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 contents
<
1 - 30
31 - 60
61 - 90
91 - 112
>
[111.] _Theor_. VI.
Page: 344 (151)
[112.] FINIS.
Page: 344 (151)
<
1 - 30
31 - 60
61 - 90
91 - 112
>
page
|<
<
(93)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div113
"
type
="
section
"
level
="
1
"
n
="
19
">
<
p
>
<
s
xml:id
="
echoid-s6178
"
xml:space
="
preserve
">
<
pb
o
="
93
"
file
="
0111
"
n
="
111
"
rhead
="
"/>
manibus. </
s
>
<
s
xml:id
="
echoid-s6179
"
xml:space
="
preserve
">propter alios qui ſimilia volet, ipſeviderit, & </
s
>
<
s
xml:id
="
echoid-s6180
"
xml:space
="
preserve
">ſibi para-
<
lb
/>
verit. </
s
>
<
s
xml:id
="
echoid-s6181
"
xml:space
="
preserve
">ego jam aliò progredior; </
s
>
<
s
xml:id
="
echoid-s6182
"
xml:space
="
preserve
">eò ſcilicet, ut locum definiam
<
lb
/>
imaginis in dato quovis refracto apparentis; </
s
>
<
s
xml:id
="
echoid-s6183
"
xml:space
="
preserve
">prætervehemur enim
<
lb
/>
illud in his certè caſibus _intricatiſſimum Problema_ (cujúſque Solutio
<
lb
/>
nullatenus aut laborem quem exigit, aut temporis jacturam compen-
<
lb
/>
ſabit) quo jubetur per datum punctum tranſeuntem refractum deſig-
<
lb
/>
nare. </
s
>
<
s
xml:id
="
echoid-s6184
"
xml:space
="
preserve
">poſitione datum igitur refractum accipimus; </
s
>
<
s
xml:id
="
echoid-s6185
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6186
"
xml:space
="
preserve
">in hoc ima-
<
lb
/>
ginis locum ex hoc uno Theoremate determinamus.</
s
>
<
s
xml:id
="
echoid-s6187
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6188
"
xml:space
="
preserve
">XXIV. </
s
>
<
s
xml:id
="
echoid-s6189
"
xml:space
="
preserve
">Duorum incidentium ANP, ARS ſibi quàm proximo-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0111-01
"
xlink:href
="
note-0111-01a
"
xml:space
="
preserve
">Fig. 146.</
note
>
rum concipiantur refracti N π, R σ ſeſe puncto Z decuſſantes; </
s
>
<
s
xml:id
="
echoid-s6190
"
xml:space
="
preserve
">biſe-
<
lb
/>
centúrque ſubtenſæ NP, N π punctis E, G; </
s
>
<
s
xml:id
="
echoid-s6191
"
xml:space
="
preserve
">(à rectis nempe CE,
<
lb
/>
CG ad illas perpendicularibus) dico rationem NZ ad GZ è ratio-
<
lb
/>
nibus CE ad CG (hoc eſt 1. </
s
>
<
s
xml:id
="
echoid-s6192
"
xml:space
="
preserve
">R), NG ad NE, ac AN ad AE
<
lb
/>
componi.</
s
>
<
s
xml:id
="
echoid-s6193
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6194
"
xml:space
="
preserve
">Ducantur enim CK ad RS, & </
s
>
<
s
xml:id
="
echoid-s6195
"
xml:space
="
preserve
">CI ad R σ perpendiculares; </
s
>
<
s
xml:id
="
echoid-s6196
"
xml:space
="
preserve
">in
<
lb
/>
que producetis CE, CG capiantur CF = CK; </
s
>
<
s
xml:id
="
echoid-s6197
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6198
"
xml:space
="
preserve
">CH = CI;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6199
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6200
"
xml:space
="
preserve
">per F ducatur TV ad NP parallela; </
s
>
<
s
xml:id
="
echoid-s6201
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6202
"
xml:space
="
preserve
">per H etiam XY ad N π
<
lb
/>
parallela. </
s
>
<
s
xml:id
="
echoid-s6203
"
xml:space
="
preserve
">Jam eſt AP. </
s
>
<
s
xml:id
="
echoid-s6204
"
xml:space
="
preserve
