Schott, Gaspar
,
Mechanica hydraulico-pneumatica. Pars I. Mechanicae Hydraulico-pnevmaticae Theoriam continet.
,
1657
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Propoſitio XIV. Theorema VI.
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Tubi non ſemper pleni æquè alti, & æqualium. forami
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num, ſed inæqualium baſium, evacuantur inæqualibus
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temporibus;
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eadem ratio temporum,
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quæ baſium.
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>PRimum patet per ſe, quia cæteris omnibus paribus major a
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quæ quantitas maius requirit tempus ad effluendum, quàm
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minor. </
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>Alterum demonſtratur, vel potiùs explicatur ſic. </
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Proportio
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temporum
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eadem quæ
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baſium
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borum</
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, quo
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ad aquæ flu
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xum.
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>Eſto tubus AB minoris baſis, & alius ACBD
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majoris, uterque cylindricus, uterque æquè altus, &
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æqualis foraminis B; ſitque diameter baſis BD tripla
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diametri baſis B: eritigitur area baſis BD noncupla
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areæ baſis B, quoniam circuli inter ſe ſunt, ut qua
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drata diametrorum, per Propoſit. 2. lib. 12. Element.
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Euclidis; quadratum
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diametri BD triplo maio
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ris diametro B, eſt nonies maius, quàm quadratum
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diametri B, ut ex Geometria practica patet. </
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igitur cylindri æquè alti ſint inter ſe, ut
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baſes, ut
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patet ex
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Geomet. practica; ſequitur, aquam tubi
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ACBD eſſe noncuplam aquæ tubi AB; ac proinde
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tempus quo exhauritur per foramen B tubus ACDB,
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noncuplum erit temporis, quo exhauritur per idem
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foramen B, tubus AB,
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cylindrus aqueus ACBD,
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non magis premit ſupra
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B, quàm cylindrulus aqueus AB,
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per dicta Propoſit. II. in Corollario, & Propoſit. VII. Annot. 2. </
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Annotatio I.
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MErſennus in Hydraulicis Phænomenis Propoſit.
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8.
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ait, conſtare ex
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obſervatione, tubum quadrupedalem, cuius baſis digitalis, uno mi
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nuto temporis totum per lineare lumen exhauriri; tubum verò quadru
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pedalem cuius baſis pedalis, ſpatio
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144.
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minutorum, ſeu duabus horis, &
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24.
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minutis. </
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>Servatur ergò inter temporaratio baſium, vt demonſtra
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vimus: Nam cùm pedis longitudo contineat, ex Merſenni mente, ut
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vidimus Propoſit. VII. huius Capitis Annot. I. digiti latitudinem
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