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

Table of contents

< >
[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.
< >
page |< < (74) of 569 > >|
9474GEOMETRIÆ quæ in cylindricis producant figuras, IM, RT, in conicis verò, O
M
, ST, ſecent verò plana tangentia in rectis, IC, MF, Od;
r ,
Tp
, So, iſtæ ergo erunt ad inuicem parallelæ, &
tangent figuras,
1116. Vnd.
Elem
.
IM, RT, OM, ST, eadem verò planaſecent plana, BG, Zl, in
22Corol. 9.50[Figure 50] rectis, CF, p.
Quod ergo figuræ,
33Corol. 18. IM, RT, vel, OM, ST, ſint ſimi-
les
baſibus, &
ijſdem ſimiliter poſitę
44@2. Et 19.
huius
.
iam oſtenſum fuit, ex quo fit, vt &

ipſarum
, &
quarumcunq; ſic in prę-
fatis
ſolidis producibilium ſimilium
figurarum
homologæ duabus qui-
buſdam
regulis, vt ex.
gr. ipſis, HG,
Yl
, ſemper æquidiſtent.
Reliquum
eſt
autem, vt probemus, CF, p,
vel
, dF, op, eſſe prædictarum in-
cidentes
.
Cumergo duę, IC, CF,
duabus
, LD.
DG, ęquidiſtentan-
5510. Vnd.
Elem
.
guli, ICF, LDG, æquales erunt,
ſic
etiam probabimus eſſe æquales,
R
p, Xfl, cum verò, IC, ſit e-
tiam
æqualis, LD, &
R , ipſi,
Xf
, necnon, CF, ipſi, DG, &
,
p, ipſi, fl, erit, IC, ad, R , vt,
CF
, ad, p, &
incidunt ipſis, IC,
MF
, R , Tp, ad eundem angu-
lum
ex eadem parte, ergo, CF,
p
, erunt incidentes ſimilium figura-
rum
, IM, RT, &
oppoſitarum tan-
66@4. huius. gentium, IC, MF;
R , Tp, ea-
dem
ratione demonſtrabimus, dF,
op
, eſſe incidentes ſimilium figura-
rum
, OM, ST, &
oppoſitarum tan-
gentium
, Od, MF;
So, Tp, eſt
autem
, dF, ad, op, vt, dE, ad,
o
&
, ſcilicet, vt, DE, ad, f & , nam,
DE
, f &
, ſunt ſimiliter ad eandem
partem
diuiſæ in punctis, do, (ete-
77@7. Vnd.
Elem
.
nim altitudines dictorum ſolidorum per plana, IF, Rp, ſimiliter ad
eandem
partem diuiduntur) ergo, dF, op, æquidiſtantes oppoſitis
tangentibus
, BE, DG, Z &
, fl, ſunt homologæ figurarum ſimi-
lium
, EDG, &
fl, quarum & oppoſitarum tangentium incidentes
erunt
ipſæ, ED, &
f. Eodem modo oſtendemus, CF, p,

Text layer

  • Dictionary

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index