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

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[431.] THEOREMA XVIII. PROPOS. XIX.
Page: 328 (308)
[432.] A. COROLL. SECTIO I.
Page: 328 (308)
[433.] B. SECTIO II.
Page: 329 (309)
[434.] C. SECTIO III.
Page: 329 (309)
[435.] D. SECTIO IV.
Page: 329 (309)
[436.] E. SECTIO V.
Page: 329 (309)
[437.] SCHOLIV M.
Page: 330 (310)
[438.] THEOREMA XIX. PROPOS. XX.
Page: 330 (310)
[439.] COROLLARIVM.
Page: 331 (311)
[440.] THEOREMA XX. PROPOS. XXI.
Page: 331 (311)
[441.] THEOREMA XXI. PROPOS. XXII.
Page: 332 (312)
[442.] THEOREMA XXII. PROPOS. XXIII.
Page: 333 (313)
[443.] COROLLARIVM.
Page: 334 (314)
[444.] THEOREMA XXIII. PROPOS. XXIV.
Page: 334 (314)
[445.] PROBLEMA II. PROPOS. XXV.
Page: 335 (315)
[446.] COROLLARIVM.
Page: 336 (316)
[447.] THEOREMA XXIV. PROPOS. XXVI.
Page: 337 (317)
[448.] THEOREMA XXV. PROPOS. XXVII.
Page: 337 (317)
[449.] COROLLARIVM I.
Page: 339 (319)
[450.] COROLLARIVM II.
Page: 339 (319)
[451.] THEOREMA XXVI. PROPOS. XXVIII.
Page: 340 (320)
[452.] COROLLARIVM.
Page: 341 (321)
[453.] THEOREMA XXVII. PROPOS. XXIX:
Page: 341 (321)
[454.] A. COROLL. SECTIO I.
Page: 341 (321)
[455.] B. SECTIO II.
Page: 342 (322)
[456.] C. SECTIO III.
Page: 342 (322)
[457.] D. SECTIO IV.
Page: 342 (322)
[458.] E. SECTIO V.
Page: 342 (322)
[459.] THEOREMA XXVIII. PROPOS. XXX.
Page: 343 (323)
[460.] A. COROLL. SECT IO I.
Page: 344 (324)
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341321LIBER IV.
COROLLARIVM.
_H_Inc patet, ſi àuæ rectæ lineæ ad axem obliquæ parabolas conſtitue-
rint, ſumpta pro regula conſtitutæ parabolæ recta eam conſtituen-
te, quoniam rectangula ſub dictis parabolis, & figuris diſtantiarum ea-
rundem ad omnia quadrata parabolæ, cuius baſis ſit ad axim recta (quæ
pro eadem ſumatur pro regula) ſunt, vt quadrata diametrorum earun-
dem ad quadratum axis illius tertia parabolæ; quod ideò illa rectangula
erunt inter ſe, vt diametrorum earundem parabolarum quadrata fuerint
quoq; inter ſe.
THEOREMA XXVII. PROPOS. XXIX:
OMnia quadrata parabolarum, regulis baſibus ſuntin-
terſe, vt omnia quadrata parallelogrammorum, in
eiſdem baſibus, & circa eoſdem axes, veldiametros exi-
ſtentium, regulis eiſdem baſibus.
Manifeſta eſt hæc propoſitio, nam omnia quadrata dictarum
parabolarum ſunt ſubdupla omnium quadratorum eorundem pa-
1121. huius rallelogrammorum, endemregulis aſſumptis, ſcilicet parabolarum
baſibus iam dictis.
A. COROLL. SECTIO I.
22A
_H_Inc colligimus concluſiones, quæ de omnibus quadratis parallelo-
grammorum collectæ ſuntin Theorematibus _9. 10. 11. 12. 13._
Lib. _2._ regulis ibidem aſſumptis, ſuppoſitis quibuſdam conditionibus
circa altitudines, vel latera æqualiter baſibus inclinata, & quadrata
baſium, vel ipſas baſes, veriſicarietiam de omnibus quadratis parabo-
larum, ſuppoſitis eiſdem conditionibus circa axes, vel altitudines, vel
circa diametros æqualiter baſibus inclinatas, & circa quadrata baſium,
vel eaſdem baſes; nam his conditionibus axibus, vel altitudmibus, vel
diametris, & quadratis baſium, vel ipſis baſibus competentibus, etiam
altitudinibus, vel lateribus parallelogrammorum, æqualiter baſibus
inclinatis, & quadratis baſium, vel eiſdem baſibus, pariter conueniunt,
quæ quidem parallelogramma ſint in eiſdem baſibus, & circa eoſdem
axes vel diametros cum parabolis; & ideò dictæ concluſiones, quæ

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