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
List of thumbnails
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 568
>
121
122
123
(399)
124
(400)
125
(401)
126
(402)
127
(403)
128
(404)
129
130
<
1 - 10
11 - 20
21 - 30
31 - 40
41 - 50
51 - 60
61 - 70
71 - 80
81 - 90
91 - 100
101 - 110
111 - 120
121 - 130
131 - 140
141 - 150
151 - 160
161 - 170
171 - 180
181 - 190
191 - 200
201 - 210
211 - 220
221 - 230
231 - 240
241 - 250
251 - 260
261 - 270
271 - 280
281 - 290
291 - 300
301 - 310
311 - 320
321 - 330
331 - 340
341 - 350
351 - 360
361 - 370
371 - 380
381 - 390
391 - 400
401 - 410
411 - 420
421 - 430
431 - 440
441 - 450
451 - 460
461 - 470
471 - 480
481 - 490
491 - 500
501 - 510
511 - 520
521 - 530
531 - 540
541 - 550
551 - 560
561 - 568
>
page
|<
<
(402)
of 568
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div132
"
type
="
section
"
level
="
1
"
n
="
57
">
<
p
>
<
s
xml:id
="
echoid-s2539
"
xml:space
="
preserve
">
<
pb
o
="
402
"
file
="
0118
"
n
="
126
"
rhead
="
CHRISTIANI HUGENII
"/>
hinc manifeſtum eſt. </
s
>
<
s
xml:id
="
echoid-s2540
"
xml:space
="
preserve
">Etenim quadratum A H majus eſt
<
lb
/>
quadratis A X & </
s
>
<
s
xml:id
="
echoid-s2541
"
xml:space
="
preserve
">X H, quum ſit angulus A X H obtuſus.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2542
"
xml:space
="
preserve
">Sed idem quadratum A H æquale ponitur quadratis A B ſeu
<
lb
/>
H X & </
s
>
<
s
xml:id
="
echoid-s2543
"
xml:space
="
preserve
">G. </
s
>
<
s
xml:id
="
echoid-s2544
"
xml:space
="
preserve
">Itaque quadratum G ſeu A E majus eſt quadrato
<
lb
/>
A X. </
s
>
<
s
xml:id
="
echoid-s2545
"
xml:space
="
preserve
">Unde apparet interſectionem E accidere inter puncta
<
lb
/>
H & </
s
>
<
s
xml:id
="
echoid-s2546
"
xml:space
="
preserve
">X.</
s
>
<
s
xml:id
="
echoid-s2547
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2548
"
xml:space
="
preserve
">Producatur B D & </
s
>
<
s
xml:id
="
echoid-s2549
"
xml:space
="
preserve
">ponatur ipſi æqualis D R. </
s
>
<
s
xml:id
="
echoid-s2550
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2551
"
xml:space
="
preserve
">ſit R K
<
lb
/>
parallela D A vel B C, eique occurrant productæ F A,
<
lb
/>
B A, H E, in punctis M, Q, K: </
s
>
<
s
xml:id
="
echoid-s2552
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2553
"
xml:space
="
preserve
">jungatur R A, & </
s
>
<
s
xml:id
="
echoid-s2554
"
xml:space
="
preserve
">
<
lb
/>
producatur ad P.</
s
>
<
s
xml:id
="
echoid-s2555
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2556
"
xml:space
="
preserve
">Quoniam igitur D R æqualis eſt D B, & </
s
>
<
s
xml:id
="
echoid-s2557
"
xml:space
="
preserve
">R Q K paral-
<
lb
/>
lela D A, erit & </
s
>
<
s
xml:id
="
echoid-s2558
"
xml:space
="
preserve
">M A æqualis A N, & </
s
>
<
s
xml:id
="
echoid-s2559
"
xml:space
="
preserve
">Q A æqualis A B;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2560
"
xml:space
="
preserve
">angulus autem B A R rectus, quum ſit in ſemicirculo,
<
lb
/>
nam tres hæ æquales ſunt D B, D A, D R. </
s
>
<
s
xml:id
="
echoid-s2561
"
xml:space
="
preserve
">Parallelæ au-
<
lb
/>
tem ſunt B Q, H E K, ergo & </
s
>
<
s
xml:id
="
echoid-s2562
"
xml:space
="
preserve
">anguli ad P recti, & </
s
>
<
s
xml:id
="
echoid-s2563
"
xml:space
="
preserve
