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

Page concordance

< >
Scan Original
51 31
52 32
53 33
54 34
55 35
56 36
57 37
58 38
59 39
60 40
61 41
62 42
63 43
64 44
65 45
66 46
67 47
68 48
69 49
70 50
71 51
72 52
73 53
74 54
75 55
76 56
77 57
78 58
79 59
80 60
< >
page |< < (73) of 569 > >|
9373LIBERI.
Sint cylindrici quicunque, AH, KY; ſeu conici in ijſdem baſibus,
&
altitudinibus (vt vna vice vtriuſq; demonſtrationem abſoluamus)
NLH
, VXY, ſimiles iuxta definit.
7. huius. Dico eoſdem etiam
eſſe
ſimiles iuxta definit.
11. Quoniam ergo vtraque prædicta ſolida
11Defin. 7. ſunt ſimilia, erunt baſes, LH, XY, ſimiles, ducantur earum oppo-
ſitę
tangentes, quę ſint homologarum regulę, ipſę, LD, HG, X f,
22Coroll. 1.49[Figure 49] Y l, quarum, &
prædictarum ſimi-
33B. Def. 10. lium figurarum incidentes ſint ipſæ,
DG
, f l, quæ etiam pro regulis alia-
44Coroll.
23
.
rum homologarum ſumi poterunt,
ſint
ergo duę quæcunque homologę
parallelę
incidentibus, D G, fl, ip-
ſæ
, LH, XY, ſi ergo per has, &
la-
55Defin. 7. tera cylindricorum, vel conicorum
iam
dictorum extendantur plana, ab
ijs
producentur in cylindricis ſimilia
parallelogramma
, &
in conicis ſimi-
lia
triangula, quę etiam erunt ad ba-
ſes
æquè ad eandem partem inclina-
ta
.
Extendantur ergo per oppoſitas
tangentes
, LD, HG;
Xf, Yl, pla-
na
tangentia tam cylindricos, quam
conicos
iam dictos, &
hęc ſimul cum
planis
baſium indefinitè producan-
tur
ad partes incidentium, DG, fl,
&
tandem per, DG, fl, cum ſint
parallelæ
, extendantur plana ipſis,
AH
, KY, parallela ſecantia iam pro-
ducta
plana in rectis, DG, GE, E
B
, BD, DE, fl, l &
, & Z, Zf, f
66Defin. 13.
vndec
. El.
&
, erunt ergo parallelepipeda, AG,
Kl
, &
priſmata, LNGD, XVlf,
7724. Vnd.
Elem
.
ergo erit parallelogrammum, BG,
ſimile
ipſi, AH, &
, Zl, ſimile, K
Y
, quæ cum ſint inter ſe ſimilia, e-
tiam
, BG, Zl, erunt ſimilia, ſic e-
tiam
oſtendemus triangula, EDG,
&
fl, eſſe ſimilia, ſub intellige iuxta
definitionem
Euclidis, ergo erunt e-
tiam
ſimilia iuxta defin.
10. Ducantur duo plana oppoſitis tangenti-
8827. huius. bus intermedia, ac parallela, altitudines dictorum ſolidorum reipectu
baſium
, LH, XY, ſumptas, ſimiliter ad eandem partem

Text layer

  • Dictionary

Text normalization

  • Original
  • Regularized
  • Normalized

Search


  • Exact
  • All forms
  • Fulltext index
  • Morphological index