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

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1vellet aſſumere triangulum rectangulum ad
B, vt notam faceret
25[Figure 25]
diſtantiam inter B &
D, ſibique perſuaderet
aut à baſi aut ab hy­
pothenusâ illius trian­
guli exhiberi diſtan­
tiam BD, longè di­
ſtaret à veritate. Du­
cta ſiquidem perpen­
dicularis BH longè
minor eſt arcu BD, cum ſit Tangens ſe­
miſsis illius arcûs: hypothenuſa verò AH
minor eſt quàm tota Tangens AD, de­
fectu æquali ipſi baſi BH; ſunt enim HB,
HD æquales, cùm vtraque ſit circulum
tangens ab eodem puncto H ducta. Qua­
propter deberet aggregatum ex baſi BH
& hypothenusâ AH accipere, vt totam
AD haberet, quæ non multùm differt ab ar­
cu BD, niſi altitudo BA fuerit mons aut ſco­
pulus.
Quod ſi tuus ille terrenæ magnitudinis

inueſtigator lineam BD pro maximâ vi­
sûs diſtantiâ aſſumpſiſſet, illa vtique media
eſt proportionalis, ex cuius quadrato per no­
tam altitudinem DA diuiſo prouenit tertius

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