Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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[161.] COROLLARIVM.
[162.] VI.
[163.] COROLLARIVM.
[164.] VII.
[165.] A. VIII.
[170.] APPENDIX. Pro antecedentium Definitionum explicatione.
[171.] POSTVLATA I.
[172.] II.
[173.] THEOREMA I. PROPOS. I.
[174.] SCHOLIVM.
[175.] THEOREMA II. PROPOS. II.
[176.] COROLLARIV M.
[177.] THEOREMA III. PROPOS. III.
[178.] COROLLARIVM.
[179.] THEOREMA IV. PROPOS. IV.
[180.] COROLLARIVM.
[181.] THEOREMA V. PROPOS. V.
[182.] THEOREMA VI. PROPOS. VI.
[183.] THEOREMA VII. PROPOS. VII.
[184.] THEOREMA VIII. PROPOS. VIII.
[185.] COROLLARIVM.
[186.] THEOREMA IX. PROPOS. IX.
[187.] COROLLARIVM.
[188.] THEOREMA X. PROPOS. X.
[189.] COROLLARIVM.
[190.] THEOREMA XI. PROPOS. XI.
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288268GEOMETRIÆ ſimiles ſunt circuli, ſemidiametros in figura genitrice, OV, haben-
tes, à trilineo autem, DCV, deſcribetur quoddam ſolidum, quod
180[Figure 180] vocetur, Apex ſphæralis, ſi, OCD, ſit
quarta circuli;
vel ſphæroidalis, ſi, OC
D, ſit quarta ellipſis, ideſt ſolidum ſimila-
re, quod poteſt dici genitum ex trilineo,
DCV, habens omnes ſuas ſimiles figuras
circulos ſemidiametros in figura genitri-
ce, DCV, ſitos habentes, eſt igitur inter
hæc duo ſimilaria ſolida, quęin particulari
hoc exemplo ſunt cylindrus, &
apex ſphę-
ralis, vel ſphæroidalis, ratio eadem ſupradictę, quam breuitatis caufa
aliter exemplificare dimiſi.
Conſimili autem vnico exemplo. f. affu-
mendo pro ſiguris ſimilibus ipſos circulos, ſemidiametros in figuris
genitricibus habentibus, breuitatis cauſa, &
ob ſeruandam in figuris
claritatem impoſterum contenti erimus.
COROLLARIVM XII.
IN Propof. 14. patet ratio ſolidi ſimilaris geniti ex, FD, ad ſoli-
dum ſimilare genitum ex figura, FQBDZ.
Appoſita. n. hic
illius figura, dimiffa, HC, &
, AP, & retenta, BD, tantum in, V,
diuifa, reuoluatur, FD, circa manentem axim, ZD, modò ſupra-
181[Figure 181] dicto, ex, FD, igitur fiet cylin-
drus, FA, &
ex figura, FQBD
Z, fiet quoddam ſolidum rotun-
dum, quod vocetur, Tympanum
fphærale, ſi, FQB, ſit ſemicircu-
lus, vel ſphæroidale, ſi, FQB, ſit
ellipſis, erunt autem hæc duo ſo-
lida ſimilaria genita ex figuris, F
D, FQBDZ, figuras ſimiles cir-
culos habentia, quorum ſemidia-
metri iacent in ſuis genitricibus fi-
guris, &
patet, quod ratio cylin-
dri, FA, ad tympanum ſphærale, vel ſphæroidale, FQRA, eſt ea-
dem ei, quam habet, BD, ad, DV, eandem autem habet quodli-
bet ſolidum ſimilare genitum ex, FD, ad ſimilare ſibi genitum ex fi-
gura, FQBDZ, qualecunque ſit.

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