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
|<
<
(101)
of 525
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div265
"
type
="
section
"
level
="
1
"
n
="
91
">
<
p
>
<
s
xml:id
="
echoid-s4864
"
xml:space
="
preserve
">
<
pb
o
="
101
"
file
="
137
"
n
="
138
"
rhead
="
Ioan. de Sacro Boſco.
"/>
lidum rectangulum contentum ſub ſemidiametro A D, & </
s
>
<
s
xml:id
="
echoid-s4865
"
xml:space
="
preserve
">tertia parte ambit@
<
lb
/>
præfati corporis inſcripti intra ſphærã G H K, minus corpore inſcripto. </
s
>
<
s
xml:id
="
echoid-s4866
"
xml:space
="
preserve
">Quo-
<
lb
/>
niã vero ambitus corporis inſcripti maior eſt ambitu ſphæræ A B C, ut demon
<
lb
/>
ſtrat Archimedes lib. </
s
>
<
s
xml:id
="
echoid-s4867
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s4868
"
xml:space
="
preserve
">de ſphæra, & </
s
>
<
s
xml:id
="
echoid-s4869
"
xml:space
="
preserve
">cylindro propoſ. </
s
>
<
s
xml:id
="
echoid-s4870
"
xml:space
="
preserve
">27. </
s
>
<
s
xml:id
="
echoid-s4871
"
xml:space
="
preserve
">atque adeo & </
s
>
<
s
xml:id
="
echoid-s4872
"
xml:space
="
preserve
">tertia
<
lb
/>
pars ambitus dicti corporis maior tertia parte ambitus ſphęræ A B C, erit ſo-
<
lb
/>
lidum rectangulum contentum ſub ſemidiametro A D, & </
s
>
<
s
xml:id
="
echoid-s4873
"
xml:space
="
preserve
">tertia parte ambitus
<
lb
/>
ſphærę A B C, hoc eſt, ſolidum E, multo minus corpore inſcripto intra ſphærã
<
lb
/>
G H K: </
s
>
<
s
xml:id
="
echoid-s4874
"
xml:space
="
preserve
">Poſita eſt autem ſphæra G H K, uel æqualis ſolido E, vel minor. </
s
>
<
s
xml:id
="
echoid-s4875
"
xml:space
="
preserve
">Igitur
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s4876
"
xml:space
="
preserve
">ſphęra G H K, minor erit corpore intra ipſam deſcripto, totum parte, quod
<
lb
/>
eſt abſurdum. </
s
>
<
s
xml:id
="
echoid-s4877
"
xml:space
="
preserve
">Quocirca ſolidum E, maius non erit ſphæra A B C.</
s
>
<
s
xml:id
="
echoid-s4878
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4879
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Sitdeinde</
emph
>
, ſi fieri poteſt, ſolidum E, minus, quàm ſphæra A B C,
<
lb
/>
excedaturq́ue à ſphæra A B C, quantitate F. </
s
>
<
s
xml:id
="
echoid-s4880
"
xml:space
="
preserve
">Intelligatur circa centrum D,
<
lb
/>
ſphæra deſcripta L M N, minor, quàm ſphæia A B C, ita tamen, ut exceſſus,
<
lb
/>
quo ſphæra L M N, ſuperatur à ſphæra A B C, non ſit maior quantitate F,
<
lb
/>
ſed uel æqualis, uel minor, hoc eſt, ut ſphæra L M N, ſit uel ęqualis ſolido
<
lb
/>
E, ſi nimirum ipſa excedatur a ſphæra A B C, quantitate F, vel maior ſolido
<
lb
/>
E, ſi uidelicet ſphæra L M N, a ſphæra A B C, ſuperetur minori quantitate,
<
lb
/>
quam F. </
s
>
<
s
xml:id
="
echoid-s4881
"
xml:space
="
preserve
">Neceſſario enim aliqua ſphæra erit, quę uel æqualis ſit ſolido E, at-
<
lb
/>
que adeo minor, quàm ſphęra A B C; </
s
>
<
s
xml:id
="
echoid-s4882
"
xml:space
="
preserve
">uel minor quidem, quàm ſphęra A B C,
<
lb
/>
maior uerò, quàm magnitu
<
unsure
/>
do E, quæ minor ponitur, quàm ſphæra A B C. </
s
>
<
s
xml:id
="
echoid-s4883
"
xml:space
="
preserve
">De-
<
lb
/>
ſcribatur deinde intra ſphæram A B C, corpus, quod minime tangat ſphęram
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-137-01
"
xlink:href
="
note-137-01a
"
xml:space
="
preserve
