Clavius, Christoph
,
Geometria practica
Text
Text Image
Image
XML
Thumbnail overview
Document information
None
Concordance
Notes
Handwritten
Figures
Content
Thumbnails
Page concordance
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
>
Scan
Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
1.
30
2
31
32
33
3
34
4
35
5
36
6
37
7
38
8
39
9
40
10
<
1 - 30
31 - 60
61 - 90
91 - 120
121 - 150
151 - 180
181 - 210
211 - 240
241 - 270
271 - 300
301 - 330
331 - 360
361 - 390
391 - 420
421 - 450
>
page
|<
<
(97)
of 450
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div237
"
type
="
section
"
level
="
1
"
n
="
106
">
<
pb
o
="
97
"
file
="
127
"
n
="
127
"
rhead
="
LIBER TERTIVS.
"/>
<
p
>
<
s
xml:id
="
echoid-s3686
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Si</
emph
>
autem dioptra per C, tranſierit, erit
<
lb
/>
altitudo A E, diſtantiæ quęſitæ E H, æqua-
<
lb
/>
<
figure
xlink:label
="
fig-127-01
"
xlink:href
="
fig-127-01a
"
number
="
55
">
<
image
file
="
127-01
"
xlink:href
="
http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/127-01
"/>
</
figure
>
lis: </
s
>
<
s
xml:id
="
echoid-s3687
"
xml:space
="
preserve
"> cum ſit vt AD, ad DC, æqualem,
<
note
symbol
="
a
"
position
="
right
"
xlink:label
="
note-127-01
"
xlink:href
="
note-127-01a
"
xml:space
="
preserve
">4. ſexti.</
note
>
A E, ad EH.</
s
>
<
s
xml:id
="
echoid-s3688
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3689
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Si</
emph
>
denique vmbra abſciſſa fuerit ver-
<
lb
/>
ſa, vt BK, erit altitudo AE, minor, quam
<
lb
/>
diſtantia E F, quod plerunq; </
s
>
<
s
xml:id
="
echoid-s3690
"
xml:space
="
preserve
">in diſtantiis
<
lb
/>
w
<
unsure
/>
etiendis accidere ſolet; </
s
>
<
s
xml:id
="
echoid-s3691
"
xml:space
="
preserve
">eritq; </
s
>
<
s
xml:id
="
echoid-s3692
"
xml:space
="
preserve
">triangu-
<
lb
/>
lum ABK, triangulo AEF, æquiangulum,
<
lb
/>
cum anguli B, E, recti ſint, & </
s
>
<
s
xml:id
="
echoid-s3693
"
xml:space
="
preserve
">
<
note
symbol
="
b
"
position
="
right
"
xlink:label
="
note-127-02
"
xlink:href
="
note-127-02a
"
xml:space
="
preserve
">29. primi.</
note
>
BAK, AFE, æquales. </
s
>
<
s
xml:id
="
echoid-s3694
"
xml:space
="
preserve
"> Quare ſi fiat,</
s
>
</
p
>
<
note
symbol
="
c
"
position
="
right
"
xml:space
="
preserve
">4. ſexti.</
note
>
<
note
style
="
it
"
position
="
right
"
xml:space
="
preserve
">
<
lb
/>
Vt part{es} vmbræ \\ verſæ BK, # ad lat{us} quadrati \\ AB, 1000. # Ita altitudo no- \\ ta AE, # ad E F, diſtan- \\ tiam,
<
lb
/>
</
note
>
<
p
>
<
s
xml:id
="
echoid-s3695
"
xml:space
="
preserve
">producetur quæſita diſtantia EF, in partibus altitudinis erectæ AE.</
s
>
<
s
xml:id
="
echoid-s3696
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3697
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s3698
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Qvando</
emph
>
diſtantia non valdè magna eſt, vel extremum eius punctum
<
lb
/>
facilè videri poteſt ſatis erit, ſi qua dratum ſupra planum Horizontis con-
<
lb
/>
ſtituatur, ita vt vmbrę verſę latus B C, ad punctum illud recta vergat. </
s
>
<
s
xml:id
="
echoid-s3699
"
xml:space
="
preserve
">Vt ſi di-
<
lb
/>
ſtantia horizontalis D M, metienda ſit, eique imponatur Quadratum erectum,
<
lb
/>
mouenda eſt dioptra, donec linea fiduciæ in extremum M, dirigatur. </
s
>
<
s
xml:id
="
echoid-s3700
"
xml:space
="
preserve
">Quara-
<
lb
/>
tione ſemper vmbra verſa BC, abſcindetur. </
s
>
<
s
xml:id
="
echoid-s3701
"
xml:space
="
preserve
">Nam ſi linea fiducię per C, tranſi-
<
lb
/>
ret, aut vmbramrectam C D, interſecaret, eſſet diſtantia vel æqualis lateri C D,
