Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
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527.01.076
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76
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2 L*IBER* S*TATICÆ*
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dem ratione ſeſquitertia ſunt enim æquealti, ſimillima ratione BF cylindrus
<
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rertii circumſcripti cujus centrum K erit du-
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plus, quarti verò cujus centrum I quadru-
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plus. </
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<
s
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xml:space
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">poſito itaque imo cylindro 4 librarum,
<
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/>
ſecundus erit 3 ℔, tertius 2 ℔, ſummus de-
<
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/>
nique I ℔: </
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>
<
s
xml:id
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xml:space
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preserve
">Pari ratione ſi imus inſcriptorum
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ſit 3 librarum, ſecundus erit 2 ℔, ultimus ver
<
lb
/>
tici proximus I ℔. </
s
>
<
s
xml:id
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xml:space
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">Quæ cum ita ſint, & </
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>
<
s
xml:id
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xml:space
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">cen-
<
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tra cylindrorum, & </
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>
<
s
xml:id
="
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xml:space
="
preserve
">ipſorum ponderoſitas
<
lb
/>
nota, centrum gravitatis circumſcriptorum
<
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cadet in L ut LE occupet {1/24} totius AD;
<
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/>
</
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>
<
s
xml:id
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xml:space
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">Trium itidem inſcriptorum gravitatis centrum cadet in S, ut S E {1/24} totius A D
<
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obtineat. </
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>
<
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xml:space
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">Quamobrem L & </
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>
<
s
xml:id
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xml:space
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">S ab E rurſum æquidiſtant.</
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>
<
s
xml:id
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xml:space
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</
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<
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<
s
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xml:space
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">Verumenimvero ſi biſectio & </
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>
<
s
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xml:space
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">cylindrorum iſta ſiguratio continuentur, ut
<
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/>
octo datum conoïdale ambiantac ſeptem induant, diſtantia centrorum & </
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>
<
s
xml:id
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xml:space
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">in-
<
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ſcriptorum & </
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>
<
s
xml:id
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xml:space
="
preserve
">circumſcriptorum ſecabunt axem æquidiſtanter à puncto E, ab-
<
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/>
erunt enim {1/48} totius A D.</
s
>
<
s
xml:id
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xml:space
="
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"/>
</
p
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<
p
>
<
s
xml:id
="
echoid-s2520
"
xml:space
="
preserve
">Denique ſi ſectio iſta viciſſim duplicetur ut ſedecim cylindri circumſcriban-
<
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tur, & </
s
>
<
s
xml:id
="
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xml:space
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">quindecim intra includantur, nihilo ſecius centra gravitatis ſolidorum
<
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inſcriptorum & </
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<
s
xml:id
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xml:space
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">circumſcriptorum pari diſtantia ab E puncto utrimque diſta-
<
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bant, videlicet {1/96} axis A D. </
s
>
<
s
xml:id
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xml:space
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">Atque adeò ſequens biſectio antecedentem di-
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ſtantiam continuò bipartito ſecat, cujus conſecutionis veritatem & </
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<
s
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xml:space
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">neceſſita-
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tem inductione continuatâ demonſtrarem, niſi brevitatis ſtudio ductus, cum
<
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/>
cuilibet in promptu ſit, iſtud omitterem.</
s
>
<
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</
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<
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<
s
xml:id
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xml:space
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">Quamobrem E gravitatis centrum dati conoïdalis erit: </
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<
s
xml:id
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xml:space
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">Enimverò ſi cen-
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trum aliud ſumatur in ipſa E L aut E S tandem continua biſectione & </
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>
<
s
xml:id
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xml:space
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">cylin-
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drorum circumſcriptione & </
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<
s
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xml:space
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">inſcriptione eò devenitur ut centrum ſolidi ex cir-
<
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cumſcriptis conflati deſcĕdat infra conoïdalis centrum; </
s
>
<
s
xml:id
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xml:space
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">vel inſcripti ſupra ejuſ-
<
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dem conoïdalis centrũ adſcendat. </
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<
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xml:space
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">Quod impoſſibile per ſe clarum fuerit; </
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<
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">cum
<
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enim ſolidum tale è cylindris circumſcriptis componi poſſit ut ejus à conoï-
<
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/>
dali differentia minor ſit quocunque ſolido, poſſit item tale ſolidum inſcribi,
<
lb
/>
utriuſque ab E puncto differentia tantulo utrimque intervallo aberit ut minus
<
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nullum effingi poſſit. </
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<
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conoïdalis gravitatis eſſe centrum.</
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</
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<
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">C*ONCLVSIO*. </
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<
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">Quod
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feciſſe oportuit.</
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<
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</
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</
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poſ. </
s
>
<
s
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xml:space
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">item ſecetur ratione dupla, conſequens eſt, ſimilem à centro æquidiſtan-
<
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tiam iſtic ab inſcriptis & </
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<
s
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xml:space
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">circumſcriptis parallelogrammis argui, qualis hic in
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cylindris adſcriptis demonſtrata eſt.</
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</
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<
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">11 THE OREMA. 24 PROPOSITIO.</
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<
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<
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">D*ATVM*. </
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<
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">ABCD conoïdale curtum, baſis ima D C, ſumma A B, axis
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verò EF. </
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<
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">Q*VAESITVM*. </
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