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
41
332
42
333
43
334
44
335
45
336
46
337
47
338
48
339
49
340
50
51
52
53
54
55
56
344
57
345
58
346
59
347
60
348
61
349
62
350
63
64
65
66
67
68
69
70
358
<
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
|<
<
(334)
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-s635
"
xml:space
="
preserve
">
<
pb
o
="
334
"
file
="
0040
"
n
="
43
"
rhead
="
ΕΞΕΤΑΣΙΣ CYCLOM.
"/>
per ea quidem quæ nos adhuc docuit V. </
s
>
<
s
xml:id
="
echoid-s636
"
xml:space
="
preserve
">Cl. </
s
>
<
s
xml:id
="
echoid-s637
"
xml:space
="
preserve
">inveniri non
<
lb
/>
poſſe. </
s
>
<
s
xml:id
="
echoid-s638
"
xml:space
="
preserve
">Etenim inventurus ex datis rationibus, ſol. </
s
>
<
s
xml:id
="
echoid-s639
"
xml:space
="
preserve
">Μ Ξ ad
<
lb
/>
ſol. </
s
>
<
s
xml:id
="
echoid-s640
"
xml:space
="
preserve
">Λ Σ, & </
s
>
<
s
xml:id
="
echoid-s641
"
xml:space
="
preserve
">ſolidi Κ Θ ad ſol. </
s
>
<
s
xml:id
="
echoid-s642
"
xml:space
="
preserve
">Δ Γ, rationem tertiam ſo-
<
lb
/>
lidi H Y ad ſol. </
s
>
<
s
xml:id
="
echoid-s643
"
xml:space
="
preserve
">X V, in hunc modum rationcinabitur, ut
<
lb
/>
videre eſt ex demonſtratione prop. </
s
>
<
s
xml:id
="
echoid-s644
"
xml:space
="
preserve
">44. </
s
>
<
s
xml:id
="
echoid-s645
"
xml:space
="
preserve
">ſuprà citatæ, cui hunc
<
lb
/>
caſum convenire liquidò conſtat. </
s
>
<
s
xml:id
="
echoid-s646
"
xml:space
="
preserve
">Dicet enim, Notæ ſunt
<
lb
/>
prima & </
s
>
<
s
xml:id
="
echoid-s647
"
xml:space
="
preserve
">ſecunda ratio, (iſtæ enim ſunt 53 ad 203, & </
s
>
<
s
xml:id
="
echoid-s648
"
xml:space
="
preserve
">5 ad
<
lb
/>
11,) ergo notum quoque quoties prima ſecundam contineat.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s649
"
xml:space
="
preserve
">Sed quoties prima continet ſecundam, toties ſecunda continet
<
lb
/>
tertiam, (hoc aſſerit prop. </
s
>
<
s
xml:id
="
echoid-s650
"
xml:space
="
preserve
">40. </
s
>
<
s
xml:id
="
echoid-s651
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s652
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s653
"
xml:space
="
preserve
">oper. </
s
>
<
s
xml:id
="
echoid-s654
"
xml:space
="
preserve
">Geom.) </
s
>
<
s
xml:id
="
echoid-s655
"
xml:space
="
preserve
">Ergo
<
lb
/>
notum quoque quoties ſecunda tertiam contineat. </
s
>
<
s
xml:id
="
echoid-s656
"
xml:space
="
preserve
">Quare cum
<
lb
/>
nota ſit ſecunda, etiam tertia nota erit, ea nimirum quam
<
lb
/>
habet ſolidum H Y ad ſol. </
s
>
<
s
xml:id
="
echoid-s657
"
xml:space
="
preserve
">X V.</
s
>
<
s
xml:id
="
echoid-s658
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s659
"
xml:space
="
preserve
">Conſequenter hoc nunc definiendum ei incumbet, Quo-
<
lb
/>
ties Ratio harum prima ſecundam contineat; </
s
>
<
s
xml:id
="
echoid-s660
"
xml:space
="
preserve
">hoc eſt, quo-
<
lb
/>
ties ratio 53 ad 203, contineat rationem 5 ad 11. </
s
>
<
s
xml:id
="
echoid-s661
"
xml:space
="
preserve
">Sed enim
<
lb
/>
quo ſenſu verbum continere hîc explicaturus eſt? </
s
>
<
s
xml:id
="
echoid-s662
"
xml:space
="
preserve
">Num eo,
<
lb
/>
ut idem ſignificet quod alibi continere per multiplicationem?
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s663
"
xml:space
="
preserve
">utque ratio 53 ad 203 rationem 5 ad 11. </
s
>
<
s
xml:id
="
echoid-s664
"
xml:space
="
preserve
">multiplicare dica-
<
lb
/>
tur vel bis (hoc eſt ut illa hujus ſit duplicata, ita enim con-
<
lb
/>
tinere intelligendum videtur in propoſitione 40. </
s
>
<
s
xml:id
="
echoid-s665
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s666
"
xml:space
="
preserve
">10,
<
lb
/>
modo citata) vel ter, vel quater, vel ſæpiùs etiam. </
s
>
<
s
xml:id
="
echoid-s667
"
xml:space
="
preserve
">Et hoc
<
lb
/>
quidem eſſe non poteſt; </
s
>
<
s
xml:id
="
echoid-s668
"
xml:space
="
preserve
">nam ratio 53 ad 203, rationis 5
<
lb
/>
ad 11, neque duplicata eſt neque triplicata vel ulterius mul-
<
lb
/>
tiplex, quum demum ratio 53 ad 256 {13/25} ſit duplicata rationis
<
lb
/>
5 ad 11.</
s
>
<
s
xml:id
="
echoid-s669
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s670
"
xml:space
="
preserve
">An igitur verbum Continere in eum ſenſum trahet, quem
<
lb
/>
habet in propoſitione 125. </
s
>
<
s
xml:id
="
echoid-s671
"
xml:space
="
preserve
">lib. </
s
>
<
s
xml:id
="
echoid-s672
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s673
"
xml:space
="
preserve
">Oper. </
s
>
<
s
xml:id
="
echoid-s674
"
xml:space
="
preserve
">Geom.</
s
>
<
s
xml:id
="
echoid-s675
"
xml:space
="
preserve
">? Vix qui-
<
lb
/>
dem illud ſuſpicari poſſum; </
s
>
<
s
xml:id
="
echoid-s676
"
xml:space
="
preserve
">ſed etiamſi vellet rurſus inde
<
lb
/>
abſurdum conſequetur. </
s
>
<
s
xml:id
="
echoid-s677
"
xml:space
="
preserve
">Nam ſecundum interpretationem iſtam;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s678
"
xml:space
="
preserve
">quoties ratio 53 ad 203 continet rationem 5 ad 11, toties
<
lb
/>
hæc ipſa continebit rationem 5075 ad 6413; </
s
>
<
s
xml:id
="
echoid-s679
"
xml:space
="
preserve
">hoc autem pa-
<
lb
/>
tebit horum numerorum inter ſe rationis examinanti ſecun-
<
lb
/>
dùm regulam dictæ propoſitionis 125. </
s
>
<
s
xml:id
="
echoid-s680
"
xml:space
="
preserve
">Eſſet igitur ratio ſoli-
<
lb
/>
di H Y ad ſol. </
s
>
<
s
xml:id
="
echoid-s681
"
xml:space
="
preserve
">X V, hoc eſt, ratio ſegmenti circuli ab ini-
<
lb
/>
tio propoſiti C H G, ad ſegmentum G H E F, eadem </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>