Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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 - 393
>
Scan
Original
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
1
20
2
21
3
22
4
23
5
24
6
25
7
26
8
27
9
28
10
29
11
30
12
<
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 - 393
>
page
|<
<
(44)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div58
"
type
="
section
"
level
="
1
"
n
="
14
">
<
p
>
<
s
xml:id
="
echoid-s2455
"
xml:space
="
preserve
">
<
pb
o
="
44
"
file
="
0062
"
n
="
62
"
rhead
="
"/>
ſimplicibus triplicatas ſubſtituendo rationes, eſt γ Q. </
s
>
<
s
xml:id
="
echoid-s2456
"
xml:space
="
preserve
">QB &</
s
>
<
s
xml:id
="
echoid-s2457
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s2458
"
xml:space
="
preserve
">YP .
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2459
"
xml:space
="
preserve
">PB. </
s
>
<
s
xml:id
="
echoid-s2460
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2461
"
xml:space
="
preserve
">his æquales rationes adjungendo eſt QN. </
s
>
<
s
xml:id
="
echoid-s2462
"
xml:space
="
preserve
">γ Q + γ Q. </
s
>
<
s
xml:id
="
echoid-s2463
"
xml:space
="
preserve
">QB&</
s
>
<
s
xml:id
="
echoid-s2464
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s2465
"
xml:space
="
preserve
">
<
lb
/>
PN . </
s
>
<
s
xml:id
="
echoid-s2466
"
xml:space
="
preserve
">YP + YP. </
s
>
<
s
xml:id
="
echoid-s2467
"
xml:space
="
preserve
">PB; </
s
>
<
s
xml:id
="
echoid-s2468
"
xml:space
="
preserve
">hoc eſt QN. </
s
>
<
s
xml:id
="
echoid-s2469
"
xml:space
="
preserve
">QB &</
s
>
<
s
xml:id
="
echoid-s2470
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s2471
"
xml:space
="
preserve
">PN. </
s
>
<
s
xml:id
="
echoid-s2472
"
xml:space
="
preserve
">PB. </
s
>
<
s
xml:id
="
echoid-s2473
"
xml:space
="
preserve
">compo-
<
lb
/>
nendóque BN. </
s
>
<
s
xml:id
="
echoid-s2474
"
xml:space
="
preserve
">QB &</
s
>
<
s
xml:id
="
echoid-s2475
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s2476
"
xml:space
="
preserve
">BN. </
s
>
<
s
xml:id
="
echoid-s2477
"
xml:space
="
preserve
">P B. </
s
>
<
s
xml:id
="
echoid-s2478
"
xml:space
="
preserve
">ergo QB &</
s
>
<
s
xml:id
="
echoid-s2479
"
xml:space
="
preserve
">lt; </
s
>
<
s
xml:id
="
echoid-s2480
"
xml:space
="
preserve
">PB. </
s
>
<
s
xml:id
="
echoid-s2481
"
xml:space
="
preserve
">unde rurſus
<
lb
/>
liquet rectam X Qipſis AB; </
s
>
<
s
xml:id
="
echoid-s2482
"
xml:space
="
preserve
">ZP interjacere: </
s
>
<
s
xml:id
="
echoid-s2483
"
xml:space
="
preserve
">Q. </
s
>
<
s
xml:id
="
echoid-s2484
"
xml:space
="
preserve
">E. </
s
>
<
s
xml:id
="
echoid-s2485
"
xml:space
="
preserve
">D.</
s
>
<
s
xml:id
="
echoid-s2486
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2487
"
xml:space
="
preserve
">XVII. </
s
>
<
s
xml:id
="
echoid-s2488
"
xml:space
="
preserve
">Conſimili prorſus argumentatione conſtabit obliquio-
<
lb
/>
rum incidentium refractos ultra punctum Z ipſam KN interſe-
<
lb
/>
care.</
s
>
<
s
xml:id
="
echoid-s2489
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2490
"
xml:space
="
preserve
">XVIII. </
s
>
<
s
xml:id
="
echoid-s2491
"
xml:space
="
preserve
">Quinimò rurſus exertiùs apparet non niſi binos refractos
<
lb
/>
in eodem puncto convenire.</
s
>
<
s
xml:id
="
echoid-s2492
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2493
"
xml:space
="
preserve
">XI X. </
s
>
<
s
xml:id
="
echoid-s2494
"
xml:space
="
preserve
">Addo cum ipſo KN concurrentes refractos circa punctum
<
lb
/>
Z conglomerari, præſertim illos, qui ad partes F (obliquius) inci-
<
lb
/>
dentes pertinent.</
s
>
<
s
xml:id
="
echoid-s2495
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2496
"
xml:space
="
preserve
">Nam accipiantur, exempli causâ, ſibi pares N S, ST ; </
s
>
<
s
xml:id
="
echoid-s2497
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2498
"
xml:space
="
preserve
">ſit BP
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0062-01
"
xlink:href
="
note-0062-01a
"
xml:space
="
preserve
