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

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11494GEOMETRIÆ lineis, vel lateribus homologis deſcriptarum figurarum; ſolida, in qui-
bus deſcriptæ figuræ ex traiectis planis producentur (quæ in ſequenti li-
bro dicuntur, ſolida ad inuicem ſimilaria genita ex dictis ſectionum por-
tionibus) erunt ſimilia, & figurarum homologarum eorundem regulæ
11_C. Def. 8._
_lib. 2._ oppoſita tangentia plana dictis iam deſcriptis figuris æquidiſtantia, quo-
rum & dictorum ſolidorum figuræ incidentes erunt dictæ ſectionum por-
tiones, vel in earum planis iacebunt. V nde colligimus omnes ſphæras
eſſe ſimiles, nam ſi ſecentur planis per axem, conceptæ figuræ fiunt ſimi-
les, ideſt circuli, quod ſi ſecentur adhuc planis ad horum circulorum pla-
22_Lẽma 31._
_huius pr._ na erectis, productæ figuræ fiunt pariter circuli deſcripti tanquam dia-
metris eiſdem rectis lineis, in quibus coincidunt circulis per axem du-
33_33. huius._ ctis, quæ diametri ſunt etiam incidentes eorundem deſcriptorum circu-
44_34. huius._ lorum, & oppoſitarum tangentium per eorum extrema ductarum, quæ
55_Lẽma 31._
_huius._ tangentes omnes inter ſe æquidiſtant, vt facilè patet, & ſunt iſtæ inci-
dentes, ſiue diametri deſcriptorum circulorum, quæ axem diuidunt fi-
militer ad eandem partem, vt ipſi axes, igitur ſpbæræ omnes ſunt ſimi-
les, & ductis duobus planis oppoſitis tangentibus vtcumq; & per axem,
66_Lẽma 31._
_huius._ qui iungit puncta contactuum ductis planis, hinc effecti circuli erunt
figuræ incidentes dictorum tangentium, & ſphærarum, & dicta plana
tangentia erunt regulæ homologarum figurarum earundem, vnde tan-
dem patet quoſuis circulos in ſphæris per centrum tranſeuntes poſſe eſſe
figuras incidentes earundem ſphærarum, & planorum oppoſitorum tan-
gentium ſphæras in extremis punctis diametrorum quorumuis dictorum
circulorum per centrum tr anſeuntium.

THEOREMA XLVI. PROPOS. XLIX.

POſita definitione particulari ſimilium ſphæroidum, ſe-
quitur & generalis ſimilium ſolidorum.

Sint ſimiles ſphæroides

63[Figure 63] iuxta definitionem particu-
larem de ipſis allatam, AB
CD, FEHG. Dico has
eſſe ſimiles iuxta definitio.
nem generalem ſimilium
ſolidorum; ductis enim pla-
nis per axes, AC, FH,
producantur in eiſdem el-
lipſes, ABCD, FEHG,
7733 huius. quæ erunt eædem illis, ex quarum reuolutione circa axes, AC, FH,
8838. huius.

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