<
lb
/>
vel minor: </
s
>
<
s
xml:id
="
echoid-s3702
"
xml:space
="
preserve
">ac proinde dimenſione nonindigeret. </
s
>
<
s
xml:id
="
echoid-s3703
"
xml:space
="
preserve
">Quoniam igitur rurſus trian-
<
lb
/>
gulum NBA, triangulo A D M, ęquiangulum eſt, propter rectos angulos B,
<
lb
/>
D, & </
s
>
<
s
xml:id
="
echoid-s3704
"
xml:space
="
preserve
">alternos æquales BAN, AMD; </
s
>
<
s
xml:id
="
echoid-s3705
"
xml:space
="
preserve
"> Si fiat,</
s
>
</
p
>
<
note
symbol
="
d
"
position
="
right
"
xml:space
="
preserve
">29. primi.</
note
>
<
note
symbol
="
e
"
position
="
right
"
xml:space
="
preserve
">4. ſexti.</
note
>
<
note
style
="
it
"
position
="
right
"
xml:space
="
preserve
">
<
lb
/>
Vt part{es} vmbræ \\ verſæ BN, # ad lat{us} quadrati \\ AB, 1000. # Ita lat{us} quadrati \\ AD, 1000. # ad DM, diſtan- \\ tiam,
<
lb
/>
</
note
>
<
p
>
<
s
xml:id
="
echoid-s3706
"
xml:space
="
preserve
">cognita erit diſtantia DM, in partibus milleſimis Iateris quadrati AD.</
s
>
<
s
xml:id
="
echoid-s3707
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3708
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s3709
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Solent</
emph
>
nonnulli Scriptores non inquirere diſtantiam propoſitam in
<
lb
/>
partibus altitudinis aſſumptę AE, vel in partibus milleſimis lateris quadrati AD;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s3710
"
xml:space
="
preserve
">ſed ſolum inueſtigant, quoties altitudo electa AE, vellatus quadrati AD, in di-
<
lb
/>
ſtantia propoſita contineatur: </
s
>
<
s
xml:id
="
echoid-s3711
"
xml:space
="
preserve
">quod idem eſt, ac ſi altitudo, autlatus vmbræ
<
lb
/>
ſtatuatur 1. </
s
>
<
s
xml:id
="
echoid-s3712
"
xml:space
="
preserve
">Atq; </
s
>
<
s
xml:id
="
echoid-s3713
"
xml:space
="
preserve
">ita diuidunt vel partes vmbrę rectę abſciſſas per totum latus
<
lb
/>
partium 1000. </
s
>
<
s
xml:id
="
echoid-s3714
"
xml:space
="
preserve
">vel totum latus vmbræ verſæ per partes vmbrę verſę abſciſlas. </
s
>
<
s
xml:id
="
echoid-s3715
"
xml:space
="
preserve
">
<
lb
/>
Nam Quotiens numerus indicat, quoties altitudo A C, vel latus Quadrati in
<
lb
/>
propoſita diſtantia comprehendatur: </
s
>
<
s
xml:id
="
echoid-s3716
"
xml:space
="
preserve
">cum ſit,</
s
>
</
p
>
<
note
style
="
it
"
position
="
right
"
xml:space
="
preserve
">
<
lb
/>
Vt totum lat{us} A D, \\ partium 1000. # ad part{es} vmbræ \\ rectæ D I, # ita altitudo A E, vel la- \\ t{us} A D, vt 1. # ad diſtantiam \\ E G, vel D I.
<
lb
/>
</
note
>
<
note
style
="
it
"
position
="
right
"
xml:space
="
preserve
">
<
lb
/>
#### Item.
<
lb
/>
Vt part{es} vmbræ ver- \\ ſæ B N, # ad totum lat{us} AB, \\ 1000. # Ita altitudo A E, vel \\ lat{us} AD, vt 1. # ad diſtantiam \\ EF, vel DM,
<
lb
/>
</
note
>
<
p
>
<
s
xml:id
="
echoid-s3717
"
xml:space
="
preserve
">Hinc enim fit, vt cum ſecundum pręceptum regulę trium tertius numerus in ſe-
<
lb
/>
cundum ſit ducendus, productuſq; </
s
>
<
s
xml:id
="
echoid-s3718
"
xml:space
="
preserve
">numerus per primum diuidendus, ſatis ſit,
<
lb
/>
ſi ſecundus per primum diuidatur: </
s
>
<
s
xml:id
="
echoid-s3719
"
xml:space
="
preserve
">quando quidem vnitas in tertio loco poſita,
<
lb
/>
ſi multiplicet ſecundum numerum, eundem ſecundum numerum procreat, &</
s
>
<
s
xml:id
="
echoid-s3720
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s3721
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s3722
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Hac</
emph
>
ratione, ſi duæ paites milleſimę abſcindantur ex vmbra verſa, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>