Casati, Paolo - Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae

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1hìc vſurpantur) 388800. Quare diameter
AE, demptis pedibus 50, erit ſtad. 388799
ped. 550. Ex qua diametro colligitur am
bitus longè maior eo, quem Macrobius cum
Eratoſthene conſtituit.

Guld. Sed lapſis in ageometriam Erato
ſthene ac Macrobio, quod ſtadia 180 tribue
rint horizontis phyſici ſemidiametro, cum
totum telluris ambitum ſtadijs 252000 de
ſinierint; quid de ijs dicendum, qui terram
paucioribus ſtadijs circumſcribentes (mil
liarijs nimirum 21600, quæ ad ſtadia Græca
180000 reuocantur, quot Ptolemæus toti
terrenæ peripheriæ conceſsit) oculum tamen
ad maiora ſpatia longo limite ducunt? Hi
ſanè longiſsimè abſunt à veritate, cum lineæ
opticæ tribuunt longitudinem ſtadiorum
vt minimum 500. Nam quadratum lineæ
opticæ eſt æquale rectangulo ſub altitudinę
oculi, & terræ diametro auctâ eâdem altitu
dine. Sit ergo D linea optica, & B ſit terræ
diameter, & A ſit altitudo: igitur DQ æqua
tur AQ+A in B. Quare ad inueniendam A
fiat expurgatio per vncias conditionarias qua
drati, ſc. per ſemiſſem coëfficientis B. Sit er
go E æqualis A+B 1/2: igitur E——B 1/2 eſt æqua
lis ipſi A. Factâ itaque prioris æquationis in
terpretatione erit æquatio inter EQ——BQ 1/4

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