Casati, Paolo
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Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae
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hìc vſurpantur) 388800. Quare diameter
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AE, demptis pedibus 50, erit ſtad. </
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<
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>388799
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ped. 550. Ex qua diametro colligitur am
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bitus longè maior eo, quem Macrobius cum
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Eratoſthene conſtituit. </
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Guld.
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> Sed lapſis in ageometriam Erato
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ſthene ac Macrobio, quod ſtadia 180 tribue
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rint horizontis phyſici ſemidiametro, cum
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totum telluris ambitum ſtadijs 252000 de
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ſinierint; quid de ijs dicendum, qui terram
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paucioribus ſtadijs circumſcribentes (mil
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liarijs nimirum 21600, quæ ad ſtadia Græca
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180000 reuocantur, quot Ptolemæus toti
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terrenæ peripheriæ conceſsit) oculum tamen
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ad maiora ſpatia longo limite ducunt? </
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<
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ſanè longiſsimè abſunt à veritate, cum lineæ
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opticæ tribuunt longitudinem ſtadiorum
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vt minimum 500. Nam quadratum lineæ
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opticæ eſt æquale rectangulo ſub altitudinę
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oculi, & terræ diametro auctâ eâdem altitu
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dine. </
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<
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>Sit ergo D linea optica, & B ſit terræ
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diameter, & A ſit altitudo: igitur DQ æqua
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tur AQ+A in B. </
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<
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>Quare ad inueniendam A
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fiat expurgatio per vncias conditionarias qua
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drati, ſc. </
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<
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>per ſemiſſem coëfficientis B. </
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>Sit er
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go E æqualis A+B 1/2: igitur E——B 1/2 eſt æqua
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lis ipſi A. </
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<
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>Factâ itaque prioris æquationis in
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terpretatione erit æquatio inter EQ——BQ 1/4 </
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