">Fig. 61.</
note
>
quarta proportionalis in ratione YB ad BN; </
s
>
<
s
xml:id
="
echoid-s2499
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2500
"
xml:space
="
preserve
">BQ quarta proportionalis
<
lb
/>
in ratione YB ad BS; </
s
>
<
s
xml:id
="
echoid-s2501
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2502
"
xml:space
="
preserve
">BR itidem quarta talis in ratione YB ad
<
lb
/>
BT; </
s
>
<
s
xml:id
="
echoid-s2503
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2504
"
xml:space
="
preserve
">à punctis P, Q, R erectæ perpendiculares ipſam NKZ
<
lb
/>
ſecent in Z, X, & </
s
>
<
s
xml:id
="
echoid-s2505
"
xml:space
="
preserve
">V. </
s
>
<
s
xml:id
="
echoid-s2506
"
xml:space
="
preserve
">patet (è mox oſtenſis) omnium ſpatio NS
<
lb
/>
incidentium refractos cum NK concurrere intra ZX; </
s
>
<
s
xml:id
="
echoid-s2507
"
xml:space
="
preserve
">nec non omnes
<
lb
/>
ipſi ST incidentium refractos intra XV cum eodem convenire. </
s
>
<
s
xml:id
="
echoid-s2508
"
xml:space
="
preserve
">por-
<
lb
/>
rò rectæ BP , BQ, BR ſe habent invicem ut _Cubi_ rectarum BN,
<
lb
/>
BS, BT, ( vel ſunt in ipſarum BN, BS, BT _ratione triplicata_ : </
s
>
<
s
xml:id
="
echoid-s2509
"
xml:space
="
preserve
">nam
<
lb
/>
BP. </
s
>
<
s
xml:id
="
echoid-s2510
"
xml:space
="
preserve
">YB :</
s
>
<
s
xml:id
="
echoid-s2511
"
xml:space
="
preserve
">: BN cub. </
s
>
<
s
xml:id
="
echoid-s2512
"
xml:space
="
preserve
">BY cub. </
s
>
<
s
xml:id
="
echoid-s2513
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2514
"
xml:space
="
preserve
">YB . </
s
>
<
s
xml:id
="
echoid-s2515
"
xml:space
="
preserve
">BQ :</
s
>
<
s
xml:id
="
echoid-s2516
"
xml:space
="
preserve
">: YB cub. </
s
>
<
s
xml:id
="
echoid-s2517
"
xml:space
="
preserve
">BS cub.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2518
"
xml:space
="
preserve
">adeóque ex æquo BP. </
s
>
<
s
xml:id
="
echoid-s2519
"
xml:space
="
preserve
">BQ :</
s
>
<
s
xml:id
="
echoid-s2520
"
xml:space
="
preserve
">: BN cub . </
s
>
<
s
xml:id
="
echoid-s2521
"
xml:space
="
preserve
">BS cub. </
s
>
<
s
xml:id
="
echoid-s2522
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2523
"
xml:space
="
preserve
">conſimili ratione
<
lb
/>
BP. </
s
>
<
s
xml:id
="
echoid-s2524
"
xml:space
="
preserve
">BR :</
s
>
<
s
xml:id
="
echoid-s2525
"
xml:space
="
preserve
">: BN cub. </
s
>
<
s
xml:id
="
echoid-s2526
"
xml:space
="
preserve
">BT cub.) </
s
>
<
s
xml:id
="
echoid-s2527
"
xml:space
="
preserve
">undè faciiè monſtrabitur eſſe PQ
<
lb
/>
multo minorem quàm QR; </
s
>
<
s
xml:id
="
echoid-s2528
"
xml:space
="
preserve
">xel ZX quàm XV (verbis parco multis
<
lb
/>
in re ſatis manifeſta) . </
s
>
<
s
xml:id
="
echoid-s2529
"
xml:space
="
preserve
">quare dicti refracti circa punctum Z ſpiſſiùs
<
lb
/>
ipſum NK decuſſabunt.</
s
>
<
s
xml:id
="
echoid-s2530
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s2531
"
xml:space
="
preserve
">XX. </
s
>
<
s
xml:id
="
echoid-s2532
"
xml:space
="
preserve
">Ex his demùm conficitur omnibus bene trutinatis, oculo
<
lb
/>
(O) centrum habenti in refracto NK uſpiam conſtituto, puncti A
<
lb
/>
imaginem ad ipſum conditione præditum toties inſinuatâ punctum Z
<
lb
/>
conſiſtere. </
s
>
<
s
xml:id
="
echoid-s2533
"
xml:space
="
preserve
">Sit enim CD pupillæ (in plano ABC jacens) _Diameter;_
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s2534
"
xml:space
="
preserve
">_axi Optico_ KN perpendicularis; </
s
>
<
s
xml:id
="
echoid-s2535
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s2536
"
xml:space
="
preserve
">per ejus extrema C, D tranſeant
<
lb
/>
refracti IM LR ipſi KN occurrentes punctis X, V. </
s
>
<
s
xml:id
="
echoid-s2537
"
xml:space
="
preserve
">ex oſtenſis patet
<
lb
/>
omnium intra ſpatium MN incidentium radiorum refractos intra ten-
<
lb
/>
minos ZX principalem refractum interſecare; </
s
>
<
s
xml:id
="
echoid-s2538
"
xml:space
="
preserve
">neque non omnes </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>