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
Table of Notes
<
1 - 7
[out of range]
>
[Note]
Page: 207
[Note]
Page: 207
[Note]
Page: 208
[Note]
Page: 208
[Note]
Page: 208
[Note]
Page: 209
[Note]
Page: 210
[Note]
Page: 211
[Note]
Page: 211
[Note]
Page: 212
[Note]
Page: 212
[Note]
Page: 212
[Note]
Page: 214
[Note]
Page: 214
[Note]
Page: 215
[Note]
Page: 217
[Note]
Page: 218
[Note]
Page: 218
[Note]
Page: 219
[Note]
Page: 219
[Note]
Page: 221
[Note]
Page: 222
[Note]
Page: 222
[Note]
Page: 223
[Note]
Page: 223
[Note]
Page: 224
[Note]
Page: 224
[Note]
Page: 225
[Note]
Page: 225
[Note]
Page: 225
<
1 - 7
[out of range]
>
page
|<
<
(56)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div222
"
type
="
section
"
level
="
1
"
n
="
31
">
<
pb
o
="
56
"
file
="
0234
"
n
="
249
"/>
</
div
>
<
div
xml:id
="
echoid-div283
"
type
="
section
"
level
="
1
"
n
="
32
">
<
head
xml:id
="
echoid-head35
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Lect</
emph
>
. VII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s10544
"
xml:space
="
preserve
">ADhuc in _Veſtibulo_ hæremus; </
s
>
<
s
xml:id
="
echoid-s10545
"
xml:space
="
preserve
">nec aliud quàm velitamus.</
s
>
<
s
xml:id
="
echoid-s10546
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10547
"
xml:space
="
preserve
">I. </
s
>
<
s
xml:id
="
echoid-s10548
"
xml:space
="
preserve
">Sint duo quanta A, B; </
s
>
<
s
xml:id
="
echoid-s10549
"
xml:space
="
preserve
">quorum majus A; </
s
>
<
s
xml:id
="
echoid-s10550
"
xml:space
="
preserve
">adſumpto tertio quo-
<
lb
/>
piam X, erit A + X. </
s
>
<
s
xml:id
="
echoid-s10551
"
xml:space
="
preserve
">B + X &</
s
>
<
s
xml:id
="
echoid-s10552
"
xml:space
="
preserve
">lt; </
s
>
<
s
xml:id
="
echoid-s10553
"
xml:space
="
preserve
">A. </
s
>
<
s
xml:id
="
echoid-s10554
"
xml:space
="
preserve
">B.</
s
>
<
s
xml:id
="
echoid-s10555
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10556
"
xml:space
="
preserve
">Nam ob X. </
s
>
<
s
xml:id
="
echoid-s10557
"
xml:space
="
preserve
">A &</
s
>
<
s
xml:id
="
echoid-s10558
"
xml:space
="
preserve
">lt; </
s
>
<
s
xml:id
="
echoid-s10559
"
xml:space
="
preserve
">X. </
s
>
<
s
xml:id
="
echoid-s10560
"
xml:space
="
preserve
">B; </
s
>
<
s
xml:id
="
echoid-s10561
"
xml:space
="
preserve
">erit componendo X + A. </
s
>
<
s
xml:id
="
echoid-s10562
"
xml:space
="
preserve
">A. </
s
>
<
s
xml:id
="
echoid-s10563
"
xml:space
="
preserve
">&</
s
>
<
s
xml:id
="
echoid-s10564
"
xml:space
="
preserve
">lt; </
s
>
<
s
xml:id
="
echoid-s10565
"
xml:space
="
preserve
">X +
<
lb
/>
B. </
s
>
<
s
xml:id
="
echoid-s10566
"
xml:space
="
preserve
">B. </
s
>
<
s
xml:id
="
echoid-s10567
"
xml:space
="
preserve
">vel permutando X + A. </
s
>
<
s
xml:id
="
echoid-s10568
"
xml:space
="
preserve
">X + B &</
s
>
<
s
xml:id
="
echoid-s10569
"
xml:space
="
preserve
">lt; </
s
>
<
s
xml:id
="
echoid-s10570
"
xml:space
="
preserve
">A. </
s
>
<
s
xml:id
="
echoid-s10571
"
xml:space
="
preserve
">B.</
s
>
<
s
xml:id
="
echoid-s10572
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10573
"
xml:space
="
preserve
">II. </
s
>
<
s
xml:id
="
echoid-s10574
"
xml:space
="
preserve
">In linea YZ ſignentur tria puncta, L, M, N; </
s
>
<
s
xml:id
="
echoid-s10575
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s10576
"
xml:space
="
preserve
">inter puncta
<
lb
/>
L, N ſumpto puncto quopiam E, alteróque G extra LN (verſus Z);
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10577
"
xml:space
="
preserve
">ſecetur EG in F, ut ſit GE. </
s
>
<
s
xml:id
="
echoid-s10578
"
xml:space
="
preserve
">EF :</
s
>
<
s
xml:id
="
echoid-s10579
"
xml:space
="
preserve
">: NL. </
s
>
<
s
xml:id
="
echoid-s10580
"
xml:space
="
preserve
">LM; </
s
>
<
s
xml:id
="
echoid-s10581
"
xml:space
="
preserve
">cadet punctum F ad
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0234-01
"
xlink:href
="
note-0234-01a
"
xml:space
="
preserve
">Fig. 61.</
note
>
partes MZ:</
s
>
<
s
xml:id
="
echoid-s10582
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10583
"
xml:space
="
preserve
">Nam eſt N E. </
s
>
<
s
xml:id
="
echoid-s10584
"
xml:space
="
preserve
">ME &</
s
>
<
s
xml:id
="
echoid-s10585
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s10586
