Huygens, Christiaan
,
Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica
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
451 - 480
481 - 510
511 - 540
541 - 568
>
Scan
Original
21
321
22
322
23
323
24
324
25
26
27
28
325
29
326
30
31
32
33
327
34
328
35
36
37
38
329
39
330
40
331
41
332
42
333
43
334
44
335
45
336
46
337
47
338
48
339
49
340
50
<
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
451 - 480
481 - 510
511 - 540
541 - 568
>
page
|<
<
(336)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div41
"
type
="
section
"
level
="
1
"
n
="
18
">
<
p
>
<
s
xml:id
="
echoid-s720
"
xml:space
="
preserve
">
<
pb
o
="
336
"
file
="
0042
"
n
="
45
"
rhead
="
ΕΞΕΤΑΣΙΣ CYCLOM.
"/>
oſtenderat facili negotio deducatur, ut jam ſtatim appa-
<
lb
/>
rebit.</
s
>
<
s
xml:id
="
echoid-s721
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">TAB. XXXVII.
<
lb
/>
Fig. 3.</
note
>
<
p
>
<
s
xml:id
="
echoid-s722
"
xml:space
="
preserve
">Repetitâ enim quatenus hîc neceſſe erit figurâ ipſius, quæ
<
lb
/>
eſt in propoſitione 99. </
s
>
<
s
xml:id
="
echoid-s723
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s724
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s725
"
xml:space
="
preserve
">Eſto Cylindrus Parabolicus,
<
lb
/>
baſes oppoſitas habens parabolas A B D, V C E; </
s
>
<
s
xml:id
="
echoid-s726
"
xml:space
="
preserve
">à quo ſit
<
lb
/>
abſciſſa Ungula A B C D, eâdem baſi & </
s
>
<
s
xml:id
="
echoid-s727
"
xml:space
="
preserve
">altitudine. </
s
>
<
s
xml:id
="
echoid-s728
"
xml:space
="
preserve
">Dico
<
lb
/>
Cylindrum ad hanc Ungulam habere rationem duplam ſeſ-
<
lb
/>
quialteram, ſive quam 5 ad 2.</
s
>
<
s
xml:id
="
echoid-s729
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s730
"
xml:space
="
preserve
">Tranſcriptis enim reliquis ex figura eadem, eſt F B dia-
<
lb
/>
meter parabolæ A B D: </
s
>
<
s
xml:id
="
echoid-s731
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s732
"
xml:space
="
preserve
">lineæ rectæ A B, B D. </
s
>
<
s
xml:id
="
echoid-s733
"
xml:space
="
preserve
">Ductâ
<
lb
/>
porrò B C rectâ in ſuperficie cylindri, ſumptâque ejus quar-
<
lb
/>
tâ parte C Q, abſcinditur plano P Q N ungula P Q C N
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s734
"
xml:space
="
preserve
">junguntur C A, C D. </
s
>
<
s
xml:id
="
echoid-s735
"
xml:space
="
preserve
">Denique toti cylindro adjuncta eſt
<
lb
/>
pyramis A D γ C æqualis parti B X D E C, quæ à cylin-
<
lb
/>
dro abſciſſa eſt plano B D E C. </
s
>
<
s
xml:id
="
echoid-s736
"
xml:space
="
preserve
">Et hactenus quidem ſuffi-
<
lb
/>
ciet nobis conſtructionem Cl. </
s
>
<
s
xml:id
="
echoid-s737
"
xml:space
="
preserve
">V. </
s
>
<
s
xml:id
="
echoid-s738
"
xml:space
="
preserve
">repetiiſſe. </
s
>
<
s
xml:id
="
echoid-s739
"
xml:space
="
preserve
">Demonſtravit
<
lb
/>
autem hæc duo quæ ſequuntur, ſicut videre eſt in dicta prop.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s740
"
xml:space
="
preserve
">99. </
s
>
<
s
xml:id
="
echoid-s741
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s742
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s743
"
xml:space
="
preserve
">Nimirum quod ungula A B C D eſt ad ungulam
<
lb
/>
P Q C N, ſicut 32 ad 1. </
s
>
<
s
xml:id
="
echoid-s744
"
xml:space
="
preserve
">Item quod hæc ungula P Q C N
<
lb
/>
eſt ad pyramidem totam A γ D B C, (quæ compoſita eſt
<
lb
/>
ex duabus pyramidibus A D B C & </
s
>
<
s
xml:id
="
echoid-s745
"
xml:space
="
preserve
">A D γ C) ut 1 ad
<
lb
/>
30.</
s
>
<
s
xml:id
="
echoid-s746
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s747
"
xml:space
="
preserve
">Erit igitur ex æquo ungula A B C D ad pyramidem
<
lb
/>
A γ D B C ut 32 ad 30, hoc eſt, ut 16 ad 15. </
s
>
<
s
xml:id
="
echoid-s748
"
xml:space
="
preserve
">Porrò cùm
<
lb
/>
parabolæ A B D octava pars ſit ſegmentum B D X, erit
<
lb
/>
quoque ſegmentum ſolidum B X D E C vel huic æqualis
<
lb
/>
pyramis A D γ C, octava pars cylindri totius parabolici
<
lb
/>
A V C E D B: </
s
>
<
s
xml:id
="
echoid-s749
"
xml:space
="
preserve
">ſed pyramis altera A D B C æquatur dua-
<
lb
/>
bus octavis ſive uni quartæ ejuſdem parabolici cylindri; </
s
>
<
s
xml:id
="
echoid-s750
"
xml:space
="
preserve
">(eſt
<
lb
/>
enim ipſa tertia pars ſui priſmatis, quod æquale eſt tribus
<
lb
/>
quartis cylindri iſtius, ut ex quadratura parabolæ conſtat)
<
lb
/>
ergo tota pyramis A γ D B C tribus octavis æquatur cylin-
<
lb
/>
dri parab. </
s
>
<
s
xml:id
="
echoid-s751
"
xml:space
="
preserve
">A V C E D B. </
s
>
<
s
xml:id
="
echoid-s752
"
xml:space
="
preserve
">Cylindrus igitur parabolicus
<
lb
/>
A V C E D B erit ad pyramidem A γ D B C, ut 8 ad 3,
<
lb
/>
hoc eſt, ut 40 ad 15; </
s
>
<
s
xml:id
="
echoid-s753
"
xml:space
="
preserve
">ſed oſtenſum eſt eandem pyramidem
<
lb
/>
A γ D B C eſſe ad ungulam A B C D ut 15 ad 16. </
s
>
<
s
xml:id
="
echoid-s754
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>