Valerio, Luca
,
De centro gravitatis solidorum
,
1604
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LMN, ſimul centrum grauitatis. </
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<
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dum erat. </
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ALITER.
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<
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>Poſito enim R centro grauitatis duarum
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magnitudinũ
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G,
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H, & S
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duarũ
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L,M, vel punctum V cadit in puncto E, vel in
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linea EB, vel in linea AE, ſi in puncto E vel in linea EB,
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cum igitur T ſit
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centrũ
">centrum</
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grauitatis trium
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magnitudinũ
">magnitudinum</
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G,H,I
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ſimul, & E ipſius I, erit punctum T propinquius termino
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A quàm punctum V. </
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<
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>Sed punctum V in linea AE cadat.
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<
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>Veligitur S centrum grauitatis duarum magnitudinum L,
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M, ſimul cadit in puncto D, ſiue in linea DB, vel in li
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nea AD. ſi in puncto D, vel in linea DB; centrum gra
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uitatis R duarum magnitudinum GH erit termino A
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propinquius quàm ipſum S, & recta ER maior quàm ES,
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Sed cadat punctum S in linea AD. </
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>Quoniam igitur ma
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ior eſt proportio G ad H, quàm L ad M: & vt G ad H,
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ita eſt DR ad RG, & vt L ad M, ita PS ad SO, ma
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ior erit proportio DR ad RC, quàm PS ad SO; mul
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to ergo maior DR ad RC, quàm DS ad SO, & multo
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maior quàm DS ad SC, & componendo maior propor
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tio DC ad CR, quàm DC ad CS; erit igitur CR mi
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nor quàm CS, atque adeo RD maior DS, addita igitur
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ED communi, erit ER maior quàm ES. </
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<
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>Rurſus quia
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componendo, & ex æquali maior eſt proportio totius GH
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ad I quàm totius LM ad N, hoc eſt maior longitudinis
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ET ad TR, quàm QV ad VS, & multo maior quàm </
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