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

Si enim fuerint inæqualia, alterum ipſorum minus erit: ſit ipſum A B C,
quod cum ſit ad partem B deficiens, patet ei circumſcribi poſſe per conti-
nuam axis B G biſectionem, & c. figuram ex Cylindris æque-altis, quæ
inſcriptum ſolidum Acuminatum A B C ſuperet minori exceſſu, quo ſoli-
dum D E F dicitur excedere idem ſolidum Acuminatum A B C: (ſuſſi-
cit enim vt circumſcripto Canoni A B C parallelogrammo A R, eius
ope, tan quam circa diametralem Canonem, ad æquidiſtantem motum
baſis A L C deſcribatur Cylindricus A R, vt vides, circumſeribens Acu-
minatum ſolidum A B C, ſic enim plano per punctum medium axis B G
applicato, bifariam ſecabitur Cylindricus, quod ſi iterum axis dimidium biſariam ſecetur, & c. relinquetur tandem Cylindricus A S, qui prædicto
exceſſu minor erit: vnde hac vltima diametri B G diuiſione per æqualia
ſegmenta, completa circumſcriptione Cylindricorum T M, X V, Z Y
æqualium altitudinum, quorum diametrales Canones ſint A S; T M; X
V; X Y; aggregatum ipſorum excedet ſolidum A B C minori quantitate,
quàm ſit primus Cylindricus A S, cum A S ſit ſemper exceſſus circum-
ſcriptæ figuræ ex Cylindricis ſuper inſcriptam ex æque - altis Cylindri-
cis, & c. ſed Cylindricus A S ponitur minor exceſſu ſolidi D E F ſuper A B
C, ergo circumſcripta figura A S M Y ex Cylindricis, ſuperat inſcriptum
ſolidum A B C minori exceſſu ipſius ſolidi D E F ſupra A B C) ſit ergo quę-
ſita figura circumſcripta, ex Cylindricis A S, T M, X V, Z Y, & c. quæ
ideò adhuc minor erit ſolido D E F, cuieadem arte circumſcribatur figura
ex totidem æque - altis Cylindricis D K; 2 3; 4 5; 6 7; quorum maximi,
diametralis Canon ſit D K ſuper baſim O F N; proximi verò diametralis
Canon ſit 2 3, & c.

333.1.

72. h.

Iam patet horum ſoli-
dorum altitudines BI, E [?]
Q in tot æquas partes ſe-
cari à parallelis baſibus
circumſcriptorum Cylin-
dricorum, in quot ſe- cãtur diametri B G, E H,
Canonum A B C, D E F. Sit igitur primi Cylindri-
ci A S altitudo 8 I, & primi D K altitudo 9 Q: & cum ſit baſis A L C, ad
baſim O F N, ita recipro-
cè altitudo E Q ad altitudinem B I, ſumptis conſequentium æque-ſubmul-
tiplicibus 9 Q, 8 I; erit baſis A L C, ad O F N, vt altitudo 9 Q, ad 8 I; quare Cylindricus A S æqualis erit Cylindrico D K. Eadem ratione de- monſtrabuntur reliqu@ Cylindric@ T M, X V, Z Y, reliquis 23, 45, 67,
æqual@a eſſe, ſingul@ ſingulis, quapropter vniuerſa figura ex Cylindricis,
circumſcripta ſolido A B C, æqualis erit vniuerſæ circumſcriptæ ſolido D
E F, ſed circumſcripta ipſi A B C demonſtrata eſt minor ſolido D E F, er-
go, & circumſcripta ſolido D E F, ipſo ſibi inſcripto ſolido minor erit, to-
tum ſua parte, quod eſt abſurdum. Non eſt ergo vllum horum Acuminato-

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