Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ erunt axes baſium eorundem ſolidorum, ipſarum nempè figurarum,
FGHN, BDCE, ſunt. n. ſolida rotunda, & plana, FMH, BA
C, per axes tranſeuntia ſunt baſibus erecta. Sint autem ſolidorum
iam dictorum axes, necnon axes, ſeu diametri figurarum, FMH,
BAC, ipſæ, OM, XA. Qura ergo ſiguræ, FMH, BAC, ſunt
fimiles portionum coni ſectiones, quarum baſes, ſiue ad earum axes,
vel diametros, MO, AX, ordinatim applicatæ ſunt, FH, BC, e-
runt homologarum earundem regulæ, ac tangentes ipſas figuras ex
vna parte, ex alia verò, quo per vertices, M, A, eiſdem ducentur æ-
quidiſtantes, earundem verò oppoſitarum tangentium, acipſarum
figurarum incidentes, MO, AX, eritque, FH, ad, BC, vt, MO,
ad, AX. Si ergo baſes, FGHN, BDCE, ſint circuli erunt figurę
ſimiles, quarum & oppoſitarum tangentium per extrema, FH, du-
ctarum incidentes fient diametri, FH, BC. Si verò ſint ſimiles el-
lipſes, quoniam, FH, BC, ſunt axes,
facilè probabimus, ſicut pro circulo fa-
ctum eſt ad Lemma Propoſ. 31. huius,
auxilio Propoſ. 40. huius, ipſas, FH,
BC, eſſe incidentes ſimilium figurarum,
FGHN, BDCE, & oppoſitarum
tangentium, quę per puncta, F, H; B,
C, ducuntur (quę ipſis, FH, BC, exi-
ſtent perpendiculares, cum ſint axes ea-
rundem figurarum.) Et eodem modo
ſi dicta ſolida ſecentur alijs planis præ-
fatis baſibus parallelis (ita tamen vt illa
diuidant ſimiliter ad eandem partem ip-
ſas, MO, AX, & ſubinde etiam altitudines ipſorum ſolidorum re-
ſpectu dictarum baſium aſſumptas) oſtendemus & productas in ſo-
lidis figuras eſſe ſimiles, & earum, ac oppoſitarum tangentium (æ-
quidiſtantium tanquam regulis duabus oppoſitis tangentibus ba-
ſium, FH, BC, per extrema, F, H; B, C, iam ductarum) inci-
dentes eſſe communes ipſarum ſectiones cum figuris, FMH, BAC,
quæ omnes erunt lineæ homologæ ſimilium figurarum, FMH, B
AC, quarum regulę, FH, BC. Ergo, ductis per, M, A, duobus
planis baſibus parallelis, quæ ipſa ſolida contingent, incidunt hiſce
oppoſitis tangentibus planisad eundem angulum ex eadem parte
plana figurarum, FMH, BAC, ſectis autem ſolidis planis paralle-
lis, vt dictum eſt, fiunt in ipſis ſimiles figuræ planæ, & earum inci-
dentes capiuntur omnes in ſimilibus figuris, FMH, BAC, quarum
ſunt homologæ, earumque regulæ ipſæ, FH, BC, & lineæ homo-
logæ figurarum homologarum duabus quibuſdam regulis, vtpotè

Waiting...

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer