Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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menſuram mihi co mpar arem, res, puto, iuxta vota ſucceſſit, vt
<
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perlegenti patebit. </
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<
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xml:space
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">Artificio autem tali v ſus ſum, quale ad pro-
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poſitas quæſtiones ab ſoluendas Algebratici adhibere ſolent; </
s
>
<
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xml:space
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">qui
<
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quidem numerorum radices, quamuis ineffabiles, ſurdas, ac igno-
<
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tas, nihilominus ſimul aggregantes, ſubtrahentes, multiplican-
<
lb
/>
tes, ac diuidentes, dummodo propoſitę rei exoptatam ſibi notitiã
<
lb
/>
enucleare valeant, ſua ſatis obyſſe munera ſibi perſuadent, Non
<
lb
/>
aliter ipſe ergo indiuiſibilium ſine linearum, liue planorum con-
<
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gerie (ijſdem vt in lib. </
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<
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s
>
<
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xml:space
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">explicatur aſſumptis) licet quoad eo-
<
lb
/>
rundem numerum innominabili, ſurda, ac ignota, quoad ma-
<
lb
/>
gnitudinem tamen conſpicuis limitibus clauſa, ad continuorum
<
lb
/>
inueſtigandam menſuram vſus ſum, vt legenti in proceſſu ope-
<
lb
/>
ris apparebit. </
s
>
<
s
xml:id
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echoid-s100
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xml:space
="
preserve
">Propoſitum mihi eſt autem ò Geometra in his ſe-
<
lb
/>
ptem libris quamplurium tam planarum, quam ſolidarum figu-
<
lb
/>
rarum dimenſionem adinuenire, quarum aliquæ etiam ab alijs,
<
lb
/>
ac præcipuè ab Euclide, & </
s
>
<
s
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xml:space
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">Archimede pertractatę fuerunt, reli-
<
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qua verò nemini, quod ſciam bucuſq; </
s
>
<
s
xml:id
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xml:space
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">attentatæ; </
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>
<
s
xml:id
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xml:space
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">vno tamem ex-
<
lb
/>
cepto Keplero, quioccaſionę Dolij Auſtriaci per virgam menſo-
<
lb
/>
riam dimetiendi, poſtquam in ſua Stereometria Archimedea
<
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xml:space
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">_Kepleri_
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_Storcome_
<
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_tria Dolio_
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_rum._</
note
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ſummariè ipſius Archimedis adinuenta ſibi opportuna recenſuit,
<
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nouis aliquando, qualeſcumq; </
s
>
<
s
xml:id
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xml:space
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">ſint, adiectis rationibus, tandem
<
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/>
cam partem ſuperaddidit, quam Stereometria Archimedeæ ſup-
<
lb
/>
plementum nuncupauit, in qua multiplicem Sectionum conica-
<
lb
/>
rum, Circuli nempè, Parabolæ, Hyperbolæ, & </
s
>
<
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xml:id
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xml:space
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">Ellipſis, necnon ea-
<
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rundem portionum circa diu erſos axes reuolutionem contempla-
<
lb
/>
tus, ſolida numero octuaginta ſeptem, præter quinque Archime-
<
lb
/>
dea, Sphæram ſcilicet, Conoides parabolicum, Conoides hyperbo-
<
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licum, Sphæroides oblongum, & </
s
>
<
s
xml:id
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xml:space
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">prolatum Geometris perquam
<
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eleganti præconio promulgauit. </
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<
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xml:space
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">Cum ergo iam expoſitam me-
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tiendarum figurarum nouam, ac, ſi dicere fas ſit, valde compen-
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dioſam methodum adinueniſſem, fæliciter mecum actum eſſe exi-
<
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/>
ſtimaui, vt hæc ſolida, præter illa Archimedea, mihi ſuppedita-
<
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rentur, circa quæ illius vim ac energiam, experiri liceret. </
s
>
<
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xml:space
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">Ne
<
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quis tamen putet me omnium dictorum ſolidorum dimenſionem
<
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fuiſſe conſequutum, ſicuti neq; </
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>
<
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xml:space
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">Keplero contingere potuit, niſi
<
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paucorum, nec ſatis fęliciter, vt prædictam Stereometriam, </
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>
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