia ratione ſecta ſit linea AB.
<
expan
abbr
="
Demõſtratũ
">Demonſtratum</
expan
>
igitur eſt
<
lb
/>
quomodo fieri poſſit vt rectæ lineę extrema
<
expan
abbr
="
ſecũdũ
">ſecundum</
expan
>
<
lb
/>
<
expan
abbr
="
datã
">datam</
expan
>
<
expan
abbr
="
rationẽ
">rationem</
expan
>
moueantur. </
s
>
<
s
>Si igitur illis extremis duæ
<
lb
/>
vires applicentur,
<
expan
abbr
="
mouebũtur
">mouebuntur</
expan
>
<
expan
abbr
="
eodẽ
">eodem</
expan
>
ipſo motu: ergo
<
lb
/>
ſecundum datam vel propoſitam rationem. </
s
>
<
s
>Quod
<
lb
/>
aſſumptum erat. </
s
>
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