Clavius, Christoph
,
In Sphaeram Ioannis de Sacro Bosco commentarius
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of handwritten notes
<
1 - 7
[out of range]
>
<
1 - 7
[out of range]
>
page
|<
<
(98)
of 525
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div254
"
type
="
section
"
level
="
1
"
n
="
87
">
<
pb
o
="
98
"
file
="
134
"
n
="
135
"
rhead
="
Comment. in I. Cap. Sphæræ
"/>
</
div
>
<
div
xml:id
="
echoid-div257
"
type
="
section
"
level
="
1
"
n
="
88
">
<
head
xml:id
="
echoid-head92
"
xml:space
="
preserve
">COROLLARIVM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s4764
"
xml:space
="
preserve
">Ex omnibusiis, quæ demonſtrata ſunt, perſpicuum eſt circu-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-134-01
"
xlink:href
="
note-134-01a
"
xml:space
="
preserve
">@Circul’ om
<
lb
/>
nibus figu-
<
lb
/>
@is rectili-
<
lb
/>
neis ſibi iſo
<
lb
/>
perimetris
<
lb
/>
maior eſt.</
note
>
lum abſolute omnium figurarum rectilinearum ſibi iſoperimetra-
<
lb
/>
rum maximum eſſe.</
s
>
<
s
xml:id
="
echoid-s4765
"
xml:space
="
preserve
"/>
</
p
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s4766
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Qvoniam</
emph
>
enim ex propoſitione 5. </
s
>
<
s
xml:id
="
echoid-s4767
"
xml:space
="
preserve
">habetur, regularium figurarum iſoperime-
<
lb
/>
trarum eam, quæ plura latera continet, eſſe maiorem: </
s
>
<
s
xml:id
="
echoid-s4768
"
xml:space
="
preserve
">Rurſus ex propoſitione 12. </
s
>
<
s
xml:id
="
echoid-s4769
"
xml:space
="
preserve
">conſtat,
<
lb
/>
inter omnes figuras iſoperimetras æqualia numero latera habentes, eam maximam eſ-
<
lb
/>
ſe, quę regularis eſt: </
s
>
<
s
xml:id
="
echoid-s4770
"
xml:space
="
preserve
">Ex hac denique 13. </
s
>
<
s
xml:id
="
echoid-s4771
"
xml:space
="
preserve
">propoſitioue perſpicuum eſt, circulum omnium
<
lb
/>
figurarum iſoperimet rarum regularium eſſe maximum: </
s
>
<
s
xml:id
="
echoid-s4772
"
xml:space
="
preserve
">Manifeſte concluditur, circu-
<
lb
/>
lum abſolute ac ſimpliciter omnium figurarum rectilinearum ſibi iſoperimetrarum ma-
<
lb
/>
ximum eſſe quod eſt propoſitum.</
s
>
<
s
xml:id
="
echoid-s4773
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div259
"
type
="
section
"
level
="
1
"
n
="
89
">
<
head
xml:id
="
echoid-head93
"
style
="
it
"
xml:space
="
preserve
">THEOR. 12. PROPOS. 14.</
head
>
<
p
style
="
it
">
<
s
xml:id
="
echoid-s4774
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Area</
emph
>
cuiuslibet pyramidis æqualis eſt ſolido rectangulo conten-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-134-02
"
xlink:href
="
note-134-02a
"
xml:space
="
preserve
">Pyramis
<
lb
/>
quælibet
<
lb
/>
cui paralle-
<
lb
/>
lepipedo ſit
<
lb
/>
@qualis.</
note
>
to ſub perpendiculari à uertice ad baſim protracta, & </
s
>
<
s
xml:id
="
echoid-s4775
"
xml:space
="
preserve
">tertia parte
<
lb
/>
baſis.</
s
>
<
s
xml:id
="
echoid-s4776
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4777
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Sit</
emph
>
pyramis, cuius baſis quotcu nque laterum A B C D E, & </
s
>
<
s
xml:id
="
echoid-s4778
"
xml:space
="
preserve
">uertex F.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4779
"
xml:space
="
preserve
">
<
figure
xlink:label
="
fig-134-01
"
xlink:href
="
fig-134-01a
"
number
="
36
">
<
image
file
="
134-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/134-01
"/>
</
figure
>
Solidum autem rectangulu
<
unsure
/>
m G N, cu-
<
lb
/>
ius baſis G H I K, æqualis ſit tertię par-
<
lb
/>
ti baſis A B C D E, altitudo uero, ſiue
<
lb
/>
perpendicularis G L, æqualis altitudini
<
lb
/>
pyramidis, ſiue perpendiculari à uerti-
<
lb
/>
ce pyramidis ad eius baſim productæ.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4780
"
xml:space
="
preserve
">Dico ſolidum rectangulum G N, ęqua-
<
lb
/>
le eſſe pyramidi A B C D E F. </
s
>
<
s
xml:id
="
echoid-s4781
"
xml:space
="
preserve
">Ducan-
<
lb
/>
tur enim ab oibus angulis baſis G H I K,
<
lb
/>
ad aliquod punctum baſis oppoſitę, ni-
<
lb
/>
mirum ad L, lineę rectæ, ita ut conſti-
<
lb
/>
tuatur pyramis G H I K L, eandem ha-
<
lb
/>
bens baſim cum ſolido G N, eand emq́ue
<
lb
/>
altitudinem & </
s
>
<
s
xml:id
="
echoid-s4782
"
xml:space
="
preserve
">cum eodem ſolido G N,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s4783
"
xml:space
="
preserve
">cum pyramide A B C D E F. </
s
>
<
s
xml:id
="
echoid-s4784
"
xml:space
="
preserve
">Quo-
<
lb
/>
niam igitur pyramis A B C D E F, tri-
<
lb
/>
pla eſt pyramidis G H I K L, ut in ſcho-
<
lb
/>
lio propoſ. </
s
>
<
s
xml:id
="
echoid-s4785
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s4786
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s4787
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s4788
"
xml:space
="
preserve
">Eucl. </
s
>
<
s
xml:id
="
echoid-s4789
"
xml:space
="
preserve
">demonſtraui-
<
lb
/>
mus: </
s
>
<
s
xml:id
="
echoid-s4790
"
xml:space
="
preserve
">Et ſolidum G N, triplum quoque
<
lb
/>
eſt, ex coroll. </
s
>
<
s
xml:id
="
echoid-s4791
"
xml:space
="
preserve
">propoſ. </
s
>
<
s
xml:id
="
echoid-s4792
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s4793
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s4794
"
xml:space
="
preserve
">12. </
s
>
<
s
xml:id
="
echoid-s4795
"
xml:space
="
preserve
">Eucl. </
s
>
<
s
xml:id
="
echoid-s4796
"
xml:space
="
preserve
">
<
lb
/>
eiuſdem pyramidis G H I K L; </
s
>
<
s
xml:id
="
echoid-s4797
"
xml:space
="
preserve
">erit ſo-
<
lb
/>
lidum G N, pyramidi A B C D E F, ęqua
<
lb
/>
le. </
s
>
<
s
xml:id
="
echoid-s4798
"
xml:space
="
preserve
">Quapropter area cuiuslibet pyrami-
<
lb
/>
dis ęqualis eſt ſolido rectãgulo, &</
s
>
<
s
xml:id
="
echoid-s4799
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s4800
"
xml:space
="
preserve
">quod
<
lb
/>
erat oſtendendum.</
s
>
<
s
xml:id
="
echoid-s4801
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>