Casati, Paolo
,
Terra machinis mota : dissertationes geometricae, mechanicae physicae hydrostaticae
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miſſi; igitur ſi baſibus æqualibus addantur
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ipſæ æquales ſuperficies ſolidi, erunt ſuperfi
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cies vaſorum æquales: id quod eſt contra hy
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potheſim. </
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<
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>Non igitur eſt vt VK ad HA ita
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AG ad KN. </
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S
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it enim iterum, ſi fieri poteſt, VK ad
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HA, vt AG ad KN: VK prima vel eſt maior
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quàm AG tertia, vel minor, vel æqualis. </
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<
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maior, ergo per 14. 5. etiam HA ſecundą
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maior eſt quàm KN quarta; eſt autem VK
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ex dictis etiam maior quàm HA; igitur VK
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eſt maxima & KN minima; igitur per 25. 5.
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VK ſimul cum KN maior eſt quàm HA &
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AG ſimul, quod eſt contra hypotheſim, iux
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ta quam VN & HG æquales ſunt. </
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<
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>Si VK mi
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nor eſt quàm AG, etiam HA minor eſt quàm
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KN; ſed HA minor eſt quàm VK ex dictis;
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ergo HA eſt omnium minima & AG
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maxima; ergo per 25.5. HG maior eſt quàm
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VN, contra hypotheſim. </
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<
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>At verò ſi demùm VK prima æqualis ſit
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AG tertiæ, etiam HA ſecunda æqualis eſt
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KN quartæ: ergo per 7.5. vt VK ad KN ita
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GA ad AH. </
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<
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>At ex demonſtratis vt VK ad KN,
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ita ſuperficies vaſis maioris minùs ſuperficie
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ſolidi ad ſuperficiem ſolidi VY, & vt GA ad
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AH, ita ſuperficies ſolidi HT, hoc eſt VY,
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ad ſuperficiem vaſis minoris minùs ſuperfi</
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