Ceva, Giovanni
,
Geometria motus
,
1692
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ſiue tempora erunt in duplicata ratione temporum iſto
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rum, vel illorum motuum. </
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">Amplitudines imaginum ſimplicium, velocitatumque
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BAC, KFG ſunto BC, KG, quæ æquales ſint. </
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tia acceleratorum motuum ab illis ſimplicibus imaginibus
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fore in duplicata ratione temporum AC ad FG (quę ſem
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per in acceleratis ponuntur eadem, ac in ſimplicibus, nec
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aliter eſſe poſſunt.) Vt FG ad GK, ita ſit AC ad CL, &
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intelligatur LAC imago alterius motus ſimilis motui, cuius
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imago BAC, vel KFG. </
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">Facilè demonſtrabitur ipſam fi
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guram LAC ſimilem eſſe ipſi KFG, & ad BAC eandem̨
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habere rationem, quam LC ad BC. </
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ad imaginem KFG componatur ex ratione imaginis BAC
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ad LAC (quæ ſunt vt BC ad CL) & ex ratione imagi
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nis ALC ad imaginem KFG, quæ ſunt in ratione compo
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ſita LC ad KG, et AC ad FG: priores verò duæ rationes
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componunt vnicam æqualitatis, ergo relinquitur, imagi
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nem BAC ad imaginem KFG eſſe vt AC ad FG; ſpatium
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verò accelerati motus ex ſimplici imagine BAC ad accele
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ratum ex ſimplici KFG nectitur ex ratione imaginum ſim
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plicium ipſarum, & ex ea diſtantiarum DE, HI à centris
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grauitatum deductarum D, H, et ſunt hæ rectæ in eadem
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ratione, ac altitudines AC, FG (nam in figuris, ſeu imagi
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nibus ſimilium motuum BAC, LAC centra grauitatum
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ſunt in eadem recta parallela ipſi BC, & in LAC, KFG
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ſunt in punctis ſimiliter poſitis, adeo ut, ſicut poſitum eſt,
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ratio ipſarum diſtantiarum in ipſis figuris LAC, KFG, ſeu
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BAC, KEG eadem ſit, ac laterum homologorum LC ad
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KG, vel AC ad FG) ergo ſpatium accelerati motus ex ſim
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plici imagine KFG, erit vt quadratum ex AC ad quadra
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tum ex FG, nempe in duplicata ratione temporum ſimpli
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cium motuum. </
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