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: 155
[Note]
Page: 156
[Note]
Page: 156
[Note]
Page: 157
[Note]
Page: 157
[Note]
Page: 157
[Note]
Page: 157
[Note]
Page: 158
[Note]
Page: 158
[Note]
Page: 158
[Note]
Page: 159
[Note]
Page: 159
[Note]
Page: 159
[Note]
Page: 159
[Note]
Page: 161
[Note]
Page: 161
[Note]
Page: 161
[Note]
Page: 161
[Note]
Page: 161
[Note]
Page: 162
[Note]
Page: 162
[Note]
Page: 163
[Note]
Page: 163
[Note]
Page: 163
[Note]
Page: 163
[Note]
Page: 163
[Note]
Page: 163
[Note]
Page: 163
[Note]
Page: 164
[Note]
Page: 164
<
1 - 8
[out of range]
>
page
|<
<
(135)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div340
"
type
="
section
"
level
="
1
"
n
="
209
">
<
p
>
<
s
xml:id
="
echoid-s3209
"
xml:space
="
preserve
">
<
pb
o
="
135
"
file
="
0155
"
n
="
155
"
rhead
="
LIBER II.
"/>
inrecta, Φ Λ, & </
s
>
<
s
xml:id
="
echoid-s3210
"
xml:space
="
preserve
">incidentem eiuſdem figuræ, nempè ipſam, 38, in
<
lb
/>
puncto, 4, igitur figuræ, BC, Π Ω, erunt duæ figurarum homolo-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0155-01
"
xlink:href
="
note-0155-01a
"
xml:space
="
preserve
">Defin. 11.
<
lb
/>
huius.</
note
>
garum ſolidorum, AP, V &</
s
>
<
s
xml:id
="
echoid-s3211
"
xml:space
="
preserve
">, &</
s
>
<
s
xml:id
="
echoid-s3212
"
xml:space
="
preserve
">, OX, Φ Λ, earum incidentes, &</
s
>
<
s
xml:id
="
echoid-s3213
"
xml:space
="
preserve
">,
<
lb
/>
LG, 38, erunt ſimiliter diuiſæ in punctis, E, 4, nam etiam altitu-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0155-02
"
xlink:href
="
note-0155-02a
"
xml:space
="
preserve
">17. Vndec.
<
lb
/>
Elem.</
note
>
dines propoſitorum ſimilium ſolidorum ſunt ſimiliter diuiſæ (ad ean-
<
lb
/>
dem partem ſub intellige) ſi igitur à punctis, O, Φ, duxerimus tan-
<
lb
/>
gentes figuras, BC, Π Ω, erunt iſtæ regulis homologarum earun-
<
lb
/>
dem figurarum parallelæ, vel pro regulis aliarum etiam aſſumi pote-
<
lb
/>
runt, & </
s
>
<
s
xml:id
="
echoid-s3214
"
xml:space
="
preserve
">quę à punctis, X, Λ, ducentur prędictis parallelę occurrent
<
lb
/>
eiſdem figuris, & </
s
>
<
s
xml:id
="
echoid-s3215
"
xml:space
="
preserve
">illas ex oppoſito prędictarum contingent, ita vt ha-
<
lb
/>
beamus (ſi & </
s
>
<
s
xml:id
="
echoid-s3216
"
xml:space
="
preserve
">iſtæ ductæ intelligantur, quæ ſint, XC, Λ Ω,) oppc-
<
lb
/>
fitas tangentes figuræ, BC, quæ erunt, BO, CX, & </
s
>
<
s
xml:id
="
echoid-s3217
"
xml:space
="
preserve
">figuræ, Π Ω,
<
lb
/>
quæ erunt, Π Φ, Ω Λ, necnon pro regulis homologarum earundem
<
lb
/>
haberi poterunt; </
s
>
<
s
xml:id
="
echoid-s3218
"
xml:space
="
preserve
">vel igitur figuræ, BC, Π Ω, adiacent ſuis inciden-
<
lb
/>
tibus, OX, Φ Λ, totę ad eandem partem, & </
s
>
<
s
xml:id
="
echoid-s3219
"
xml:space
="
preserve
">interius integrę exiſten-
<
lb
/>
tes, vel non, ſi ſic factum erit, quod volumus, ſi non transferantur
<
lb
/>
omnes lineæ figurarum, BC, Π Ω, regulis eiſdem tangentibus, in
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0155-03
"
xlink:href
="
note-0155-03a
"
xml:space
="
preserve
">Vide A.
