Ceva, Giovanni
,
Geometria motus
,
1692
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022/01/022.jpg
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geneſes GHKL, YZ 43. & ſit pariter HI ad IK, vt ſegmen
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tum ABFE ad EFCD. </
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<
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">Sit ſimiliter Z
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ad
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4 vt ſeg
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mentum NPQV ad VQRT, ductiſque applicatis IM, QV,
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manifeſtum eſt, vt velocitas AB æqualis eſt velocitati GH,
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ſic EF æqualem fore ipſi IM; nam quia ſpatium
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tranſactũ
">tranſactum</
expan
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iuxta imaginem ABFE ad ſpatium tranſactum imagine
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EFCD eſt vt illa ad hanc imaginem, nempe vt HI ad IK,
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erit mobile inſtanti F in puncto I, & ideo inibi erit veloci
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tas eadem, quam habet mobile inſtanti F, ſcilicet æquales
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erunt EF, IM. </
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<
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">Eodem modo erunt æquales QV,
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2, &
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ſunt etiam æquales NP, YZ, ergo ſicut ſe habet AB ad EF,
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ita erit GH ad MI, & vt eſt NP ad
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Vq.
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ita erit YZ ad 2
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Præterea concipiatur figura OPRSXO ſimilis ipſi ABCD,
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ſcilicet ſit CB ad PR vt AB ad OP, vel (cum ſint BF ad
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FC ita PQ ad QR, vt EF ad homologam XQ, erit ſeg
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mentum ABFE ad ſibi ſimile ſegmentum OPQX in dupli
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cata ratione laterum homologorum EF ad XQ, & item in
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<
expan
abbr
="
eadẽ
">eadem</
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>
duplicata ratione erunt interſe ſimilia
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expan
abbr
="
ſegmẽta
">ſegmenta</
expan
>
EFCD
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ad XQRS, ſed cum etiam OPQX ſegmentum ad NPQV,
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& XQRS ad ſegmentum VQRT ſint in eadem ratione
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eiuſdem QX ad QV, erit ex æquali ſegmentum ABFE ad
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ſegmentum NPQV, vt ſegmentum EFCD ad VQRT, &
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permutando, ſegmentum ABFE ad ſegmentum EFCD ha
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bebit eandem rationem, ac ſegmentum NPQV ad VQRT
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ſcilicet erit HI ad IK vt Z
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ad
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4, ob idque conſtat ge
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neſium applicatas vnius proportionales eſſe applicatis al
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terius, quare ſimiles motus erunt, qui fiunt iuxta imagines
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velocitatum propoſitas. </
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Pr.
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2.
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huius.
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PROP. VIII. THEOR. VIII.
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<
s
id
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">SPatia, quæ curruntur ſimilibus motibus ſunt in ratione
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compoſita temporum, & homologarum velocitatum,
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inter quas ſunt extremæ, aut primæ. </
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