">AN :</
s
>
<
s
xml:id
="
echoid-s6205
"
xml:space
="
preserve
">: arc PS. </
s
>
<
s
xml:id
="
echoid-s6206
"
xml:space
="
preserve
">arc NR (ob ſumptam
<
lb
/>
arcuum indefinitam parvitatem). </
s
>
<
s
xml:id
="
echoid-s6207
"
xml:space
="
preserve
">ergò {AP ±: </
s
>
<
s
xml:id
="
echoid-s6208
"
xml:space
="
preserve
">AN/2}. </
s
>
<
s
xml:id
="
echoid-s6209
"
xml:space
="
preserve
">AN :</
s
>
<
s
xml:id
="
echoid-s6210
"
xml:space
="
preserve
">:
<
lb
/>
{arc PS ±: </
s
>
<
s
xml:id
="
echoid-s6211
"
xml:space
="
preserve
">arc. </
s
>
<
s
xml:id
="
echoid-s6212
"
xml:space
="
preserve
">NR/2}. </
s
>
<
s
xml:id
="
echoid-s6213
"
xml:space
="
preserve
">arc NR. </
s
>
<
s
xml:id
="
echoid-s6214
"
xml:space
="
preserve
">hoc eſt AE. </
s
>
<
s
xml:id
="
echoid-s6215
"
xml:space
="
preserve
">AN :</
s
>
<
s
xml:id
="
echoid-s6216
"
xml:space
="
preserve
">: arc NT. </
s
>
<
s
xml:id
="
echoid-s6217
"
xml:space
="
preserve
">arc
<
lb
/>
NR. </
s
>
<
s
xml:id
="
echoid-s6218
"
xml:space
="
preserve
">item eſt NZ. </
s
>
<
s
xml:id
="
echoid-s6219
"
xml:space
="
preserve
">Z π :</
s
>
<
s
xml:id
="
echoid-s6220
"
xml:space
="
preserve
">: arc NR. </
s
>
<
s
xml:id
="
echoid-s6221
"
xml:space
="
preserve
">arc πσ. </
s
>
<
s
xml:id
="
echoid-s6222
"
xml:space
="
preserve
">ac indè NZ. </
s
>
<
s
xml:id
="
echoid-s6223
"
xml:space
="
preserve
">
<
lb
/>
{NZ ±: </
s
>
<
s
xml:id
="
echoid-s6224
"
xml:space
="
preserve
">Z π/2} :</
s
>
<
s
xml:id
="
echoid-s6225
"
xml:space
="
preserve
">: arc NR. </
s
>
<
s
xml:id
="
echoid-s6226
"
xml:space
="
preserve
">{arc NR ±: </
s
>
<
s
xml:id
="
echoid-s6227
"
xml:space
="
preserve
">πσ/2}. </
s
>
<
s
xml:id
="
echoid-s6228
"
xml:space
="
preserve
">hoc eſt NZ. </
s
>
<
s
xml:id
="
echoid-s6229
"
xml:space
="
preserve
">ZG :</
s
>
<
s
xml:id
="
echoid-s6230
"
xml:space
="
preserve
">:
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0111-02
"
xlink:href
="
note-0111-02a
"
xml:space
="
preserve
">_Lect. 9._
<
lb
/>
_Num. iI_</
note
>
NR. </
s
>
<
s
xml:id
="
echoid-s6231
"
xml:space
="
preserve
">arc NX. </
s
>
<
s
xml:id
="
echoid-s6232
"
xml:space
="
preserve
">ergò, rationes æquales adjungendo, eſt. </
s
>
<
s
xml:id
="
echoid-s6233
"
xml:space
="
preserve
">AE. </
s
>
<
s
xml:id
="
echoid-s6234
"
xml:space
="
preserve
">AN
<
lb
/>
+ NZ. </
s
>
<
s
xml:id
="
echoid-s6235
"
xml:space
="
preserve
">ZG = arc NT. </
s
>
<
s
xml:id
="
echoid-s6236
"
xml:space
="
preserve
">arc NR + arc NR. </
s
>
<
s
xml:id
="
echoid-s6237
"
xml:space
="
preserve
">arc NX = arc
<
lb
/>
NT. </
s
>
<
s
xml:id
="
echoid-s6238
"
xml:space
="
preserve
">arc NX. </
s
>
<
s
xml:id
="
echoid-s6239
"
xml:space
="
preserve
">quoniam autem eſt CE. </
s
>
<
s
xml:id
="
echoid-s6240
"
xml:space
="
preserve
">CG :</
s
>
<
s
xml:id
="
echoid-s6241
"
xml:space
="
preserve
">: (I. </
s
>
<
s
xml:id
="
echoid-s6242
"
xml:space
="
preserve
">R :</
s
>
<
s
xml:id
="
echoid-s6243
"
xml:space
="
preserve
">: CK.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6244
"
xml:space
="
preserve
">CI :</
s
>
<
s
xml:id
="
echoid-s6245
"
xml:space
="
preserve
">:) CF. </
s
>
<
s
xml:id
="
echoid-s6246
"
xml:space
="
preserve
">CH. </
s
>
<
s
xml:id
="
echoid-s6247
"
xml:space
="
preserve
