Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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<
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xml:space
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">A puncto intra ſphæram dato, ad eius concauam ſuperficiem,
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_MAXIMAM, & </
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<
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xml:space
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</
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<
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<
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xml:space
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">ESto ſphæra, cuius centrum A, & </
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<
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xml:space
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ctum B ad concauam ſphæræ ſuperficiem _MAXIMAM_, & </
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<
s
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xml:space
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rectam lineam ducere.</
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<
s
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xml:space
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">Si punctum B fuerit in centro ſphæræ, patet tunc neque _MAXIMAM,_
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neque _MINIMAM_ dari, cum omnes eductæ à centro ad ſphærę ſuperficiem
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ſint æquales.</
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<
s
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trum: </
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<
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xml:space
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">iungatur cum centro A recta B A, quæ
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hinc inde producta occurrat ſphęricæ ſuperficiei
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in punctis C, D. </
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eſſe _MAXIMAM_, reliquam B C _MINIMAM_.</
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<
s
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xml:space
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">Si enim circà axim C D intelligatur quicun-
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que _MAXIMVS_ ſphæræ circulus C D F: </
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<
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linearum ex B ad peripheriam C D F ducibi-
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lium, B D in qua centrum A, eſſe _MAXIMAM_,
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& </
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</
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<
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xml:space
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">Siverò ducta ſit quælibet alia B E extra peri-
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pheriam C D F, ſphæricæ ſuperficiei occurrens
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in E; </
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<
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<
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num, cuius communis ſectio cum ſphæræ ſuperficie erit cuiuſdam _MAXIMI_
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circuli peripheria C E D, & </
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<
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xml:space
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<
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xml:space
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">quare B D, in qua eſt
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centrum, cum ſit _MAXIMA_, erit maior B E; </
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<
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xml:space
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">& </
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">B C, cum ſit _MINIMA_
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minor erit eadem B E, & </
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<
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que B D eſt _MAXIMA_ ad vniuerſam ſphæræ ſuperficiem ducibilium ex da-
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to puncto B, & </
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<
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</
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<
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<
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xml:space
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">A puncto intra Conum rectum, vel Conoides Parabolicum,
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aut Hyperbolicum dato, ad eius concauam ſuperficiem, MI-
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NIMAM rectam lineam ducere.</
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</
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">vt in prima ſigura, vel Conoides Parabolicum, aut
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Hyperbolicum, vt in ſecunda, cuius axis A B, & </
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">oporteat per punctum
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intra ipſum datum ad concauam ſolidi ſuperficiem _MINIMAM_ rectam li-
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neam ducere.</
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ment. Có-
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mand. in
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12. Arch.
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de Co.
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noid. &
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Spheroid,</
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<
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">Secetur ſolidum plano per axem A B, ac per datum punctum ducto effi-
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ciente in ſolidi ſuperficie ſectionem D A E, quæ eadem erit, ac ipſius ſo- lidi genitrix ſectio, & </
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<
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<
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<
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