Borelli, Giovanni Alfonso, De motionibus naturalibus a gravitate pendentibus, 1670

Page concordance

< >
< >
page |< < of 579 > >|
<archimedes>
<text>
<body>
<chap>
<p type="main">
<s id="s.002559">
<arrow.to.target n="marg667"/>
<lb/>
tempore V percurrat ſpatium Z, & fiat IB medią
<lb/>
proportionalis inter altitudines AB, & DE. dico
<expan abbr="tẽ-pus">tem
<lb/>
pus</expan>
T minus eſſe
<expan abbr="tẽpore">tempore</expan>
V, ſed
<expan abbr="tẽpus">tempus</expan>
<expan abbr="minorẽ">minorem</expan>
<lb/>
<expan abbr="proportionẽ">proportionem</expan>
habere,
<expan abbr="quã">quam</expan>
IB habet ad DE; fiat vel in­
<lb/>
telligatur figura GBC æquè alta, ac eſt DEF
<expan abbr="eiuſdẽ-que">eiuſdem­
<lb/>
que</expan>
materiei habens
<expan abbr="eãdẽ">eandem</expan>
baſim BC, hac lege vt mo­
<lb/>
<expan abbr="proportionẽ">proportionem</expan>
habeat, quam
<lb/>
altitudo AB ad GB, ſitque Y tempus, quo GBC ſur­
<lb/>
ſum infra aquam aſcendendo percurrit idem ſpatium
<lb/>
X. quoniam ſunt duo folida homogenea ABC, & GB
<lb/>
C eamdem baſim BC habentia, quorum moles eam­
<lb/>
dem proportionem habent, quam altitudo AB ad G
<lb/>
B, ſeù ad DE, & ſimiliter poſita ſunt dum aſcendunt
<lb/>
<arrow.to.target n="marg668"/>
<lb/>
per ſpatia æqualia X, X; igitur tempus T, quo ABC
<lb/>
pertranſit ſpatium X ad tempus Y, quo GBC idipſum
<lb/>
ſpatium percurrit, eamdem proportionem habet,
<expan abbr="quã">quam</expan>
<lb/>
DE ad IB. poſtea quia ſunt duo alia ſolida homogenea
<lb/>
æquè alta GBC, & DEF quorum baſes planæ BC, &
<lb/>
EF eamdem proportionem habent, quam moles eo­
<lb/>
rum, ergo tempora Y, & V, quibus in eodem fluido
<lb/>
<arrow.to.target n="marg669"/>
<lb/>
aqueo aſcendendo percurrunt ſpatia æqualia X, & Z
<lb/>
parùm inter ſe differunt, eritque tempus V minus
<expan abbr="quã">quam</expan>
<lb/>
Y, ſed maiorem proportionem ad ipſum habet, quàm
<lb/>
DE ad IB, ac proindè tempus V maius erit, quàm T,
<lb/>
& ideò celeriùs aſcendet ABC, quàm DEF, ſed iņ
<lb/>
minori proportione, quam habet IB ad DE, idemque
<lb/>
concludetur in deſcenſu, quod erat &c. </s>
</p>
</chap>
</body>
</text>
</archimedes>