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

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[Item 1.]
[2.] TURNER COLLECTION
[3.] THE LIBRARY UNIVERSITY OF KEELE
[4.] GEOMETRIA INDIVISIBILIBVS CONTIN VOR VM Noua quadam ratione promota. _AVTHORE_ P. BONAVENTVRA CAVALERIO MEDIOLANEN _Ordinis S.Hieron. Olim in Almo Bononien. Archigym._ _Prim. Mathematicarum Profeſſ._ In hac poftrema edictione ab erroribus expurgata. _Ad Illuſtriſs. D. D._ MARTIVM VRSINVM PENNÆ MARCHIONEM &c.
[5.] BONONIÆ, M. DC. LIII.
[6.] _ILLVSTRISSIME_ MARCHIO
[7.] PRÆFATIO
[8.] In huius Libri Autorem.
[9.] In Librum Geometriæ.
[10.] Ad Libri Auctorem.
[11.] Ad Librum Geometriæ.
[12.] DeLibro Geometriæ.
[13.] De Libro Geometriæ.
[14.] Ad Autorem Libri Geometriæ.
[15.] CAVALERII LIBER PRIMVS. In quo præcipuè de ſectionibus Cylindricorum, & Conicorum, nec non ſimilibus figuris quædam element aria præmittuntur; ac aliquæ Pro-poſitiones lemmaticæ pro ſequen-tibus Libris oſtenduntur. DIFINITIONES. A. I.
[16.] B.
[17.] C.
[18.] A. II.
[19.] B.
[20.] C.
[21.] D.
[22.] E.
[23.] SCHOLIVM.
[24.] III.
[25.] A. IV.
[26.] COROLLARIVM.
[27.] B.
[28.] V.
[29.] VI.
[30.] VII.
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3010GEOMETRIÆ deinde inter eadem plana tangentia eiſdem æquidiſtantia
11D. Def.2. vtcumque plana ducta fuerint, altitudines ſolidorum, re-
ſpectu
dictorum tangentium ſumptas, ſimiliter ad eandem
partem
diuidentia, reperiamus figuras exhis planis in di-
22A.Def.10. ctis ſolidis conceptas eſſe ſimiles, vel ſi plures producan-
tur
, tot numero in vno, quot in alio ſolido produci, quæ
33E.Def.10. fint binæ ſimiles, &
quæ ſunt vnius ſolidi ſimiliter inter ſe
diſpoſitę
, ac quę ſunt alterius, &
omnium homologas dua-
bus
quibuſdam rectis lineis communiter, tamquam earum-
dem
regulis, æquidiſtare.
(ſic. n. earum homologæ cum
quibuſuis
alijs duabus regulis angulos æquales cum præ-
dictis
facientibus, vt infra Prop.
23. huius oſtendetur, e-
tiam
haberi poterunt) Vnde ſiregulæ homologarum acci-
piantur
cum incidentibus planis concurrentes, &
conce-
ptarum
in ſolidis ſimilium figurarum ductæ in ſingulis op-
poſitæ
tangentes præfatis regulis Parallelę producantur, ſt
opus
ſit, quouſq;
prædictis incidentibus planis occurrant,
&
binarum quarumcumque oppoſitarum tangentium pun-
cta
occurſuum iungantur rectis lineis, etiam has iungentes
reperiamus
ſingulas eſſe incidentes ſuarum ſimilium figu-
rarum
, &
oppoſitarum tangentium, ac omnes dictas inci-
dentes
concipi in figuris ſimilibus, quarum, &
ipſæ inci-
dentes
ſint homologæ, &
omnium regulæ communes ſe-
ctiones
planorum incidentium, &
oppoſitorum planorum
tangentium
.
Has omnes, inquam, conditiones ſimilia ſo-
lida
in vniuerſum habere ſuppono.

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