Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

Non inutile autem mibi videtur eſſe animaduerter e pro huius confir-
matione, hoc pro vero ſuppoſito, quam plurima, quæ ab Euclide, Ar-
chimede, & alijs oſtenſa ſunt, à me pariter fuiſſe demonſtrata, meaſq; concluſiones ad vnguem cum illorum concluſionibus concordare, quod
euidens ſignum eſſe poteſt, me in principijs vera aſſumpſiſſe, licet ſciam,
& ex falſis principijs ſophiſticè vera aliquando deduci poſſe, quod ta-
men in tot, & tot concluſionibus, methodo geometrica demonſtratis mihi
accidiſſe abſurdum putarem: Hoc tamen addo, non tanquam præfatæ ve-
ritatis legitimum fundamentum, ſed vt non negligendum, immò ſummè
expendendum illius argumentum, quod ſequentia percurrenti continuò
magis, ac magis eluceſcet.

175. THEOREMA II. PROPOS. II.

AEqualium planarum figurarum omnes lineæ ſunt ęqua-
les, & æqualium ſolidarum omnia plana ſunt æqua-
lia, regula quauis affumpta.

Sint duę æquales planę figuræ, ADC, AEB, in figura, ADC,
ſit regula, AC, vtcunque, & in figura, AEB, regula vtcunque ſit,
AB. Dico omnes lineas figuræ, ADC, regula, AC, ęquales eſſe
omnibus lineis figurę, AEB, regula, AB; intelligatur ſiguram, A
EB, ita ſuperponi figuræ, ADC, vt regulæ ſint ad inuicem ſuper-
poſitę, velut eſt, AB, in, AC, vel ſaltem ęquidiſtent, vel ergo tota
figura congruit toti, vel pars parti, congruat pars parti, ergo con-
gruentium harum partium omnes lineæ erunt
pariter congruentes, ſcilicet omnes lineę, AD
B, partis figurę, AEB, erunt congruentes om-
nibus lineis, ADB, partis figuræ, ADC, ſu
perponantur adhuc reſiduæ harum figurarum
partes, hac lege tamen, vt omnes earundem li-
neæ regulis, AB, AC, fiue regulę communi,
AB, vel, AC, ſemper ſituentur æquidiſtantes,
& hoc ſemper fiat, donec omnes refiduę partes ad inuicem ſuperpo-
ſitæ fuerint, quia ergo integræ figuræ ſunt æquales erunt dictæ par-
tes ſuperpoſitæ inuicem congruentes, ergo & earum omnes lineæ
erunt pariter congruentes, magnitudines autem congruentes ſunt
ad inuicem æquales, ergo omnes lineæ partium figuræ, AEB, ſi-
mul ſumptarum. ſ. omnes lineæ figuræ, AEB, ſumptæ regula, A
B, erunt ęquales omnibus lineis partium figurę, ADC, quibus prę-
dictæ partes congruerunt, ſimul ſumptarum. . omnibus lineis figu-

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