<
lb
/>
15. huius
<
lb
/>
propèfin.</
note
>
figuras ipſis, OX, Φ Λ, adiacentes, pro vt in Prop. </
s
>
<
s
xml:id
="
echoid-s3220
"
xml:space
="
preserve
">15. </
s
>
<
s
xml:id
="
echoid-s3221
"
xml:space
="
preserve
">effectum eſt,
<
lb
/>
hinc autem reſultantes figurę ſint, OZX, Φ Γ Λ, quę per talem con-
<
lb
/>
ſtructionem ad eandem partem incidentium, & </
s
>
<
s
xml:id
="
echoid-s3222
"
xml:space
="
preserve
">interius integrę nc-
<
lb
/>
bis proueniunt. </
s
>
<
s
xml:id
="
echoid-s3223
"
xml:space
="
preserve
">Similiter ſi intelligamus ducta alia duo plana prędi-
<
lb
/>
ctis ęquidiſtantia, quę ſolida propoſita ita ſecent, vt fiant in ipſis non
<
lb
/>
vnica in ſingulis figura, ſed plures, ex. </
s
>
<
s
xml:id
="
echoid-s3224
"
xml:space
="
preserve
">gr. </
s
>
<
s
xml:id
="
echoid-s3225
"
xml:space
="
preserve
">in ſolido, AP, figurę, R,
<
lb
/>
I, & </
s
>
<
s
xml:id
="
echoid-s3226
"
xml:space
="
preserve
">in, V &</
s
>
<
s
xml:id
="
echoid-s3227
"
xml:space
="
preserve
">, figuræ, ℟, N, eadem autem ſecent figuras inciden-
<
lb
/>
tes in rectis, SY, Β Δ, & </
s
>
<
s
xml:id
="
echoid-s3228
"
xml:space
="
preserve
">rectas, LG, 38, in punctis, K, {10/ }, dum-
<
lb
/>
modo hæc plana pariter ſecent altitudines dictas propoſitorum ſoli-
<
lb
/>
dorum ſimiliter ad eandem partem, erunt figurę, R, I, binę ſimiles, & </
s
>
<
s
xml:id
="
echoid-s3229
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0155-04
"
xlink:href
="
note-0155-04a
"
xml:space
="
preserve
">E. Def. 10.
<
lb
/>
lib. 1.</
note
>
ſimiliter poſitę, ac figurę, ℟, N, .</
s
>
<
s
xml:id
="
echoid-s3230
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s3231
"
xml:space
="
preserve
">I, ſimilis ipſi, N, &</
s
>
<
s
xml:id
="
echoid-s3232
"
xml:space
="
preserve
">, R, ipſi, ℟, & </
s
>
<
s
xml:id
="
echoid-s3233
"
xml:space
="
preserve
">
<
lb
/>
linearum homologarum earundem regulæ ipſis, CX, Ω Λ, æquidi-
<
lb
/>
ſtabunt, ipſę autem rectę, S, Y; </
s
>
<
s
xml:id
="
echoid-s3234
"
xml:space
="
preserve
">β, Δ, erunt earundem incidentes,
<
lb
/>
vt, S, β, ipſarum, R, ℟, &</
s
>
<
s
xml:id
="
echoid-s3235
"
xml:space
="
preserve
">, Y, Δ, ipſarum, I, N, ſi igitur figurę,
<
lb
/>
R, I, ℟, N, non adiacent ſuis incidentibus, transferantur ſingula-
<
lb
/>
rum omnes lineę, regula ſemper, pro figuris, RI, ipſa, CX, & </
s
>
<
s
xml:id
="
echoid-s3236
"
xml:space
="
preserve
">pro
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0155-05
"
xlink:href
="
note-0155-05a
"
xml:space
="
preserve
">Videad
<
lb
/>
fig. A.</
note
>
figuris, ℟, N, ipſa, Ω Λ, in figuras adiacentes lineis homologis figu-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0155-06
"
xlink:href
="
note-0155-06a
"
xml:space
="
preserve
">Piop. 15.
<
lb
/>
huius.</
note
>
rarum, H {00/ }, Σ 2, vt ſint nobis inuentæ figuræ, S, Y, β Δ, quæ
<
lb
/>
adiaceant homologis lineis figurarum incidentium, H, {00/ }, Σ 2: </
s
>
<
s
xml:id
="
echoid-s3237
"
xml:space
="
preserve
">Si
<
lb
/>
igitur eandem methodum ſeruemus in cæteris figuris, quæ ex lectio-
<
lb
/>
ne planorum tangentibus æquidiſtantium in dictis ſolidis producun-
<
lb
/>
tur, transferentes nempè omnes earum lineas homologas, regulis
<
lb
/>
ſemper ipſis, CX, Ω Λ, in figuras adiacentes lineis homologis figu-
<
lb
/>
rarum incidentium, H, {00/ }, Σ 2, quę reperientur totę ad eandem par-
<
lb
/>
tem, & </
s
>
<
s
xml:id
="
echoid-s3238
"
xml:space
="
preserve
">interius integrę, tandem nobis erunt comparata duo </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>