Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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punctis, P, O, occurrentes, ductis autem duobus planis quomodo-
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cumque baſibus parallelis, & </
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<
s
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xml:space
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">ſecantibus altitudines, FC, PO, ſimi-
<
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liter ad eandem partem in punctis, Λ Γ, eadem ſecent latera homo-
<
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loga ex. </
s
>
<
s
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echoid-s1616
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xml:space
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">gr. </
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<
s
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xml:space
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">IH, QS, in punctis, Π Z. </
s
>
<
s
xml:id
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echoid-s1618
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xml:space
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">Dico in eiſdem ſecari ſimi-
<
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liter ad eandem partem. </
s
>
<
s
xml:id
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echoid-s1619
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xml:space
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">Producantur ergo, HI, SQ, hinc inde,
<
lb
/>
ita vt (niſi hocipſis contingat abſque eo, quod producantur) ad pla-
<
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na baſium, DAB, KMN, & </
s
>
<
s
xml:id
="
echoid-s1620
"
xml:space
="
preserve
">eiſdem æquidiſtantia plana per ver-
<
lb
/>
tices, F, P, ducta, terminentur, vt in punctis, L, T, G, R, à pun-
<
lb
/>
ctis verò, G, R, demittantur ad plana dictarum baſium perpendicu-
<
lb
/>
lares, GE, RX, illis incidentes in, E, X, & </
s
>
<
s
xml:id
="
echoid-s1621
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xml:space
="
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">iungantur, L, E, TX.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1622
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xml:space
="
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">Sìmiliter à verticibus, F, P, ad puncta baſium, B, N, ducantur, F
<
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B, PN, & </
s
>
<
s
xml:id
="
echoid-s1623
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xml:space
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">iungantur, BC, NO. </
s
>
<
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echoid-s1624
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xml:space
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">Quoniam ergo latera homolo-
<
lb
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ga, HI, SQ, continent cumhomologis lateribus ſimilium trian-
<
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gulorum, AID, MQK, ad eandem partem baſibus, DAB, KM
<
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N, inclinatorum (quia, IADB, QMNK, eſſent ſimiles pyrami-
<
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des) angulos ęquales, & </
s
>
<
s
xml:id
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echoid-s1625
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xml:space
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">producta incidunt in plana dictarum baſium
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xlink:label
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xlink:href
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xml:space
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">Ex Lem.
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5.</
note
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in, L, T, erunt eiſdem æqualiter inclinata, ergo anguli, GLE, R
<
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number
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43
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0082-01
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figure
>
TX, erunt ęquales,
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&</
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>
<
s
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xml:space
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">, GEL, RXT,
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ſunt recti, ergo triã-
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gula, GLE, RT
<
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X, ſimilia erunt, er-
<
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go, GL, ad, RT,
<
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erit vt, GE, ad, R
<
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X, ideſt vt, FC, ad
<
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PO. </
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>
<
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xml:space
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">Vlterius ſi iun-
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geremus, FA, FD,
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PM, PK, fierent
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ſimiles pyramides,
<
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FDAB, PKMN, vnde pateret, FB, PN, eſſe ad plana baſium,
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<
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position
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xlink:label
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note-0082-02
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xlink:href
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xml:space
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">Ex Lem.
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4.</
note
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DAB, KMN, ſimiliter inclinata, & </
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<
s
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echoid-s1628
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xml:space
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">ſubinde angulos, FBC, P
<
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NO, eſſe ęquales, & </
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>
<
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xml:space
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">cum ſint recti, FCB, PNO, triangula, FB
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C, PNO, eſſe æquiangula, & </
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>
<
s
xml:id
="
echoid-s1630
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xml:space
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">vt, FC, ad, PO, ita eſſe, FB, ad,
<
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PN, etiam manifeſtum eſſet, ſed vt, FC, ad, PO, ita eſt, GL, ad,
<
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/>
RT, & </
s
>
<
s
xml:id
="
echoid-s1631
"
xml:space
="
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">vt, FB, ad, PN, ita, BD, ad, NK, & </
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>
<
s
xml:id
="
echoid-s1632
"
xml:space
="
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">ita quodcunque
<
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latus in ſolido, FHB, ad latus ſibi homologum in ſolido, PSN,
<
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ideſt ita, IH, ad, QS, ergo vt, GL, ad, RT, ita, HI, ad, SQ,
<
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<
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position
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xlink:label
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xlink:href
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xml:space
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">19. Quin.
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Elem.</
note
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& </
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<
s
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echoid-s1633
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">ita compoſitum ex reſiduis, LH, IG, ad compoſitum ex reſiduis,
<
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TS, QR, ſunt autem, LH, TS, latera homologa ſimilium pyra-
<
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<
note
position
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xlink:label
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note-0082-04
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xlink:href
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note-0082-04a
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xml:space
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">Ex Lem.
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5.</
note
>
midum, HLAD, STMK, ergo vt, HA, ad, SM, velvt, HI,
<
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ad, SQ, ita, HL, ad, ST, ergo etiam reliqua, IG, ad reliquam,
<
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QR, eſt vt, HI, ad, SQ, vel vt altitudo, FC, ad, PO, vel vt, </
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