Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER VI.
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321
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0467-01
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xlink:href
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<
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<
s
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xml:space
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">Sit ſpiralis ex prima reuolutione@@o, OP℟QX, primus circu-
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lus, ΩkXF, cuius, radius, & </
s
>
<
s
xml:id
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echoid-s11501
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xml:space
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preserve
">voluta ſit, OX, ſpiralis, ℟Q, minor
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ea, quæ ſub prima reuolutione fit, nec habet terminum initium
<
lb
/>
ſpiralis, iunctis autem, OA, OQ, & </
s
>
<
s
xml:id
="
echoid-s11502
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xml:space
="
preserve
">ijs vſque ad circumferentiam,
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lb
/>
FΩΚΧ, productis, cui incidant in, Ω, F. </
s
>
<
s
xml:id
="
echoid-s11503
"
xml:space
="
preserve
">Dico trilineum, ℟OQ,
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lb
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ad ſectorem, AOQ eſſe vt rectangulum, AO℟, cum {1/3}. </
s
>
<
s
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echoid-s11504
"
xml:space
="
preserve
">quadrati,
<
lb
/>
A℟, ad quadratum, AO. </
s
>
<
s
xml:id
="
echoid-s11505
"
xml:space
="
preserve
">Exponatur parallelogrammum rectan-
<
lb
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gulum, ED, cuius latus, CD, ſit æqualeipſi, OX, &</
s
>
<
s
xml:id
="
echoid-s11506
"
xml:space
="
preserve
">, BD, circum-
<
lb
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ferentiæ, FΩΚΧ, & </
s
>
<
s
xml:id
="
echoid-s11507
"
xml:space
="
preserve
">ſit iuncta, BC, &</
s
>
<
s
xml:id
="
echoid-s11508
"
xml:space
="
preserve
">, CT, ſit æqualis circumferẽ-
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lb
/>
tiæ, XkΩ, TM, circumferentiæ, ΩF, &</
s
>
<
s
xml:id
="
echoid-s11509
"
xml:space
="
preserve
">, ME, circumferentiæ, FX,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s11510
"
xml:space
="
preserve
">per puncta, M, T, ducanturipſi, CD, parallelæ, MH, TN,
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lb
/>
quarum, MH, ſecet, BC, in, I, & </
s
>
<
s
xml:id
="
echoid-s11511
"
xml:space
="
preserve
">per, I, ipſi, EC, parallela duca-
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tur, IG, erit ergo, MC, æqualis circumferentiæ, XkΩF, & </
s
>
<
s
xml:id
="
echoid-s11512
"
xml:space
="
preserve
">quia
<
lb
/>
circumferentia, ΧFΩκ, ad circumferentiã, FΩkX, eſt vt, XO, ad,
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<
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xml:space
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preserve
">7. huius.
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4. Sexti
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Elem.</
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OQ, ideſt, EC, ad, CM, eſt vt, XO, ad, OQ, eſt autem, EC, ad,
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lb
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CM, vt, EB, ad, MI, ergo, EB, ad, MI, erit vt, XO, ad, OQ, ſunt
<
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autem ipſæ, XO, EB, æquales, ergo etiam æquales eruntiplæ, </
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