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
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 - 393
>
271
(78)
272
(79)
273
(80)
274
(81)
275
(82)
276
(83)
277
(84)
278
(85)
279
(86)
280
(87)
<
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 - 393
>
page
|<
<
(123)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div500
"
type
="
section
"
level
="
1
"
n
="
58
">
<
pb
o
="
123
"
file
="
0301
"
n
="
316
"
rhead
="
"/>
</
div
>
<
div
xml:id
="
echoid-div502
"
type
="
section
"
level
="
1
"
n
="
59
">
<
head
xml:id
="
echoid-head62
"
xml:space
="
preserve
">_Exemp_. II.</
head
>
<
p
>
<
s
xml:id
="
echoid-s14876
"
xml:space
="
preserve
">Sit ADG _circuli_ quâdrans, & </
s
>
<
s
xml:id
="
echoid-s14877
"
xml:space
="
preserve
">habere debeat TP ad PM ratio-
<
lb
/>
nem eandem quam PE ad R; </
s
>
<
s
xml:id
="
echoid-s14878
"
xml:space
="
preserve
">eſt ergo PY æqualis _tangenti_ arcûs GE;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s14879
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s14880
"
xml:space
="
preserve
">ſpat. </
s
>
<
s
xml:id
="
echoid-s14881
"
xml:space
="
preserve
">APYY = R x arc. </
s
>
<
s
xml:id
="
echoid-s14882
"
xml:space
="
preserve
">AE. </
s
>
<
s
xml:id
="
echoid-s14883
"
xml:space
="
preserve
">adeóque PM = arc. </
s
>
<
s
xml:id
="
echoid-s14884
"
xml:space
="
preserve
">AE.</
s
>
<
s
xml:id
="
echoid-s14885
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
<
div
xml:id
="
echoid-div503
"
type
="
section
"
level
="
1
"
n
="
60
">
<
head
xml:id
="
echoid-head63
"
xml:space
="
preserve
">_Probl_. III.</
head
>
<
p
>
<
s
xml:id
="
echoid-s14886
"
xml:space
="
preserve
">Proponatur figura quælibet ADB (cujus _axis_ AD, _baſis_ DB)
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0301-01
"
xlink:href
="
note-0301-01a
"
xml:space
="
preserve
">Fig. 185.</
note
>
reperiatur curva KZL, proprietate talis, ut ductâ rectâ ZPM ad
<
lb
/>
DB utcunque parallela quæ lineas expoſitas ſecet ut cernis) poſitóque
<
lb
/>
rectam ZT tangere curvam KZL, ſit intercepta TP æqualis ipſi
<
lb
/>
PM.</
s
>
<
s
xml:id
="
echoid-s14887
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14888
"
xml:space
="
preserve
">Hocità perſicietur. </
s
>
<
s
xml:id
="
echoid-s14889
"
xml:space
="
preserve
">Sit curva OYY talis, ut adſumptâ quâdam
<
lb
/>
R, protractâque PMY, ſit PM. </
s
>
<
s
xml:id
="
echoid-s14890
"
xml:space
="
preserve
">R:</
s
>
<
s
xml:id
="
echoid-s14891
"
xml:space
="
preserve
">: R. </
s
>
<
s
xml:id
="
echoid-s14892
"
xml:space
="
preserve
">PY; </
s
>
<
s
xml:id
="
echoid-s14893
"
xml:space
="
preserve
">tum liberè adſump-
<
lb
/>
tâ DL (in BD protensâ) ſit DL. </
s
>
<
s
xml:id
="
echoid-s14894
"
xml:space
="
preserve
">R:</
s
>
<
s
xml:id
="
echoid-s14895
"
xml:space
="
preserve
">: R. </
s
>
<
s
xml:id
="
echoid-s14896
"
xml:space
="
preserve
">LE; </
s
>
<
s
xml:id
="
echoid-s14897
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s14898
"
xml:space
="
preserve
">_aſymptotis_ DL,
<
lb
/>
