Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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GEOMETRIÆ
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">SI à circulo, vel ellipſi per lineam ad eorum axim, vel dia-
<
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metrum ordinatim applicatam vtcunque portio abſcin-
<
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datur, ſit autem parallelogrammum in eadem altitudine cum
<
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dicta portione, ſed in baſi æquali ſecundę diametro, & </
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<
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xml:space
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baſis ipſius portionis: </
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<
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xml:space
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">Omnia quadrata dicti parallelogram-
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miad omnia quadrata dictę pottionis erunt, vt rectangulum
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ſub dimidia eiuſdem axis, vel diametri, & </
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<
s
xml:id
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xml:space
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">ſub eiuſdem dimi-
<
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diæ tripla, ad rectangulum ſub axi, vel diametro abſciſſæ
<
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portionis, & </
s
>
<
s
xml:id
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xml:space
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">ſub compoſita ex axe, vel diametro reliquę por-
<
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tionis, & </
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<
s
xml:id
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echoid-s4919
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xml:space
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">dimidia totius axis, vel diametri.</
s
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<
s
xml:id
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xml:space
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</
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<
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<
s
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xml:space
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">Sit igitur circulus, vel ellipſis, BVOR, eius axis, vel diameter,
<
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BO, ordinatim ad ipſum applicata, VR, vtcumq; </
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>
<
s
xml:id
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echoid-s4922
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xml:space
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preserve
">abſcindens por-
<
lb
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tionem, VBR, ſit verò ſecunda diameter, CF, & </
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>
<
s
xml:id
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echoid-s4923
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xml:space
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">producta, VR,
<
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ita vt, PN, ſit æqualis ipſi, CF, &</
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>
<
s
xml:id
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xml:space
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">, PM, ipſi, CA, in baſi, PN,
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& </
s
>
<
s
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xml:space
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">altitudine portionis, VBR, ſit parallelogrammum, DN, & </
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>
<
s
xml:id
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xml:space
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">cir-
<
lb
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ca axim, vel diametrum, BM. </
s
>
<
s
xml:id
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xml:space
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">Dico ergo omnia quadrata paralle-
<
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logrammi, DN, regula, VR, ad omnia quadrata portionis, VBR,
<
lb
/>
eſſe vt rectangulum ſub, BA, & </
s
>
<
s
xml:id
="
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xml:space
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">tripla, AO, ad rectangulum ſub, B
<
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<
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xlink:label
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fig-0220-01
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fig-0220-01a
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number
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133
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0220-01
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xlink:href
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http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0220-01
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M, & </
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<
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<
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xml:space
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">iun
<
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gantur, VB, PB; </
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<
s
xml:id
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xml:space
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">Omńia ergo quadrata
<
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ſemiportionis, BCVM, ad omnia qua-
<
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drata trianguli, BVM, ſunt vt, AO, O
<
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M, ad, OM, .</
s
>
<
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xml:space
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">i. </
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<
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xml:space
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">ſumpta, BM, commu-
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<
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xlink:label
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xlink:href
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xml:space
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">Exant.</
note
>
ni altitudine, vt rectangulum ſub, BM,
<
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MOA, ad rectangulum, BMO, omnia
<
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<
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position
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left
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xlink:label
="
note-0220-02
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xlink:href
="
note-0220-02a
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xml:space
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">5. Lib.2.</
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autem quadrata trianguli, BVM, ad
<
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<
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xlink:label
="
note-0220-03
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xlink:href
="
note-0220-03a
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xml:space
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">PerB.Co.
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rollar.22.
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lib.2.</
note
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omnia quadrata trianguli, BPM, ſunt
<
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vt quadratum, VM, ad quadratum, P
<
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M, velad quadratum, CA, .</
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<
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xml:space
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">i. </
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<
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xml:space
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">vt rectan-
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xlink:label
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xlink:href
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note-0220-04a
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xml:space
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">Ex 40. l.1.
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& eiuſdẽ
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Scholio.</
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gulum, OMB, ad rectangulum, OAB, ergo ex æquali, & </
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<
s
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tendo omnia quadrata trianguli, BPM, ad omnia quadrata ſemi-
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portionis, BVM, erunt vt rectangulum, BAO, ad rectangulum
<
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<
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xlink:label
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note-0220-05a
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">24. Lib. 2.</
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ſub, BM, &</
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<
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<
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">antecedentium tripla.</
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<
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">ſ. </
s
>
<
s
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">omnia quadrata
<
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parallelogrammi, DM, ad omnia quadrata ſemiportionis, BVM,
<
lb
/>
<
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left
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xlink:label
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note-0220-06
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xlink:href
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note-0220-06a
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xml:space
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">8. Lib.2.</
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vel omnia quadrata parallelogrammi, DN, ad omnia quadrata
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portionis, VBR, erunt vt rectangulum ſub, BA, & </
s
>
<
s
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