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: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 56
[Note]
Page: 57
[Note]
Page: 57
[Note]
Page: 58
[Note]
Page: 58
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 59
[Note]
Page: 60
[Note]
Page: 60
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 61
[Note]
Page: 62
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 63
[Note]
Page: 64
[Note]
Page: 64
[Note]
Page: 64
[Note]
Page: 64
[Note]
Page: 65
[Note]
Page: 66
[Note]
Page: 66
<
1 - 8
[out of range]
>
page
|<
<
(112)
of 569
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div273
"
type
="
section
"
level
="
1
"
n
="
174
">
<
pb
o
="
112
"
file
="
0132
"
n
="
132
"
rhead
="
GEOMETRIÆ
"/>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s2655
"
xml:space
="
preserve
">Non inutile autem mibi videtur eſſe animaduerter e pro huius confir-
<
lb
/>
matione, hoc pro vero ſuppoſito, quam plurima, quæ ab Euclide, Ar-
<
lb
/>
chimede, & </
s
>
<
s
xml:id
="
echoid-s2656
"
xml:space
="
preserve
">alijs oſtenſa ſunt, à me pariter fuiſſe demonſtrata, meaſq;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2657
"
xml:space
="
preserve
">concluſiones ad vnguem cum illorum concluſionibus concordare, quod
<
lb
/>
euidens ſignum eſſe poteſt, me in principijs vera aſſumpſiſſe, licet ſciam,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2658
"
xml:space
="
preserve
">ex falſis principijs ſophiſticè vera aliquando deduci poſſe, quod ta-
<
lb
/>
men in tot, & </
s
>
<
s
xml:id
="
echoid-s2659
"
xml:space
="
preserve
">tot concluſionibus, methodo geometrica demonſtratis mihi
<
lb
/>
accidiſſe abſurdum putarem: </
s
>
<
s
xml:id
="
echoid-s2660
"
xml:space
="
preserve
">Hoc tamen addo, non tanquam præfatæ ve-
<
lb
/>
ritatis legitimum fundamentum, ſed vt non negligendum, immò ſummè
<
lb
/>
expendendum illius argumentum, quod ſequentia percurrenti continuò
<
lb
/>
magis, ac magis eluceſcet.</
s
>
<
s
xml:id
="
echoid-s2661
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div274
"
type
="
section
"
level
="
1
"
n
="
175
">
<
head
xml:id
="
echoid-head190
"
xml:space
="
preserve
">THEOREMA II. PROPOS. II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2662
"
xml:space
="
preserve
">AEqualium planarum figurarum omnes lineæ ſunt ęqua-
<
lb
/>
les, & </
s
>
<
s
xml:id
="
echoid-s2663
"
xml:space
="
preserve
">æqualium ſolidarum omnia plana ſunt æqua-
<
lb
/>
lia, regula quauis affumpta.</
s
>
<
s
xml:id
="
echoid-s2664
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2665
"
xml:space
="
preserve
">Sint duę æquales planę figuræ, ADC, AEB, in figura, ADC,
<
lb
/>
ſit regula, AC, vtcunque, & </
s
>
<
s
xml:id
="
echoid-s2666
"
xml:space
="
preserve
">in figura, AEB, regula vtcunque ſit,
<
lb
/>
AB. </
s
>
<
s
xml:id
="
echoid-s2667
"
xml:space
="
preserve
">Dico omnes lineas figuræ, ADC, regula, AC, ęquales eſſe
<
lb
/>
omnibus lineis figurę, AEB, regula, AB; </
s
>
<
s
xml:id
="
echoid-s2668
"
xml:space
="
preserve
">intelligatur ſiguram, A
<
lb
/>
EB, ita ſuperponi figuræ, ADC, vt regulæ ſint ad inuicem ſuper-
<
lb
/>
poſitę, velut eſt, AB, in, AC, vel ſaltem ęquidiſtent, vel ergo tota
<
lb
/>
figura congruit toti, vel pars parti, congruat pars parti, ergo con-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0132-01
"
xlink:href
="
note-0132-01a
"
xml:space
="
preserve
">Poſtul. 1.
<
lb
/>
huius.</
note
>
<
figure
xlink:label
="
fig-0132-01
"
xlink:href
="
fig-0132-01a
"
number
="
72
">
<
image
file
="
0132-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0132-01
"/>
</
figure
>
gruentium harum partium omnes lineæ erunt
<
lb
/>
pariter congruentes, ſcilicet omnes lineę, AD
<
lb
/>
B, partis figurę, AEB, erunt congruentes om-
<
lb
/>
nibus lineis, ADB, partis figuræ, ADC, ſu
<
lb
/>
perponantur adhuc reſiduæ harum figurarum
<
lb
/>
partes, hac lege tamen, vt omnes earundem li-
<
lb
/>
neæ regulis, AB, AC, fiue regulę communi,
<
lb
/>
AB, vel, AC, ſemper ſituentur æquidiſtantes,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2669
"
xml:space
="
preserve
">hoc ſemper fiat, donec omnes refiduę partes ad inuicem ſuperpo-
<
lb
/>
ſitæ fuerint, quia ergo integræ figuræ ſunt æquales erunt dictæ par-
<
lb
/>
tes ſuperpoſitæ inuicem congruentes, ergo & </
s
>
<
s
xml:id
="
echoid-s2670
"
xml:space
="
preserve
">earum omnes lineæ
<
lb
/>
erunt pariter congruentes, magnitudines autem congruentes ſunt
<
lb
/>
ad inuicem æquales, ergo omnes lineæ partium figuræ, AEB, ſi-
<
lb
/>
mul ſumptarum.</
s
>
<
s
xml:id
="
echoid-s2671
"
xml:space
="
preserve
">ſ. </
s
>
<
s
xml:id
="
echoid-s2672
"
xml:space
="
preserve
">omnes lineæ figuræ, AEB, ſumptæ regula, A
<
lb
/>
B, erunt ęquales omnibus lineis partium figurę, ADC, quibus prę-
<
lb
/>
dictæ partes congruerunt, ſimul ſumptarum.</
s
>
<
s
xml:id
="
echoid-s2673
"
xml:space
="
preserve
">. omnibus lineis </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>