Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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nobis deſumptum eſt, vt inſpicienti manifeſtum erit. </
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<
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lector nos præter dicta ſolida alia pariter quamplurima, quæ non
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ſunt exgrege ſuperius enumeratorum, etiam contemplari. </
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<
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">Præ
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cæteris autem maximam buiuſce demonſtrandi methodi vniuer-
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ſalitatem non reticebo, quod enim alij de vna, vel ſaltem paucis
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ſolidorum ſpeciebus, nos de infinitis continuò demonctramus, ne-
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xml:space
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_Elem._</
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dum enim hic ex. </
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<
s
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xml:space
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xml:space
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_Duod. Elẽ._</
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pyramidis, in eadem baſi, & </
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">altitudine cum eo exiſtentis, triplũ
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xml:space
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">_Def. 3._
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_l.1._</
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eſſe, ſed quacumq, in baſi variatione facta, quæ nullo aſſignato
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numero coarctatur, ſolidum eidem inſiſtens, quod cylindricum
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<
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xml:space
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">_Sect. 9._
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_Cor. 4. 34._
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_l.2._</
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vocumus, eſſe triplum eius, quod in eadem baſi, & </
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cum eo conſtitutum, conicum appellamus; </
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<
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">_Def. 4.l.1._</
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lidorũ ſpecies numero indefinitas eſſe manifeſtò apparet: </
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">Ex hoc
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autẽ vnico exemplo, tamquam ex vngue Leonem, dignoſcet ſtu-
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dioſus, quanto Geometricus ager per hac fertilior, & </
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<
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">amplior fiat,
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hanc vniuer ſalitatem namq; </
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<
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">circa omnia penè ſolida à nobis hic
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conſiderata iugiter proſequemur. </
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Libro, vt plurimum lemmata proponuntur, quæ ad ſequentium
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librorum doctrinam capiendam neceſſaria videntur, licet in eiſ-
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dem plurima quoque ſint ſuigratia ſimpliciter demonſtrata: </
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3.</
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">& </
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">Libro ſolida e xaminantur, quæ ex conicis ſectionibus
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ſuamgeneſim agnoſcunt. </
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">In 6. </
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<
s
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">agitur de ſpatijs helicis, hac ſo-
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lidis ab eiſdem genitis, problemataq; </
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<
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">circa predemonſtrata con-
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ſtruuntur. </
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<
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">Lib noſtram infinitatis indiuiſibi-
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lium Oceanum emenſamratem, alia inſtituta methodo, in portũ
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deducimus, vt in illius infinitatis ſcopulis periclitandi omnis tã-
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dem tollatur ambiguitas. </
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<
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">Scio tamen hæc prima fronte leuiter
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perpendentibus, quippe quæ per iamdiù tritam Geometriæ ſemi-
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tam haud fuerint inquiſita, minus eſſe probanda; </
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<
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tis ſtomaci tumentes flatus initio ſupprimentes ad extremam hui-
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us doctrinæ metam peruenire haud dedignabuntur, forte ſuper
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hæc minimè amplius nauſeabunt; </
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thodum prius damnare velit, quam hæc omnia puro mentis ocu-
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lo, ſinceroq; </
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<
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">illius affectu fuerit perluſtratus, hic enim talir atio-
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ne de monſtrata cum aliorum inuentis ad vnguem concordare iu-
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giter animaduertet. </
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