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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obliqua. </
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<
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<
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<
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xml:space
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">Ann@@ere &
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abnudere pa-
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ralleliſm
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o op-
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ponuntur.</
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abnuet.</
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<
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<
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">D*ATVM*. </
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<
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xml:space
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">AB columna duabus lineis eſto ſuſtentata, CD quidem ad
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horizontem perpendiculari, EF vero (ſi poſſit) ad eandem obliquâ, & </
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<
s
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">GH
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columnæ pendula gravitatis diametrus. </
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<
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">Q*VAESITVM*. </
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<
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xml:space
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">Veritas propofitio-
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nis à nobis demonſtrari debet. </
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<
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">P*RAEPARATIO*. </
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<
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continuantor mutuo ſe in I interſecantes.</
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<
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<
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">DEMONSTRATIO.</
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<
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xml:space
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">Quocunque in ſitu columna de lineis CD, EF fuerit ſuſpenſa, eundem
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in quovis puncto firmo continuatarũ linearum ſervabit, quod anguli I CE & </
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<
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IEC non mutentur. </
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<
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xml:space
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">Poſito igitur, I firmum pun-
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/527.01.048-01
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ctum eſſe duarum linearum commune, columna
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ex eo ſuſpenſa datum ſitum retinebit, & </
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<
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dula gravitatis diametrus erit. </
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<
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xml:space
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">Atqui illud neuti-
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quam fieri poteſt, quod GH iſti parallela, ea ipſa
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ſit. </
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<
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xml:space
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">Eadem demonſtratio fuerit, rectà EF in oppo-
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ſitam partem inclinatâ. </
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>
<
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xml:space
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">Si igitur IC horizonti eſt
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perpendicularis reliqua EF eidem nó poteſt eſſe
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obliqua, neceſſariò igitur perpendicularis etiam
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fuerit: </
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>
<
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xml:space
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">Et per conſequens ſi EF horizonti eft
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obliqua, etiam reliqua obliqua fuerit.</
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<
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xml:space
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">Porro, quia EF, A verſus annuit, etiam reliquam, quæ in dato ſitu co-
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lumnam ſervat, EF verſus annuere neceſſe eſt. </
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<
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xml:space
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">Ab ea enim (ſi poteſt) decli-
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net, ut CK, ſecans EI continuatam in K, perpendicularis per K, ob dictam
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cauſam, columnæ pendula gravitatis diametrus erit, quod magis abſurdũ eft,
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quam eandem illam per I cadere. </
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<
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xml:space
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">Neque hic igitur reliqua linea, columnam
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in dato ſitu ſervans, ab EF declinat, neque parallela eſt, quod antea demon-
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ftratum eſt, in latum autem decedere manifeſtè abſurdum eſt. </
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<
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ceſſariò EF verſus annuit. </
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<
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xml:space
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">Si vero EF in oppoſitam partem abiret, conſimi-
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liter etiam reliquam ab illa abire, & </
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<
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æquilibria ſunt, erit quemadmodum linea obliquè extol-
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bls-
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quium & re-
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ctum intelli-
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ge rectè &
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obliquè extol-
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lens.</
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lans, ad lineam rectè extollĕtem: </
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<
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<
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<
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<
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rum pondera, columnam in dato ſitu detinentia, ſunt G, H, quidem obliquè,
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I, K verò rectè extollentia, & </
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tollentes. </
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<
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& </
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