Stevin, Simon
,
Mathematicorum hypomnematum... : T. 4: De Statica : cum appendice et additamentis
,
1605
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*DE* S*TATICÆ ELEMENTIS*.
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funt. </
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<
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xml:space
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">Verum quæcunque binæ proportiones quaternûm terminorum, ſecun-
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dos quartosq́ue terminos equales habent, reliquos æquè rationales, id eſt pro-
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portionales habebunt. </
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<
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xml:space
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<
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<
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xml:space
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æquatur columnæ ponderi, quod puncto V, ſuper puncto Æ quieſcit;
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</
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<
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xml:space
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">pondusq́ue Δ ponderi, quod R puncto quieſcit ſuper OE. </
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xml:space
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ad T V: </
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<
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">ita pondus puncto Æ innitens, ad pondus OE innixum.</
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<
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<
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xml:space
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V ductis, pondera quæ antea ſuper quieſcent@bus punctis erant, etiam nunc
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eſſe poſſunt. </
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">V perpendiculares, exempli cauſa, ducantur,
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in iiſque puncta ut Y, & </
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Y 2 ℔, in λ 4 ℔ quieſcere manifeſtũ eſt, unde theorematis veritas manifeſta eſt.</
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tum axis inter gravitatis centrum & </
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punctum ſiniſtrum, ad eju ſdem ſegmentum inter gravi-
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tatis centrum & </
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</
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<
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">ita ſuſtentatum pondus columnæ dextro puncto, ad pon-
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dus quod ſuſtinetur ſiniſtro.</
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ejusq́ue axis E F gravitatis centrum G,
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puncta quibus columna ſuſtinetur H, I, quà
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perpendiculares K L, M N ductæ axem
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in O, P ſecant. </
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G P: </
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xml:space
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pondus reliquum quod H ſuſtinet: </
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demonſtratio ex conſectario 17 propoſit.
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</
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fuſius de neceſſaria hujus veritateagatur, ſi
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Hloco O eſſe fingamus, ratio põderis pun-
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cto H ſuſtentati ad pondus P ſuſtentatum
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erit, quæ eſt G P ad G O, per 17 propoſit.
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</
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deſcĕdere ponamus intervallo ab H uſque
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in O, pondus H puncto ſuſtentatũ per 3 po-
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ſtulatum, idem manèt. </
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quod in puncto P quieſcit, etiam puncto I
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quieſcere oſtĕdetur, ut igitur G O ad G P: </
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ita põdus quod I ſuſtinet ad pondus quod
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ſuſtinetur in H. </
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<
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punctis, &</
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