Ceva, Giovanni
,
Geometria motus
,
1692
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MO curretur iuxta imaginem BHIF, nempe compoſito
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motu, & tempore AG. </
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Tab.
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4.
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Fig.
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2.</
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Def.
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3
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prima.
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Pr.
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2.
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primą
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huius.
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">2. Se nunc ſecent lineæ BF, HI in C. </
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rallela alteri æquidiſtantium AB, GF. </
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parte, quòd mobile compoſito motu, & iuxta imaginem
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HBC feretur verſus O tempore AD; ſit ergo ſpatium, quod
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curreretur illa imagine, PR, & ob id LO ad PR eandem̨
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habebit rationem quam imago ABFG ad imaginem̨
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HBC. </
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Tab.
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4.
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fig.
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3.</
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Pr.
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2.
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prima
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">Similiter dum mobile mouetur tempore DG iuxta ima
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gines DCIG, DCFG, feretur verè ſecundùm imaginem̨
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FCI verſus L, quamobrem ſi ſpatium, quod exigeretur
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hac imagine ſit RQ, habebit iſtud ad LO eandem rationem,
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quam imago CFI ad imaginem ABFG, & ideo ex æquali
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QR ad PR ſe habebit vt imago CFI ad imaginem HBC; ſi
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igitur ponatur ABFG maior imagine AHIG, demptà co
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muniter AHCFG relinquetur HBC maior imagine CEI, &
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ideo etiam PR maior QR: curritur verò PR versùs R tem
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pore AD, & RQ versùs P tempore DG, ergo toto tempo
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re AG curretur PQ differentia ſpatiorum PR, RQ Cum
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verò HBC ad CFI, ſit vt PR ad RQ, erit diuidendo vt ex
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ceſſus imaginis HBC ſupra imaginem FCI ad imaginem̨
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iſtam, ita PQ ad QR, & oſtenſum eſt QR ad LO, ſicut ima
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go FCI ad imaginem ABFG, ergo ex æquali exceſſus ima
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ginis HBC ſupra imaginem AHIG habebit eandem ratio
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nem ad imaginem AHIG, ac PQ ad LO, at eſt in illa
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ratione etiam LM ad LO (eſt enim LO ad MO vt imago
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ABFG ad imaginem AHIG) ergo PQ erit æqualis LM,
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atque adeo mobile dum currit vtroque motu, hoc eſt iux
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ta ſimul duas imagines propoſitas contrariorum motuum,
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peraget ſpatium LM versùs O ſecundùm imaginem, quæ
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differentia eſt propoſitarum ABFG, AHIG, tempore AG.
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<
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