Fabri, Honoré
,
Dialogi physici in quibus de motu terrae disputatur
,
1665
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minore longitudinis, per quam quadrupla quantitas eodem tempore ef
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fluat, ad iſtud problema præparatorium res reducitur; dato Quadrato, cui
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ſubtractum ſit ſubquadruplum, id eſt Quadrato ſemilateris, invenire Qua
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dratum cui ſubtracto rectangulo, ſub eius latere, & quarta parte laceris
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prioris, reſiduum ſit quadruplum, primi reſidui, ſen triplum primi Qua
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drati. </
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id
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">Supponamus CB eſſe latus, ſeu Diame
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trum baſis minoris fiſtulæ, & LA eſſe Quadra
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tum quæſitum, ita vt ſubtracto HE ſub latere LH,
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& LE æquali MB, quæ eſt ſub quadrupla BA,
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reſiduum EA ſit triplum Quadrati CA: ſit au
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tem latus Quadrati 12 KN, quod mihi notum
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eſt, hoc enim eſt triplum Quadrati CA; ſit etiam
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KR, æqualis MB, mihi notæ, eſt enim ſubqua
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drupla BA; his præmiſſis, ſic formo problema
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decretorium: Data media proportionali, ſcilicet
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KN, & differentia extremarum, ſcilicet KR, invenire
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extremas; dividatur RK bifariam in S & ſub radio SN
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deſcribatur ſemicirculus ONB, erunt KO, KP, extre
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mæ quæſitæ, vt patet; igitur KO eſt latus quæſitum,
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æquale ſcilicet LH. </
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<
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">Pari modo procedam ſi velim ha
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bere fiſtulam ejuſdem longitudinis, ex qua eodem tem
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pore tripla, vel dupla quantitas effluat. </
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Auguſtin.
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<
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"> Non paucæ mihi ſuboriuntur difficultates circa hæc, quæ à
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te dicta ſunt; primò enim, ſi longitudo fiſtulæ GH
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tale impedimentum affert, vt vnam quartam
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partem motus auferat; igitur dupla longitudo
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GI, duplum auferet; igitur quadrupla totum
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motum; nihil aquæ igitur ex illa efflueret, quod
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abſurdum eſt. </
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Antim.
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<
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id
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"> Siſte quæſo, neque enim huc Hydrau
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lica traducenda eſt, cùm ſit res longioris operæ;
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dicam igitur breviter, motum retardari poſſe in
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infinitum, vt nemo. neſcit; vnde ſi longitudo fi
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ſtulæ GH. Subtrahit
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. </
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<
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id
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"> velocitatis, longitudo
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GI ſubtrahet 1/4. & dupla GI
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& dupla ejus
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totam; ſed huc vſque ſupponitur fiſtula ſemper
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plena, eaque in ſitu horizontali ; vbi autem
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aqua ea tarditate, movetur, vt pars aquæ ſuprema proprio pondere quaſi
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per planum inclinatum ire poſſit, deſcendit haud dubiè, & tunc ſuperior
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fiſtulæ cavitas, vacua reſtat: ſed quæſo te ad rem noſtram redeamus, cùm
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hæc hujus inſtituti non ſint. </
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Auguſtin.
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<
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"> Inde tantùm colligo, quantum detrimentum ij patiantur in
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diſtributione aquarum, qui parvas fiſtulas habent, & quantum viciſſim
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commodi ij, qui magnas habent; nempe illi, cui aquæ vncia competit, da
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tur fiſtula, cujus baſis Diameter v. g. vncia eſt; alteri verò cui competunt </
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