Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 8
[out of range]
>
[Note]
Page: 36
[Note]
Page: 37
[Note]
Page: 37
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 38
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 40
[Note]
Page: 41
[Note]
Page: 41
[Note]
Page: 41
[Note]
Page: 41
[Note]
Page: 44
[Note]
Page: 44
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 45
[Note]
Page: 46
[Note]
Page: 46
[Note]
Page: 46
[Note]
Page: 47
[Note]
Page: 48
[Note]
Page: 49
[Note]
Page: 49
[Note]
Page: 49
[Note]
Page: 50
[Note]
Page: 50
[Note]
Page: 50
<
1 - 8
[out of range]
>
page
|<
<
(69)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div175
"
type
="
section
"
level
="
1
"
n
="
115
">
<
p
>
<
s
xml:id
="
echoid-s1762
"
xml:space
="
preserve
">
<
pb
o
="
69
"
file
="
0089
"
n
="
89
"
rhead
="
LIBER I.
"/>
incidentes, ac oppoſitarum tangentium, HK, MN, Vu, Zg, ip-
<
lb
/>
ſas, KN, ug, ſi. </
s
>
<
s
xml:id
="
echoid-s1763
"
xml:space
="
preserve
">n. </
s
>
<
s
xml:id
="
echoid-s1764
"
xml:space
="
preserve
">iungeremus, MK, Zu, probaretur, MH, ad,
<
lb
/>
HK, eſſe vt, ZV, ad, Vu, (ſunt. </
s
>
<
s
xml:id
="
echoid-s1765
"
xml:space
="
preserve
">n. </
s
>
<
s
xml:id
="
echoid-s1766
"
xml:space
="
preserve
">ſimiles figuræ, HMPL, V
<
lb
/>
ZdY, necnon, LPK, Ydu, circumſtant autem latera proportio-
<
lb
/>
nalia angulos æquales, MHK, ZVu, & </
s
>
<
s
xml:id
="
echoid-s1767
"
xml:space
="
preserve
">ideò oſtenderemus trian-
<
lb
/>
gula, MHK, ZVu, eſſe ſimilia, vnde pateret angulos, HKM,
<
lb
/>
VuZ, eſſe æquales, ſed etiam, HKN, Vug, ſunt ęquales, ergo
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0089-01
"
xlink:href
="
note-0089-01a
"
xml:space
="
preserve
">6. Sex. El.</
note
>
pateret angulos, MKN, Zug, eſſe æquales, ſunt autem etiam æ-
<
lb
/>
quales, MNK, Zgu, ergo triangula, MKN, Zug, eſſent æ-
<
lb
/>
quiangula, vnde, MN, ad, Zg, eſſet vt, KN, ad, ug, incidunt
<
lb
/>
autem, KN, ug, oppoſitis tangentibus, HK, MN, Vu, Zg, ad
<
lb
/>
eundem angulum ex eadem parte, ergo ipſarum tangentium, ac fi-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0089-02
"
xlink:href
="
note-0089-02a
"
xml:space
="
preserve
">24. huius.</
note
>
gurarum ſunt incidentes, KN, ug, cum verò, KN, ad, ug, ſit vt,
<
lb
/>
MK, ad, Zu, ideſt vt, MH, ad, ZV, vel vt quoduis ſolidorum
<
lb
/>
latus homologum ad quoduis latus homologum, ideſt vt, GO, ad,
<
lb
/>
8f, ideſt vt, OD, ad, f℟; </
s
>
<
s
xml:id
="
echoid-s1768
"
xml:space
="
preserve
">OD, autem ad, f℟, ſit vt, Bo, ad, Qf,
<
lb
/>
ideò, KN, ad, ug, erit vt, BO, ad, Qf, & </
s
>
<
s
xml:id
="
echoid-s1769
"
xml:space
="
preserve
">diuidunt ſimiliter ad
<
lb
/>
eandem partem ipſas, BO, Qf, in punctis, Ku, quæ incidunt ip-
<
lb
/>
ſis, BC, OD, Qf, R℟, ad eundem angulum ex eadem parte, ſunt
<
lb
/>
.</
s
>
<
s
xml:id
="
echoid-s1770
"
xml:space
="
preserve
">n. </
s
>
<
s
xml:id
="
echoid-s1771
"
xml:space
="
preserve
">anguli, BOD, Qf℟, æquales, quod & </
s
>
<
s
xml:id
="
echoid-s1772
"
xml:space
="
preserve
">de cæteris incidentibus
<
lb
/>
probabitur, ergo figurę, BODC, Qf℟R, quę capiunt omnes di-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0089-03
"
xlink:href
="
note-0089-03a
"
xml:space
="
preserve
">Deſio. 10.
