Clavius, Christoph
,
Geometria practica
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Table of Notes
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
[out of range]
>
[Note]
Page: 107
[Note]
Page: 108
[Note]
Page: 108
[Note]
Page: 108
[Note]
Page: 108
[Note]
Page: 108
[Note]
Page: 108
[Note]
Page: 109
[Note]
Page: 109
[Note]
Page: 109
[Note]
Page: 109
[Note]
Page: 109
[Note]
Page: 109
[Note]
Page: 109
[Note]
Page: 109
[Note]
Page: 110
[Note]
Page: 110
[Note]
Page: 110
[Note]
Page: 111
[Note]
Page: 111
[Note]
Page: 111
[Note]
Page: 111
[Note]
Page: 111
[Note]
Page: 111
[Note]
Page: 111
[Note]
Page: 111
[Note]
Page: 111
[Note]
Page: 112
[Note]
Page: 112
[Note]
Page: 112
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 213
[out of range]
>
page
|<
<
(340)
of 450
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div972
"
type
="
section
"
level
="
1
"
n
="
346
">
<
p
>
<
s
xml:id
="
echoid-s15807
"
xml:space
="
preserve
">
<
pb
o
="
340
"
file
="
368
"
n
="
368
"
rhead
="
GEOMETR. PRACT.
"/>
lis, conficietur eodem pacto rectangulum ex tribus conflatum æquale tribus
<
lb
/>
trapeziis, &</
s
>
<
s
xml:id
="
echoid-s15808
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s15809
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15810
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Vltimo</
emph
>
porrò triangulo, ſi quod fuerit, conſtituetur rectangulum
<
note
symbol
="
a
"
position
="
left
"
xlink:label
="
note-368-01
"
xlink:href
="
note-368-01a
"
xml:space
="
preserve
">ſchol. 41.
<
lb
/>
primi.</
note
>
I
<
unsure
/>
e ſupra ſemiſſem baſis, in eadem altitudine cum triangulo.</
s
>
<
s
xml:id
="
echoid-s15811
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div975
"
type
="
section
"
level
="
1
"
n
="
347
">
<
head
xml:id
="
echoid-head374
"
xml:space
="
preserve
">THEOR. 4. PROPOS. 7.</
head
>
<
p
>
<
s
xml:id
="
echoid-s15812
"
xml:space
="
preserve
">SI ex duobus punctis ad vnum punctum cuiuſuis lineæ rectæ, quæ
<
lb
/>
communis ſectio ſit plani per duo puncta ducti cum alio quopiam
<
lb
/>
plano, duæ rectæ ducantur, facientes cum illa duos angulos æquales:
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s15813
"
xml:space
="
preserve
">erunt duæ hæ rectæ breuiores quibuſcunque aliis duabus rectis, quæ
<
lb
/>
ex eiſdem duobus punctis ad aliud punctum eiuſdem lineæ rectæ
<
lb
/>
ducuntur.</
s
>
<
s
xml:id
="
echoid-s15814
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15815
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Ex</
emph
>
duobus punctis A, B, ad C, punctum in recta CD, ita vt planum per CD,
<
lb
/>
du ctum tranſeat reuolutum per A, B, ducantur duæ rectæ AC, BC, facientes an-
<
lb
/>
gulos A C F, B C D, æquales: </
s
>
<
s
xml:id
="
echoid-s15816
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s15817
"
xml:space
="
preserve
">ex eiſdem punctis A, B, ducantur primum ad
<
lb
/>
aliud punctum D, ad dextram ipſius C, aliæ duæ rectæ AD, BD. </
s
>
<
s
xml:id
="
echoid-s15818
"
xml:space
="
preserve
">Dico AC, BC,
<
lb
/>
eſſe breuiores, quam AD, BD. </
s
>
<
s
xml:id
="
echoid-s15819
"
xml:space
="
preserve
">Producta enim AC, verſus C, fiat CE, ipſi CB,
<
lb
/>
æqualis, iungaturque DE. </
s
>
<
s
xml:id
="
echoid-s15820
"
xml:space
="
preserve
">Et quia angulus ACF, angulo BCD, ponitur æqua-
<
lb
/>
lis, eſtque angulus ACF, angulo ECD, ad verticem æqualis, erit quoque
<
note
symbol
="
b
"
position
="
left
"
xlink:label
="
note-368-02
"
xlink:href
="
note-368-02a
"
xml:space
="
preserve
">15. primi.</
note
>
gulus BCD, angulo ECD, æqualis. </
s
>
<
s
xml:id
="
echoid-s15821
"
xml:space
="
preserve
">Cum ergo & </
s
>
<
s
xml:id
="
echoid-s15822
"
xml:space
="
preserve
">duo latera BC, CD, duobus
<
lb
/>
lateribus EC, CD, æqualia ſint: </
s
>
<
s
xml:id
="
echoid-s15823
"
xml:space
="
preserve
"> erit
<
note
symbol
="
c
"
position
="
left
"
xlink:label
="
note-368-03
"
xlink:href
="
note-368-03a
"