"
xml:space
="
preserve
">NL. </
s
>
<
s
xml:id
="
echoid-s10587
"
xml:space
="
preserve
">ML :</
s
>
<
s
xml:id
="
echoid-s10588
"
xml:space
="
preserve
">: GE. </
s
>
<
s
xml:id
="
echoid-s10589
"
xml:space
="
preserve
">FE &</
s
>
<
s
xml:id
="
echoid-s10590
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s10591
"
xml:space
="
preserve
">NE. </
s
>
<
s
xml:id
="
echoid-s10592
"
xml:space
="
preserve
">PE.</
s
>
<
s
xml:id
="
echoid-s10593
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-0234-02
"
xlink:href
="
note-0234-02a
"
xml:space
="
preserve
">* I _hujus_.</
note
>
ergo FE &</
s
>
<
s
xml:id
="
echoid-s10594
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s10595
"
xml:space
="
preserve
">ME.</
s
>
<
s
xml:id
="
echoid-s10596
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10597
"
xml:space
="
preserve
">III. </
s
>
<
s
xml:id
="
echoid-s10598
"
xml:space
="
preserve
">Sint rectæ BA, DC parallelæ item rectæ BD, GP parallelæ;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10599
"
xml:space
="
preserve
">pérque punctum B ducantur utcunque duæ rectæ BT, BS ipſam GP
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0234-03
"
xlink:href
="
note-0234-03a
"
xml:space
="
preserve
">Fig. 62.</
note
>
ſecantes punctis L, K, dico fore D S. </
s
>
<
s
xml:id
="
echoid-s10600
"
xml:space
="
preserve
">DT :</
s
>
<
s
xml:id
="
echoid-s10601
"
xml:space
="
preserve
">: KG. </
s
>
<
s
xml:id
="
echoid-s10602
"
xml:space
="
preserve
">LG.</
s
>
<
s
xml:id
="
echoid-s10603
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10604
"
xml:space
="
preserve
">Nam eſt KG. </
s
>
<
s
xml:id
="
echoid-s10605
"
xml:space
="
preserve
">LG = KG. </
s
>
<
s
xml:id
="
echoid-s10606
"
xml:space
="
preserve
">GB + GB. </
s
>
<
s
xml:id
="
echoid-s10607
"
xml:space
="
preserve
">LG = PK. </
s
>
<
s
xml:id
="
echoid-s10608
"
xml:space
="
preserve
">PS +
<
lb
/>
PT. </
s
>
<
s
xml:id
="
echoid-s10609
"
xml:space
="
preserve
">PL = DB. </
s
>
<
s
xml:id
="
echoid-s10610
"
xml:space
="
preserve
">DS + DT. </
s
>
<
s
xml:id
="
echoid-s10611
"
xml:space
="
preserve
">DB = DT. </
s
>
<
s
xml:id
="
echoid-s10612
"
xml:space
="
preserve
">DS.</
s
>
<
s
xml:id
="
echoid-s10613
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10614
"
xml:space
="
preserve
">IV. </
s
>
<
s
xml:id
="
echoid-s10615
"
xml:space
="
preserve
">Eſto triangulum BDT, basíque DB parallelam quamvis PG
<
lb
/>
interſecent per B ductæ quæpiam duæ rectæ BS, BR punctis L, K;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10616
"
xml:space
="
preserve
">dico fore LG x TD + KL x RD. </
s
>
<
s
xml:id
="
echoid-s10617
"
xml:space
="
preserve
">KG x TD :</
s
>
<
s
xml:id
="
echoid-s10618
"
xml:space
="
preserve
">: RD. </
s
>
<
s
xml:id
="
echoid-s10619
"
xml:space
="
preserve
">SD.</
s
>
<
s
xml:id
="
echoid-s10620
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10621
"
xml:space
="
preserve
">Sumantur enim BM = GP, & </
s
>
<
s
xml:id
="
echoid-s10622
"
xml:space
="
preserve
">BN = LP; </
s
>
<
s
xml:id
="
echoid-s10623
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s10624
"
xml:space
="
preserve
">BO = KP;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10625
"
xml:space
="
preserve
">
<
note
position
="
left
"
xlink:label
="
note-0234-04
"
xlink:href
="
note-0234-04a
"
xml:space
="
preserve
">Fig. 63</
note
>
unde conſtat junctas PM, PN, PO ipſis TB, SB, RB (reſpectivè)
<
lb
/>
parallelas eſſe. </
s
>
<
s
xml:id
="
echoid-s10626
"
xml:space
="
preserve
">Et quoniam eſt DM. </
s
>
<
s
xml:id
="
echoid-s10627
"
xml:space
="
preserve
">PD :</
s
>
<
s
xml:id
="
echoid-s10628
"
xml:space
="
preserve
">: DB. </
s
>
<
s
xml:id
="
echoid-s10629
"
xml:space
="
preserve
">TD. </
s
>
<
s
xml:id
="
echoid-s10630
"
xml:space
="
preserve
">erit DM x
<
lb
/>
TD = PD x
<
emph
style
="
sc
">Db</
emph
>
. </
s
>
<
s
xml:id
="
echoid-s10631
"
xml:space
="
preserve
">Similiter eſt DN x SD = PD x DB. </
s
>
<
s
xml:id
="
echoid-s10632
"
xml:space
="
preserve
">quare
<
lb
/>
DM x TD = DN x SD = DM x SD + MN x SD, tranſpo-
<
lb
/>
nendóque DM x TD - DM x SD = MN x SD. </
s
>
<
s
xml:id
="
echoid-s10633
"
xml:space
="
preserve
">Simili </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>