Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER II. tione ipſius, MP, ad, Ω & , ideò figura, MZP, ad figuram, Ω ℟
& habebit rationem compofitam ex duabus rationibus ipſius, MP,
ad, Ω & , . i. duplam eius, quam habet, MP, ad, Ω & , ſiue, KM,
ad, Π Ω, quæ illis ſunt æquales, ſed & figuræ, ABD, φ Σ Λ, ſunt
æquales figuris, MZP, Ω ℟ & , ergo ſigura, ABD, ad figuram, Φ
Σ Λ, duplam rationem habebit eius, quam habet, KM, ad, Π Ω,
quia vero, KM, & , Π Ω, ſunt incidentes ſimilium figurarum, AB
D, Φ Σ Λ, ideò, vt, KM, ad, Π Ω, ita erit, BEID, ſimul ad, Σ 2,
3 Λ, ſimul, vel ita, BE, ad, Σ 2, ſiue, ID, ad, 3 Λ, ergo figura,
ABD, ad figuram, Φ Σ Λ, duplam rationem habebit eius, quam
habet, BE, ad, Σ 2, vel, ID, ad, 3 Λ, . i. erunt iſtæ ſimiles figuræ
in dupla ratione linearum, vel laterum homologorum, BE, Σ 2, vel,
ID, 3 Λ, vel aliarum quarumcumque homologarum præfatis regu-
lis æquidiſtantium, quod oſtendere opus erat.

203.1.

Defin. 12.
lib. 1.
Defnilo,
Quin. El.
B. Def. 10.
lib. 1.
Coroll. 1.
22. lib. @.

204. COROLLARIVM I.

_E_T quia dictæ figuræ planæ ſimiles oſtenſæ ſunt eſſe in dupla ratione
linearum, vel laterum homologorum, quæ æquidiſtant regulis vt-
cunque ſumptis, patet eaſdem eſſe in dupla ratione quarumuis homolo-
garum, & duas quaſdam homologas ſumptas cum quibuſdam regulis, eſſe
inter ſe, vt alias quaslibet duas homologas, cum alijs quibuſuis regulis, eſſe
aſſumptas, quod etiam in Corollario Lemmatis 48. Lib. 1. aliunde dedu-
ctum eſt.

205. COROLLARIVM II.

_V_Niuersè inſuper manifeſtum eſt, ſitres rectæ lineæ deinceps pro-
portionales fuerint, vt prima ad tertiam, ita eſſe figuram planam
deſcriptam à prima ad eam, quæ à ſecunda de ſcribitur; & huius conuer-
ſum, dummodò deſcribentes ſint ſimilium deſcriptarum figurarum lineæ,
ſiue latera homologa.

206. THEOREMA XVI. PROPOS. XVI.

SI quatuor rectæ lineæ proportionales fuerint, prima au-
tem, & ſecunda ſimiles figuras planas deſcripſerint, & tertia, & quarta alias figuras planas ſimiles, licet etiam præ-
dictis diſſimiles eſſent, ita vt deſcribentes ſint earum lineæ,
vel latera homologa, figura primæ ad figuram lecundæ erit,

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