Borelli, Giovanni Alfonso
,
De motionibus naturalibus a gravitate pendentibus
,
1670
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punctum I eſſe centrum grauitatis communis ponde
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rum A, & B (cum funes nullius ponderis
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ſupponãtur
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)
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deinde reuoluta trochlea
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aſcẽdat
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pondus B ad L, &
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oppoſitum pondus A deſcendat vſque ad K
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coniũga-turque
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turque</
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recta KL ſecans rectam AB
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in G. dico duo pondera A, & B iņ
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communi eorum centro grauitatis
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I circa libræ centrum ſtabile G mo
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tu directo, & perpendiculari ad
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horizontem
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deſcẽdere
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. </
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<
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chleæ reuolutione
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tãtumdẽ
">tantumdem</
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<
expan
abbr
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deſcẽ-dit
">deſcen
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dit</
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terminus funis A quanta eſt ex
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plicatio funis è rota CDE, & pon
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dus B aſcendit quantum funis BQS
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circumuoluitur circa rotam QSR
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cùmque duæ rotæ concentricè con
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nexæ ſimul tempore
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abbr
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reuoluãtur
">reuoluantur</
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cir
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ca fixum axim F, ergo deſcenſus AK
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ad
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aſcẽſum
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BL eamdem proportio
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nem habet, quam peripheria CDE ad peripheriam R
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SQ, ſeu
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eamdẽ
">eamdem</
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proportionem, quam habet radius
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FE ad radium
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Fq;
">Fque</
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quare in triangulis AGK, & BGL
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ſimilibus, ob æquidiſtantiam laterum AK, & BL, erit
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AG ad GB vt KG ad GL, ſeu vt AK ad BL;
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proindeq;
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in eodem puncto fixo G duæ libræ AB, & KL ſe mutuò
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ſecabunt in eadem proportione, quam habent motus
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eorumdem terminorum, vnde, ex mechanicis, erit
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punctum G centrum, & fulcimentum firmum̨
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vtriuſque libræ AB, & KL poſtremò ducatur per I </
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