">erit
<
lb
/>
H P æqualis P K. </
s
>
<
s
xml:id
="
echoid-s2564
"
xml:space
="
preserve
">Eſt itaque quadratum A H æquale qua-
<
lb
/>
drato A E unà cum rectangulo H E K . </
s
>
<
s
xml:id
="
echoid-s2565
"
xml:space
="
preserve
">Sed idem
<
note
symbol
="
*
"
position
="
left
"
xlink:label
="
note-0118-01
"
xlink:href
="
note-0118-01a
"
xml:space
="
preserve
">12.2 Elem.</
note
>
tum A H æquale eſt etiam quadratis ex G ſeu A E, & </
s
>
<
s
xml:id
="
echoid-s2566
"
xml:space
="
preserve
">ex
<
lb
/>
A B. </
s
>
<
s
xml:id
="
echoid-s2567
"
xml:space
="
preserve
">Itaque quadr. </
s
>
<
s
xml:id
="
echoid-s2568
"
xml:space
="
preserve
">A B æquale erit rectangulo K E H.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2569
"
xml:space
="
preserve
">Ac propterea K E ad A B ut A B ad E H. </
s
>
<
s
xml:id
="
echoid-s2570
"
xml:space
="
preserve
">Verum ut K E
<
lb
/>
ad A B ſeu Q A ita eſt E M ad M A: </
s
>
<
s
xml:id
="
echoid-s2571
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2572
"
xml:space
="
preserve
">ut A B ad E H
<
lb
/>
ita A F ad F E. </
s
>
<
s
xml:id
="
echoid-s2573
"
xml:space
="
preserve
">Igitur E M ad M A ut A F ad F E: </
s
>
<
s
xml:id
="
echoid-s2574
"
xml:space
="
preserve
">Et
<
lb
/>
proinde E A ad A M ut E A ad E F. </
s
>
<
s
xml:id
="
echoid-s2575
"
xml:space
="
preserve
">Æqualis eſt igi-
<
lb
/>
tur E F ipſi A M; </
s
>
<
s
xml:id
="
echoid-s2576
"
xml:space
="
preserve
">quare & </
s
>
<
s
xml:id
="
echoid-s2577
"
xml:space
="
preserve
">ipſi A N. </
s
>
<
s
xml:id
="
echoid-s2578
"
xml:space
="
preserve
">Ideoque & </
s
>
<
s
xml:id
="
echoid-s2579
"
xml:space
="
preserve
">F N
<
lb
/>
ipſi A E, hoc eſt, datæ G. </
s
>
<
s
xml:id
="
echoid-s2580
"
xml:space
="
preserve
">Quod erat demonſtrandum.</
s
>
<
s
xml:id
="
echoid-s2581
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2582
"
xml:space
="
preserve
">Sit denuo datus rhomdus A D B C, cujus producta la-
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0118-02
"
xlink:href
="
note-0118-02a
"
xml:space
="
preserve
">TAB. XLII.
<
lb
/>
Fig. 4.</
note
>
tera B D, B C; </
s
>
<
s
xml:id
="
echoid-s2583
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2584
"
xml:space
="
preserve
">data ſit linea G. </
s
>
<
s
xml:id
="
echoid-s2585
"
xml:space
="
preserve
">Oportet ducere re-
<
lb
/>
ctam N F tranſeuntem per angulum A, quæque æqualis ſit
<
lb
/>
ipſi G.</
s
>
<
s
xml:id
="
echoid-s2586
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2587
"
xml:space
="
preserve
">Ducatur diameter B A, eique ad angulos rectos R A L.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2588
"
xml:space
="
preserve
">Si igitur G minor detur quam R L, problema conſtrui ne-
<
lb
/>
quit, uti ſupra quoque dictum fuit. </
s
>
<
s
xml:id
="
echoid-s2589
"
xml:space
="
preserve
">Si vero æqualis, jam fa-
<
lb
/>
ctum eſt quod quærebatur. </
s
>
<
s
xml:id
="
echoid-s2590
"
xml:space
="
preserve
">Sit igitur G major quam R L. </
s
>
<
s
xml:id
="
echoid-s2591
"
xml:space
="
preserve
">
<
lb
/>
Erit in ſchemate adjecto, ſicut propoſitum eſt, conſtru-
<
lb
/>
ctio & </
s
>
<
s
xml:id
="
echoid-s2592
"
xml:space
="
preserve
">demonſtratio eadem quæ in caſu præcedenti.</
s
>
<
s
xml:id
="
echoid-s2593
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>