">17. duod.</
note
>
L M N; </
s
>
<
s
xml:id
="
echoid-s4884
"
xml:space
="
preserve
">ita ut unaquæque perpendicularium ex centro D, ad baſes huius cor-
<
lb
/>
poris inſcripti cadentium minor ſit ſemidiametro A D. </
s
>
<
s
xml:id
="
echoid-s4885
"
xml:space
="
preserve
">Si igitur à centro D,
<
lb
/>
ad omnes eius angulos lineæ extendantur, ut totum corpus in pyramides re-
<
lb
/>
ſoluatur, quarum baſes ſunt eędem, quæ corporis A B C, uertex autem com-
<
lb
/>
munis centrum D; </
s
>
<
s
xml:id
="
echoid-s4886
"
xml:space
="
preserve
">erit quælibet pyramis æqualis (per 14. </
s
>
<
s
xml:id
="
echoid-s4887
"
xml:space
="
preserve
">propoſ. </
s
>
<
s
xml:id
="
echoid-s4888
"
xml:space
="
preserve
">huius) ſoli-
<
lb
/>
do rectangulo contento ſub eius perpendiculari, & </
s
>
<
s
xml:id
="
echoid-s4889
"
xml:space
="
preserve
">tertia parte baſis, Et ideo
<
lb
/>
ſolidum rectan gulum contentum ſub ſemidiametro A D, & </
s
>
<
s
xml:id
="
echoid-s4890
"
xml:space
="
preserve
">tertia baſis cuiuſ-
<
lb
/>
uis pyramidis, maius erit pyramide ipſa. </
s
>
<
s
xml:id
="
echoid-s4891
"
xml:space
="
preserve
">Et quoniam omnia ſolida rectangu-
<
lb
/>
la contenta ſub ſingulis perpendicularibus ex centro D, ad baſes corporis di-
<
lb
/>
cti protractis, & </
s
>
<
s
xml:id
="
echoid-s4892
"
xml:space
="
preserve
">ſingulis tertijs partibus baſium, ſimul ęqualia ſunt toti corpo-
<
lb
/>
ri, eſſiciunt autem omnes tertię partes baſium ſimul tertiam partem ambitus
<
lb
/>
corporis; </
s
>
<
s
xml:id
="
echoid-s4893
"
xml:space
="
preserve
">erit ſolidum rectangulum contentum ſub ſemidiametro A D, & </
s
>
<
s
xml:id
="
echoid-s4894
"
xml:space
="
preserve
">ter-
<
lb
/>
tia parte ambitus dicti corporis ſphærę A B C, inſcripti, maius corpore inſcri-
<
lb
/>
pto. </
s
>
<
s
xml:id
="
echoid-s4895
"
xml:space
="
preserve
">Cum igitur ambitus ſphærę A B C, maior ſit ambitu corporis ſibi in ſcripti
<
lb
/>
atque adeo & </
s
>
<
s
xml:id
="
echoid-s4896
"
xml:space
="
preserve
">tertia pars ambitus ſphæræ maior tertia parte ambitus dicti cor-
<
lb
/>
poris, erit ſolidum rectan gulum contentum ſub A D, ſemidiametro, & </
s
>
<
s
xml:id
="
echoid-s4897
"
xml:space
="
preserve
">tertia
<
lb
/>
parte ambitus ſphærę A B C, hoc eſt, ſolidum E, multo maius corpore inſcri-
<
lb
/>
pto intra ſphæram A B C: </
s
>
<
s
xml:id
="
echoid-s4898
"
xml:space
="
preserve
">Ponebatur autem ſphæra L M N, uel æqualis ſoli-
<
lb
/>
do E, uel maior. </
s
>
<
s
xml:id
="
echoid-s4899
"
xml:space
="
preserve
">Igitur & </
s
>
<
s
xml:id
="
echoid-s4900
"
xml:space
="
preserve
">ſphęra L M N, maior erit corpore intra ſphęram
<
lb
/>
A B C, deſcripto, pars toto, quod eſt abſurdum. </
s
>
<
s
xml:id
="
echoid-s4901
"
xml:space
="
preserve
">Non igitur ſolidum E, minus
<
lb
/>
erit ſphęra A B C. </
s
>
<
s
xml:id
="
echoid-s4902
"
xml:space
="
preserve
">Cum ergo neque maius ſit oſtenſum, ęquale omnino erit.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4903
"
xml:space
="
preserve
">Ac propterea area cuiuslibet ſphæræ æqualis eſt ſolido rectangulo compre-
<
lb
/>
henſo ſub ſemidiametro ſphæræ, & </
s
>
<
s
xml:id
="
echoid-s4904
"
xml:space
="
preserve
">tertia parte ambitus ſphæræ, quod demon-
<
lb
/>
ſtrandum erat.</
s
>
<
s
xml:id
="
echoid-s4905
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>