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. </s>
              <s>Non igitur eſt vt VK ad HA ita
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              AG ad KN. </s>
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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. </s>
              <s>Si
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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. </s>
              <s>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
                <expan abbr="omniũ">omnium</expan>
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              maxima; ergo per 25.5. HG maior eſt quàm
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              VN, contra hypotheſim. </s>
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              <s>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. </s>
              <s>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</s>
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