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
121
122
123
399
124
400
125
401
126
402
127
403
128
404
129
130
131
132
133
134
135
136
137
138
139
140
413
141
414
142
415
143
416
144
417
145
418
146
419
147
420
148
421
149
422
150
423
<
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
|<
<
(403)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div132
"
type
="
section
"
level
="
1
"
n
="
57
">
<
pb
o
="
403
"
file
="
0119
"
n
="
127
"
rhead
="
ILLUST. QUORUND. PROB. CONSTRUCT.
"/>
<
p
>
<
s
xml:id
="
echoid-s2594
"
xml:space
="
preserve
">Illud autem hic aliter eſt oſtendendum, quod ad lineam
<
lb
/>
H E poni poteſt A E ipſi G æqualis. </
s
>
<
s
xml:id
="
echoid-s2595
"
xml:space
="
preserve
">Sit R S æqualis R B,
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2596
"
xml:space
="
preserve
">jungatur A S. </
s
>
<
s
xml:id
="
echoid-s2597
"
xml:space
="
preserve
">Quoniam igitur in triangulo B A S à ver-
<
lb
/>
tice ad mediam baſin ducta eſt A R, erunt quadrata B R
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s2598
"
xml:space
="
preserve
">R A ſimul ſumpta, hoc eſt, quadratum B A cum duplo
<
lb
/>
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0119-01
"
xlink:href
="
note-0119-01a
"
xml:space
="
preserve
">per 122.
<
lb
/>
lib.7. Pappi.</
note
>
quadrato A R, ſubdupla quadratorum B A, A S . </
s
>
<
s
xml:id
="
echoid-s2599
"
xml:space
="
preserve
">Itaque quadratum A B duplum cum quadruplo quadrato A R, hoc
<
lb
/>
eſt, cum quadrato R L, æquabitur quadratis B A, A S.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2600
"
xml:space
="
preserve
">Quare ablato utrimque quadrato B A, erit quadratum A S
<
lb
/>
æquale quadratis B A & </
s
>
<
s
xml:id
="
echoid-s2601
"
xml:space
="
preserve
">R L, ac proinde minus quam quadr. </
s
>
<
s
xml:id
="
echoid-s2602
"
xml:space
="
preserve
">
<
lb
/>
A H; </
s
>
<
s
xml:id
="
echoid-s2603
"
xml:space
="
preserve
">nam hoc æquale eſt quadratis A B & </
s
>
<
s
xml:id
="
echoid-s2604
"
xml:space
="
preserve
">G. </
s
>
<
s
xml:id
="
echoid-s2605
"
xml:space
="
preserve
">Eſt igitur
<
lb
/>
A S minor quam A H. </
s
>
<
s
xml:id
="
echoid-s2606
"
xml:space
="
preserve
">Sed major eſt quam A R. </
s
>
<
s
xml:id
="
echoid-s2607
"
xml:space
="
preserve
">Ergo pun-
<
lb
/>
ctum S cadit inter R & </
s
>
<
s
xml:id
="
echoid-s2608
"
xml:space
="
preserve
">H; </
s
>
<
s
xml:id
="
echoid-s2609
"
xml:space
="
preserve
">angulus enim A R H obtuſus
<
lb
/>
eſt. </
s
>
<
s
xml:id
="
echoid-s2610
"
xml:space
="
preserve
">Major itaque eſt R H quam R S vel R B. </
s
>
<
s
xml:id
="
echoid-s2611
"
xml:space
="
preserve
">Et quum
<
lb
/>
propter triangulos ſimiles ſit R H ad H P ut R B ad B A,
<
lb
/>
erit quoque H P major quam B A; </
s
>
<
s
xml:id
="
echoid-s2612
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2613
"
xml:space
="
preserve
">quadratum H P ma-
<
lb
/>
jus quadrato A B. </
s
>
<
s
xml:id
="
echoid-s2614
"
xml:space
="
preserve
">At quadratum H P cum quadrato P A
<
lb
/>
æquatur quadrato A H, hoc eſt, quadratis B A & </
s
>
<
s
xml:id
="
echoid-s2615
"
xml:space
="
preserve
">G. </
s
>
<
s
xml:id
="
echoid-s2616
"
xml:space
="
preserve
">Er-
<
lb
/>
go cum quadratum H P ſit majus quadrato A B, erit invi-
<
lb
/>
cem quadr. </
s
>
<
s
xml:id
="
echoid-s2617
"
xml:space
="
preserve
">P A minus quam quadr. </
s
>
<
s
xml:id
="
echoid-s2618
"
xml:space
="
preserve
">G. </
s
>
<
s
xml:id
="
echoid-s2619
"
xml:space
="
preserve
">Patet igitur quod
<
lb
/>
ſi centro A circumferentia deſcribatur radio A E ipſi G æ-
<
lb
/>
quali, ea lineam H E ſecabit.</
s
>
<
s
xml:id
="
echoid-s2620
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div137
"
type
="
section
"
level
="
1
"
n
="
58
">
<
head
xml:id
="
echoid-head87
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Probl.</
emph
>
VIII.</
head
>
<
head
xml:id
="
echoid-head88
"
style
="
it
"
xml:space
="
preserve
">In Conchoide linea invenire confinia
<
lb
/>
flexus contrarii.</
head
>
<
p
>
<
s
xml:id
="
echoid-s2621
"
xml:space
="
preserve
">Conchoidem intelligimus quam Nicomedes excogitavit;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2622
"
xml:space
="
preserve
">
<
note
position
="
right
"
xlink:label
="
note-0119-02
"
xlink:href
="
note-0119-02a
"
xml:space
="
preserve
">TAB. XLII.
<
lb
/>
Fig. 5.</
note
>
quâ & </
s
>
<
s
xml:id
="
echoid-s2623
"
xml:space
="
preserve
">angulum diviſit trifariam, & </
s
>
<
s
xml:id
="
echoid-s2624
"
xml:space
="
preserve
">duas medias invenit
<
lb
/>
proportionales: </
s
>
<
s
xml:id
="
echoid-s2625
"
xml:space
="
preserve
">Eſto ea C Q D, polus G, regula autem
<
lb
/>
A B cujus ope deſcripta eſt; </
s
>
<
s
xml:id
="
echoid-s2626
"
xml:space
="
preserve
">quam ſecet G Q ad angulos
<
lb
/>
rectos. </
s
>
<
s
xml:id
="
echoid-s2627
"
xml:space
="
preserve
">Hæc igitur lineæ proprietas eſt, ut ductâ ad ipſam
<
lb
/>
rectâ qualibet ex G puncto, pars hujus inter conchoidem & </
s
>
<
s
xml:id
="
echoid-s2628
"
xml:space
="
preserve
">
<
lb
/>
rectam A B intercepta ſit ipſi A Q æqualis.</
s
>
<
s
xml:id
="
echoid-s2629
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2630
"
xml:space
="
preserve
">Quum autem appareat partem quandam Conchoidis ut in
<
lb
/>
ſchemate ſubjecto C Q D verſus polum G cavam eſſe, </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>