xml:space
="
preserve
">4. primi.</
note
>
<
figure
xlink:label
="
fig-368-01
"
xlink:href
="
fig-368-01a
"
number
="
259
">
<
image
file
="
368-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/368-01
"/>
</
figure
>
D B, baſi D E, æqualis; </
s
>
<
s
xml:id
="
echoid-s15824
"
xml:space
="
preserve
">ac proinde A D,
<
lb
/>
D B, ſimul ipſis A D, D E. </
s
>
<
s
xml:id
="
echoid-s15825
"
xml:space
="
preserve
">ſimul æquales
<
lb
/>
erunt. </
s
>
<
s
xml:id
="
echoid-s15826
"
xml:space
="
preserve
"> Sunt autem A D, D E,
<
note
symbol
="
d
"
position
="
left
"
xlink:label
="
note-368-04
"
xlink:href
="
note-368-04a
"
xml:space
="
preserve
">@primi.</
note
>
quam AE, hoc eſt, quam AC, CB; </
s
>
<
s
xml:id
="
echoid-s15827
"
xml:space
="
preserve
">quod
<
lb
/>
CB, CE, poſitæ ſint æquale@. </
s
>
<
s
xml:id
="
echoid-s15828
"
xml:space
="
preserve
">Igitur & </
s
>
<
s
xml:id
="
echoid-s15829
"
xml:space
="
preserve
">AD,
<
lb
/>
BD, maiores erunt, quam AC, BC. </
s
>
<
s
xml:id
="
echoid-s15830
"
xml:space
="
preserve
">quod
<
lb
/>
eſt propoſitum.</
s
>
<
s
xml:id
="
echoid-s15831
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15832
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Dvcantvr</
emph
>
deinde ex punctis A, B,
<
lb
/>
ad aliud punctum F, ad ſiniſtram ipſius C,
<
lb
/>
aliæ duæ rectæ AF, BF. </
s
>
<
s
xml:id
="
echoid-s15833
"
xml:space
="
preserve
">Dico rurſus A C,
<
lb
/>
BC, breuiores eſſe, quam AF, BF. </
s
>
<
s
xml:id
="
echoid-s15834
"
xml:space
="
preserve
">Producta enim rurſum AC, ſumptaque CE,
<
lb
/>
ipſi CB, æquali, iungatur EF. </
s
>
<
s
xml:id
="
echoid-s15835
"
xml:space
="
preserve
">Et quoniam anguli ACF, BCD, æquales ponun-
<
lb
/>
tur; </
s
>
<
s
xml:id
="
echoid-s15836
"
xml:space
="
preserve
"> eſtque ACF, angulo ECD, ad verticem æqualis; </
s
>
<
s
xml:id
="
echoid-s15837
"
xml:space
="
preserve
">erunt qu@que
<
note
symbol
="
e
"
position
="
left
"
xlink:label
="
note-368-05
"
xlink:href
="
note-368-05a
"
xml:space
="
preserve
">15. primi.</
note
>
BCD, ECD, æquales: </
s
>
<
s
xml:id
="
echoid-s15838
"
xml:space
="
preserve
">ac proinde & </
s
>
<
s
xml:id
="
echoid-s15839
"
xml:space
="
preserve
">ex duobus rectis reliqui BCF, ECF, æqua-
<
lb
/>
les erunt. </
s
>
<
s
xml:id
="
echoid-s15840
"
xml:space
="
preserve
">Cum ergo & </
s
>
<
s
xml:id
="
echoid-s15841
"
xml:space
="
preserve
">duo latera BC, CF, duobus lateribus EC, CF, æqualia
<
lb
/>
ſint; </
s
>
<
s
xml:id
="
echoid-s15842
"
xml:space
="
preserve
"> erit quo que baſis BF, baſi EF, æqualis: </
s
>
<
s
xml:id
="
echoid-s15843
"
xml:space
="
preserve
">Ac proinde AF, FE, ipſis AF,
<
note
symbol
="
f
"
position
="
left
"
xlink:label
="
note-368-06
"
xlink:href
="
note-368-06a
"
xml:space
="
preserve
">4. primi.</
note
>
æquales erunt. </
s
>
<
s
xml:id
="
echoid-s15844
"
xml:space
="
preserve
"> Sunt autem AF, FE, maiores, quam AE, hoc eſt, quam AC,
<
note
symbol
="
g
"
position
="
left
"
xlink:label
="
note-368-07
"
xlink:href
="
note-368-07a
"
xml:space
="
preserve
">20. primi.</
note
>
quod BC, CE, poſitæ ſint æquales. </
s
>
<
s
xml:id
="
echoid-s15845
"
xml:space
="
preserve
">Igitur & </
s
>
<
s
xml:id
="
echoid-s15846
"
xml:space
="
preserve
">AF, BF, maiores erunt, quam A C,
<
lb
/>
CB. </
s
>
<
s
xml:id
="
echoid-s15847
"
xml:space
="
preserve
">quod eſt propoſitum.</
s
>
<
s
xml:id
="
echoid-s15848
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div978
"
type
="
section
"
level
="
1
"
n
="
348
">
<
head
xml:id
="
echoid-head375
"
xml:space
="
preserve
">SCHOLIVM.</
head
>
<
p
>
<
s
xml:id
="
echoid-s15849
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Qvia</
emph
>
ergo Natura non impedita agit per lineas breuiſsimas; </
s
>
<
s
xml:id
="
echoid-s15850
"
xml:space
="
preserve
">fit, vtradius
<
lb
/>
Solis, vel viſualis cadens ex A, in planum terſum D F, ita vt reflectatur ad </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>