Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
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1 L*IBER* S*TATICÆ*
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xml:space
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</
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<
s
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xml:space
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">quemadmodum axis ſegmentum inter gravitatis cen-
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trum punctumq́ue ſiniſtrum, ad ejuſdem ſegmentum in-
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ter gravitatis centrum punctumq́ue dextrum: </
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<
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lumnæ pondus ſuper puncto dextro quieſcens, ad reli-
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quum ponderis ſuper ſiniſtro quieſcentis.</
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<
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">D*ATVM*. </
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">ABCD columna 6 ℔ pendeat, ſecta quemadmodum in 1 pro-
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poſitione, duobus punctis R, V, ſuper OE, Æ quieſcens.</
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<
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">Q*VAESITVM*. </
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xml:space
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tum T R ad ejuſdem T V: </
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<
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xml:space
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">ita eſſe pondus puncto V quieſcens in Æ, ad re-
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liquum ponderis puncto R, ſuper OE quieſcentis.</
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Æ 4 ℔ ſuper OE verò 2 ℔ quieſcunt, ex
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1 conſect. </
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2 ℔ etiam dupla eſtratio; </
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T R ad T V: </
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cto Æ eſt, ad reliquum ponderis quieſcen-
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tis ſuper OE.</
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">Verumenimvero generalis conſectarii
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neceſſitas demonſtretur; </
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tor, ut R Z æquetur R V, ſumptoq́ue R
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pro puncto fixo, ex Z pondus
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114 ℔ ſuſpendi neceſſe eſt, ut
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columna ſuo in ſitu cõſervetur,
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ex 3 propoſit. </
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<
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">quod verò ex V,
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columnam eodĕ in ſitu, quo Æ,
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ſervat, parem cum 11 potentiam
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habere ex 13 propoſitione ne-
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ceſſe eſt. </
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">In Æ igitur pondus par
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ipſi 11 quieſcit. </
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in Φ continuator, ut V Φ æque-
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tur V R, ſumptoq́ue V pro pun-
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cto firmo, de Φ ſuſpendi Δ 2 ℔
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neceſſe eſt, ut columna eodem in ſitu ſuſtineatur, per 3 exemplum. </
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verò ex R columnam ſive vectem eodem in ſitu ſuſtinet, quo OE, r
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antun-
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dem potentiæ habet, quantum Δ, per 13 propoſit. </
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cens æquatur ponderi Δ. </
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">Quandoquidem autem 11, ex R communi fulci-
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menti puncto, contra columnam ſitu æquilibre eſt, ratio radii T R eſt ad ra-
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dium R Z, quæ eſt 11 ad columnam, per 1 propoſitionem. </
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firmo puncto uſurpato, ratio radii T V ad radium V Φ eadem eſt cum ra-
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z
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ione Δ, ad columnam, atque R Z æquatur V Φ Duæ igitur proportiones
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nobishic ſunt quaternûm terminorum, quorum ſecundi quartique </
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