">vel permutando CE. </
s
>
<
s
xml:id
="
echoid-s6248
"
xml:space
="
preserve
">CF :</
s
>
<
s
xml:id
="
echoid-s6249
"
xml:space
="
preserve
">: CG. </
s
>
<
s
xml:id
="
echoid-s6250
"
xml:space
="
preserve
">CH; </
s
>
<
s
xml:id
="
echoid-s6251
"
xml:space
="
preserve
">erit,
<
lb
/>
juxta præmonſtrata, arc NT. </
s
>
<
s
xml:id
="
echoid-s6252
"
xml:space
="
preserve
">arc NX = NG. </
s
>
<
s
xml:id
="
echoid-s6253
"
xml:space
="
preserve
">NE + CE. </
s
>
<
s
xml:id
="
echoid-s6254
"
xml:space
="
preserve
">CG.</
s
>
<
s
xml:id
="
echoid-s6255
"
xml:space
="
preserve
">
<
note
symbol
="
*
"
position
="
right
"
xlink:label
="
note-0111-03
"
xlink:href
="
note-0111-03a
"
xml:space
="
preserve
">_12 Lect._
<
lb
/>
_Num. 6._</
note
>
quapropter erit AE. </
s
>
<
s
xml:id
="
echoid-s6256
"
xml:space
="
preserve
">AN + NZ. </
s
>
<
s
xml:id
="
echoid-s6257
"
xml:space
="
preserve
">ZG = NG. </
s
>
<
s
xml:id
="
echoid-s6258
"
xml:space
="
preserve
">NF + CE.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6259
"
xml:space
="
preserve
">CG. </
s
>
<
s
xml:id
="
echoid-s6260
"
xml:space
="
preserve
">unde (rationes hinc indè pares ſubducendo) erit NZ. </
s
>
<
s
xml:id
="
echoid-s6261
"
xml:space
="
preserve
">ZG :</
s
>
<
s
xml:id
="
echoid-s6262
"
xml:space
="
preserve
">:
<
lb
/>
+ CE. </
s
>
<
s
xml:id
="
echoid-s6263
"
xml:space
="
preserve
">CG + NG. </
s
>
<
s
xml:id
="
echoid-s6264
"
xml:space
="
preserve
">NE + AN. </
s
>
<
s
xml:id
="
echoid-s6265
"
xml:space
="
preserve
">AE. </
s
>
<
s
xml:id
="
echoid-s6266
"
xml:space
="
preserve
">Quod propoſitum fuit
<
lb
/>
oſtendere.</
s
>
<
s
xml:id
="
echoid-s6267
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s6268
"
xml:space
="
preserve
">XXV. </
s
>
<
s
xml:id
="
echoid-s6269
"
xml:space
="
preserve
">Hinc, ſi fiat CE. </
s
>
<
s
xml:id
="
echoid-s6270
"
xml:space
="
preserve
">CG :</
s
>
<
s
xml:id
="
echoid-s6271
"
xml:space
="
preserve
">: NE. </
s
>
<
s
xml:id
="
echoid-s6272
"
xml:space
="
preserve
">L; </
s
>
<
s
xml:id
="
echoid-s6273
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s6274
"
xml:space
="
preserve
">AN. </
s
>
<
s
xml:id
="
echoid-s6275
"
xml:space
="
preserve
">AE :</
s
>
<
s
xml:id
="
echoid-s6276
"
xml:space
="
preserve
">: L.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s6277
"
xml:space
="
preserve
">M; </
s
>
<
s
xml:id
="
echoid-s6278
"
xml:space
="
preserve
">erit NZ ZG :</
s
>
<
s
xml:id
="
echoid-s6279
"
xml:space
="
preserve
">: NG. </
s
>
<
s
xml:id
="
echoid-s6280
"
xml:space
="
preserve
">M. </
s
>
<
s
xml:id
="
echoid-s6281
"
xml:space
="
preserve
">Nam NG. </
s
>
<
s
xml:id
="
echoid-s6282
"
xml:space
="
preserve
">NE + CE. </
s
>
<
s
xml:id
="
echoid-s6283
"
xml:space
="
preserve
">CG
<
lb
/>
+ AN. </
s
>
<
s
xml:id
="
echoid-s6284
"
xml:space
="
preserve
">AE = NG. </
s
>
<
s
xml:id
="
echoid-s6285
"
xml:space
="
preserve
">NE + NE. </
s
>
<
s
xml:id
="
echoid-s6286
"
xml:space
="
preserve
">L. </
s
>
<
s
xml:id
="
echoid-s6287
"
xml:space
="
preserve
">+ L. </
s
>
<
s
xml:id
="
echoid-s6288
"
xml:space
="
preserve
">M = NG. </
s
>
<
s
xml:id
="
echoid-s6289
"
xml:space
="
preserve
">M.</
s
>
<
s
xml:id
="
echoid-s6290
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>