DG per E deſcribatur _Hyperbola_ EXX; </
s
>
<
s
xml:id
="
echoid-s14899
"
xml:space
="
preserve
">tum ſit ſpatium LEXH æ-
<
lb
/>
quale ſpatio DOYP, & </
s
>
<
s
xml:id
="
echoid-s14900
"
xml:space
="
preserve
">protractæ XH, YP concurrant in Z; </
s
>
<
s
xml:id
="
echoid-s14901
"
xml:space
="
preserve
">erit
<
lb
/>
Z in curva quæſita; </
s
>
<
s
xml:id
="
echoid-s14902
"
xml:space
="
preserve
">quam ſi tangat ZT, erit TP = PM.</
s
>
<
s
xml:id
="
echoid-s14903
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14904
"
xml:space
="
preserve
">Adnotetur, ſi propoſita ſigura ſit _rectangulum Parallelogrammum_
<
lb
/>
ADBC, quod curvæ KZL hæc erit proprietas, ut ſit DH eodem
<
lb
/>
ordine inter DL, DO media _Geometricè_ proportionalis, quo DP
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0301-02
"
xlink:href
="
note-0301-02a
"
xml:space
="
preserve
">Fig. 186.</
note
>
inter DA & </
s
>
<
s
xml:id
="
echoid-s14905
"
xml:space
="
preserve
">θ
<
unsure
/>
(ſeu nihilum) eſt media _Aritbmeticè_; </
s
>
<
s
xml:id
="
echoid-s14906
"
xml:space
="
preserve
">quod ſi liberè
<
lb
/>
juxta proprietatem hanc deſcribatur curva KZL, & </
s
>
<
s
xml:id
="
echoid-s14907
"
xml:space
="
preserve
">_Mechanicè_ re-
<
lb
/>
periatur tangens ZT, indè quadrabitur _hyperbolicum ſpatium_ LEXH;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s14908
"
xml:space
="
preserve
">erit utique hoc æquale _rectangulo_ ex TP, AP.</
s
>
<
s
xml:id
="
echoid-s14909
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s14910
"
xml:space
="
preserve
">Subnotari poſſit fore 1. </
s
>
<
s
xml:id
="
echoid-s14911
"
xml:space
="
preserve
">Spat. </
s
>
<
s
xml:id
="
echoid-s14912
"
xml:space
="
preserve
">ADLK = R x DL - DO. </
s
>
<
s
xml:id
="
echoid-s14913
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s14914
"
xml:space
="
preserve
">Sum.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s14915
"
xml:space
="
preserve
">mam ZPq = R x : </
s
>
<
s
xml:id
="
echoid-s14916
"
xml:space
="
preserve
">{DLq - DOq/2}. </
s
>
<
s
xml:id
="
echoid-s14917
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s14918
"
xml:space
="
preserve
">ſummam ZP cub. </
s
>
<
s
xml:id
="
echoid-s14919
"
xml:space
="
preserve
">= R x
<
lb
/>
{DLcub. </
s
>
<
s
xml:id
="
echoid-s14920
"
xml:space
="
preserve
">- DOcub.</
s
>
<
s
xml:id
="
echoid-s14921
"
xml:space
="
preserve
">/3} &</
s
>
<
s
xml:id
="
echoid-s14922
"
xml:space
="
preserve
">c
<
unsure
/>
. </
s
>
<
s
xml:id
="
echoid-s14923
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s14924
"
xml:space
="
preserve
">Siponatur φ eſſe centrum gr. </
s
>
<
s
xml:id
="
echoid-s14925
"
xml:space
="
preserve
">figu-
<
lb
/>
ræ ADLK, ducantúrque φψ ad AD, & </
s
>
<
s
xml:id
="
echoid-s14926
"
xml:space
="
preserve
">φξ ad DL perpendicu-
<
lb
/>
lares, fore φψ = {DL + DO/4}, & </
s
>
<
s
xml:id
="
echoid-s14927
"
xml:space
="
preserve
">φξ = R - {AD x DO/LO}.</
s
>
<
s
xml:id
="
echoid-s14928
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>