Full text: Viviani, Vincenzio: De maximis et minimis, geometrica divinatio

ſe æquidiſtant: vel tandem ad integram circuli peripheriam à contactibus I,
L in figurarum reuolutione deſcriptam in quinta, & ſexta vbi axes ſimul
congruunt.

298.1.

0257-01

Cum enim harum ſectionum axes, vel congruant ſimul, vel æquidiſtent,
quæ ad vnum ipſorum plana ducentur erecta, alteri quoque erecta erunt,
deſcribentque circulos in proprijs ſolidis, quorum centra in ipſ@s ax [...] s ca-
dent: vnde cum axes ſimul congruent, vt in prima, quinta, & ſexta, huiuſ-
modi circuli erunt concentrici; at ſi æquidiſtent, vt in reliquis, circuli erunt
eccentrici, & communes ſectiones horum planorum cum ipſis ſectionibus
A B C, D E F erunt eorundem circulorum diametri: quare ducto quocun-
que plano A D F C ad axes erecto, non per contactus I, vel L tranſeunte,
efficiente verò in ſectione A B C diametrum A C, in ſectione autem D E F
diametrum D F: patet in prima, ſecunda, quarta, quinta, & ſexta figura,
in quibus ſectio D E F inſcripta eſt ſectioni A B C diametrum D F totam
cadere intra diametrum A C, ac ideo circulum ex D F inſolido D E F
diſiunctum eſſe à circulo ex A C in ſolido A B C, vel per armillam A D
C, vt in prima, ſecunda, & ſexta, ob circulorum concentricitatem, vel
per armillam excentricam A D C, in ſecunda, & quarta ob ipſorum cir-
culorum excentricitatem. Rurſus in tertia figura in qua ſectio D E F to-
ta cadit extra A B C, prædicta diameter D F tota cadet extra diametrum
A C, ideoque circulus ex D F in ſolido D E F totus cadet extra circulum
ex A C in ſolido A B C, & hoc ſemper: quare in ſingulis figuris vbicun-
que ductum ſit planum A D F C, præter ad contactus, huiuſmodi ſolida
erunt in totum diſiuncta, ex quo nullibi ſe mutuò ſecabunt.

298.1.

0258-01

Præterea cum in prima figura ſectionum contactus ſit in ipſo axium verti-
ce, patet, & ſolida circa communem axim ab ipſis ſectionibus genita in eo-
dem puncto ſe mutuò contingere. In ſecunda verò tertia, & quarta ducto
plano ad axes erecto per punctum contactus I, in ſolido A B C efficientæ [?]
circulum, cuius diameter ſit I M, at in ſolido D E F circulum, cuius diame-

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