<
lb
/>
huius.</
note
>
ctas incidentes, ſunt ſimiles, & </
s
>
<
s
xml:id
="
echoid-s1773
"
xml:space
="
preserve
">arum homologę ipſę incidentes, qua-
<
lb
/>
rum omnium regulæ ſunt, OD, f℟, & </
s
>
<
s
xml:id
="
echoid-s1774
"
xml:space
="
preserve
">ſunt ipſę figurę, BD, Q℟,
<
lb
/>
æquè ad eandem partem ipſis baſibus inclinatę, cum ſint in planis fi-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0089-04
"
xlink:href
="
note-0089-04a
"
xml:space
="
preserve
">Lem. 1.</
note
>
gurarum, oOS, sfp, ergo dicta ſolida ſunt etiam ſimilia iuxta de-
<
lb
/>
fin. </
s
>
<
s
xml:id
="
echoid-s1775
"
xml:space
="
preserve
">11. </
s
>
<
s
xml:id
="
echoid-s1776
"
xml:space
="
preserve
">huius. </
s
>
<
s
xml:id
="
echoid-s1777
"
xml:space
="
preserve
">quod ſi plana, GOo, 8fs, non eſſent in ambitu ſi-
<
lb
/>
milium dictorum ſolidorum, facilè tamen oſtenderemus portiones
<
lb
/>
ſolidorum vltra eadem plana exiſtentes eſſe ſimiles, ac ipſarum, & </
s
>
<
s
xml:id
="
echoid-s1778
"
xml:space
="
preserve
">
<
lb
/>
oppoſitorum tangentium planorum iam dictorum incidentes repe-
<
lb
/>
riri in planis figurarum, BD, Q℟, cum eiſdem integrantes figuras
<
lb
/>
incidentes integrorum ſimilium ſolidorum, ac dictorum oppoſito-
<
lb
/>
rum tangentium, quod ſpeculanti facilè innoteſcet, hoc autem erat
<
lb
/>
oſtendendum.</
s
>
<
s
xml:id
="
echoid-s1779
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div177
"
type
="
section
"
level
="
1
"
n
="
116
">
<
head
xml:id
="
echoid-head127
"
xml:space
="
preserve
">LEMMA.</
head
>
<
p
>
<
s
xml:id
="
echoid-s1780
"
xml:space
="
preserve
">CIrculi omnes, necnon femicirculi ſunt ſimiles iuxta meam deſi-
<
lb
/>
nitionem ſimilium planarum figurarum, & </
s
>
<
s
xml:id
="
echoid-s1781
"
xml:space
="
preserve
">eorum, & </
s
>
<
s
xml:id
="
echoid-s1782
"
xml:space
="
preserve
">tangen-
<
lb
/>
tium oppoſitarum, quæ ab extremitatibus diamertrorum ducuntur,
<
lb
/>
incidentes ſunt ipſi diametri.</
s
>
<
s
xml:id
="
echoid-s1783
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1784
"
xml:space
="
preserve
">Sint circuli, ABCD, ONQ, quorum diametri, AC, OQ, per
<
lb
/>
quorum extrema ducantur tangentes, FA, GC, HO, LQ. </
s
>
<
s
xml:id
="
echoid-s1785
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>