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

Table of contents

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[461.] B. SECTIO II.
[462.] C. SECTIO III.
[463.] D. SECTIO IV.
[464.] E. SECTIO V.
[465.] THEOREMA XXIX. PROPOS. XXXI.
[466.] THEOREMA XXX. PROPOS. XXXII.
[467.] COROLLARIVM.
[468.] THEOREMA XXXI. PROPOS. XXXIII.
[469.] THEOREMA XXXII. PROPOS. XXXIV.
[470.] COROLLARIVM.
[471.] THEOREMA XXXIII. PROPOS. XXXV.
[472.] COROLLARIVM.
[473.] THEOREMA XXXIV. PROPOS. XXXVI.
[474.] THEOREMA XXXV. PROPOS. XXXVII.
[475.] THEOREMA XXXVI. PROP. XXXVIII.
[476.] THEOREMA XXXVII. PROP. XXXIX.
[477.] THEOREMA XXXVIII. PROP. XL.
[478.] COROLLARIVM.
[479.] THEOREMA XXXIX. PROPOS. XLI
[480.] THEOREMA XL. PROPOS. XLII.
[481.] THEOREMA XLI. PROPOS. XLIII.
[482.] THEOREMA XLII. PROPOS. XLIV.
[483.] THEOREMA XLIII. PROP. XLV.
[484.] THEOREMA XLIV. PROP. XLVI.
[485.] THEOREMA XLV. PROP. XLVII.
[486.] THEOREMA XLVI. PROPOS. XLVIII.
[487.] THEOREMA XLVII. PROPOS. XLIX.
[488.] THEOREMA XLVIII. PROPOS. L.
[489.] THEOREMA XLIX. PROPOS. LI.
[490.] SCHOLIVM.
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435415LIBER V.
COROLLARIVM VI.
IN Prop. 6. expoſita eius figura, & vt fiat noſtrum exemplum ea-
295[Figure 295] dein circa, EM, reuoluta, patet pla-
num tranſiens per, SV, æquid ſtans ba-
ſi, FG, a cono de, FEG, reſecare conoi-
dem, SEV, quæ ad conum, SEV, habet
rationem datam, quam nempè habet H
R, ad, RL, idq;
diſcimus efficere quo-
cunque ſolido ſimilari exiſtente, FEG,
cuius figura genitrix ſit, FEG, à quo .
ſ.
ſciemus abſcindere per planũ baſi ęqui-
diſtans ſolidum ſibi ſimilare, quod nem-
pè erit genitũ ex hyperbola, SEV, quod
ad ſolidum ſibi ſimilare genitum ex triã-
gulo, SEV, habeat rationem datam,
dummodo data ratio ſit quidem maioris
in æqualitatis, ſed minor ſexquialtera.
COROLLARIVM VII.
IN Prop. 7. expoſita eius figura, dimiſsis tamen rectis, ED, SO
296[Figure 296] XO, &
parallelogrammis,
GX, GR, eadem reuoluatur cir-
ca manentem axim, CV, vt ex
triangulo, HCR, fiat conus, H
CR, &
ex hyperbola, SOX, co-
nois, SOX, patet ergo conum,
HCR, ad conoidem, SOX, eſſe
in ratione compoſita ex ea, quã
habet quadratum, SX, ad qua-
dratum, HR, &
rectangulum,
AVO, ad rectangulum, BVC.

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