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
>
161
162
163
(6)
164
165
166
(7)
167
168
169
(8)
170
<
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
|<
<
(48)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div222
"
type
="
section
"
level
="
1
"
n
="
31
">
<
p
>
<
s
xml:id
="
echoid-s9918
"
xml:space
="
preserve
">
<
pb
o
="
48
"
file
="
0226
"
n
="
241
"
rhead
="
"/>
linea OOO talis, ut ſi è D utcunque ducatur recta DO, ſecans
<
lb
/>
anguli latera punctis M, N, habeat DM ad NO ſemper eandem
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0226-01
"
xlink:href
="
note-0226-01a
"
xml:space
="
preserve
">Fig. 43.</
note
>
rationem (puta X ad Y) erit etiam linea OOO hyperbola.</
s
>
<
s
xml:id
="
echoid-s9919
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s9920
"
xml:space
="
preserve
">Nam ducatur DL ad BC parallela; </
s
>
<
s
xml:id
="
echoid-s9921
"
xml:space
="
preserve
">ſitque DL. </
s
>
<
s
xml:id
="
echoid-s9922
"
xml:space
="
preserve
">DE:</
s
>
<
s
xml:id
="
echoid-s9923
"
xml:space
="
preserve
">: X. </
s
>
<
s
xml:id
="
echoid-s9924
"
xml:space
="
preserve
">Y;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9925
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s9926
"
xml:space
="
preserve
">per E ducatur ER ad AB parallela; </
s
>
<
s
xml:id
="
echoid-s9927
"
xml:space
="
preserve
">ſecans BC in Z; </
s
>
<
s
xml:id
="
echoid-s9928
"
xml:space
="
preserve
">de-
<
lb
/>
mum per O ducatur OH ad BA parallela.</
s
>
<
s
xml:id
="
echoid-s9929
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s9930
"
xml:space
="
preserve
">Eſt jam DL. </
s
>
<
s
xml:id
="
echoid-s9931
"
xml:space
="
preserve
">DE:</
s
>
<
s
xml:id
="
echoid-s9932
"
xml:space
="
preserve
">: DM. </
s
>
<
s
xml:id
="
echoid-s9933
"
xml:space
="
preserve
">NO:</
s
>
<
s
xml:id
="
echoid-s9934
"
xml:space
="
preserve
">: LM. </
s
>
<
s
xml:id
="
echoid-s9935
"
xml:space
="
preserve
">GO (ob ſimilia tri-
<
lb
/>
angula DLM, NGO):</
s
>
<
s
xml:id
="
echoid-s9936
"
xml:space
="
preserve
">: LM x DH. </
s
>
<
s
xml:id
="
echoid-s9937
"
xml:space
="
preserve
">GO x DH item DL x
<
lb
/>
HO = LM x DH (ob DL. </
s
>
<
s
xml:id
="
echoid-s9938
"
xml:space
="
preserve
">LM:</
s
>
<
s
xml:id
="
echoid-s9939
"
xml:space
="
preserve
">: DH. </
s
>
<
s
xml:id
="
echoid-s9940
"
xml:space
="
preserve
">HO) quare DL. </
s
>
<
s
xml:id
="
echoid-s9941
"
xml:space
="
preserve
">DE:</
s
>
<
s
xml:id
="
echoid-s9942
"
xml:space
="
preserve
">:
<
lb
/>
DL x HO. </
s
>
<
s
xml:id
="
echoid-s9943
"
xml:space
="
preserve
">GO x DH hoc eſt DL x HO. </
s
>
<
s
xml:id
="
echoid-s9944
"
xml:space
="
preserve
">DE x HO:</
s
>
<
s
xml:id
="
echoid-s9945
"
xml:space
="
preserve
">: DL x HO.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9946
"
xml:space
="
preserve
">GO x DH adeóq; </
s
>
<
s
xml:id
="
echoid-s9947
"
xml:space
="
preserve
">DE x HO = GO x DH. </
s
>
<
s
xml:id
="
echoid-s9948
"
xml:space
="
preserve
">hoc eſt DE x HG + DE x
<
lb
/>
GO = GO x DE + GO x EH quare (communi ſublato) eſt
<
lb
/>
DE x HG = GO x EH; </
s
>
<
s
xml:id
="
echoid-s9949
"
xml:space
="
preserve
">ſeu DE x HG = GO x ZG. </
s
>
<
s
xml:id
="
echoid-s9950
"
xml:space
="
preserve
">Pa-
<
lb
/>
tet itaque curvam OOO eſſe _hyperbolam_ cujus _aſymptoti_ ZR
<
lb
/>
ZC.</
s
>
<
s
xml:id
="
echoid-s9951
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s9952
"
xml:space
="
preserve
">_Coroll_. </
s
>
<
s
xml:id
="
echoid-s9953
"
xml:space
="
preserve
">Si ratio data ſit æqualitatis (ceu DM = NO,) ipſæ AB,
<
lb
/>
CB aſymptoti erunt.</
s
>
<
s
xml:id
="
echoid-s9954
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s9955
"
xml:space
="
preserve
">Sequentia quædam, quia magìs id perſpicuum videtur, Alge-
<
lb
/>
bricè monſtrabimus.</
s
>
<
s
xml:id
="
echoid-s9956
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s9957
"
xml:space
="
preserve
">X. </
s
>
<
s
xml:id
="
echoid-s9958
"
xml:space
="
preserve
">Eſto poſitione data recta ID, in qua punctum deſignatum D,
<
lb
/>
ſit item curva DNN talis ut in ID ſumpto quopiam puncto G, & </
s
>
<
s
xml:id
="
echoid-s9959
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0226-02
"
xlink:href
="
note-0226-02a
"
xml:space
="
preserve
">Fig. 44.</
note
>
ductâ rectâ GN ad poſitionem datam IK paràllelá; </
s
>
<
s
xml:id
="
echoid-s9960
"
xml:space
="
preserve
">tum adſumptis
<
lb
/>
determinatis rectis _m, b_; </
s
>
<
s
xml:id
="
echoid-s9961
"
xml:space
="
preserve
">poſitiſq; </
s
>
<
s
xml:id
="
echoid-s9962
"
xml:space
="
preserve
">DG = _x_, & </
s
>
<
s
xml:id
="
echoid-s9963
"
xml:space
="
preserve
">GN = _y_; </
s
>
<
s
xml:id
="
echoid-s9964
"
xml:space
="
preserve
">ſit
<
lb
/>
conſtantèr _m y_ + _x y_ = {_m_/_b_}_x x_; </
s
>
<
s
xml:id
="
echoid-s9965
"
xml:space
="
preserve
">erit linea DNN _hyperbola_; </
s
>
<
s
xml:id
="
echoid-s9966
"
xml:space
="
preserve
">quæ
<
lb
/>
ſic determinatur; </
s
>
<
s
xml:id
="
echoid-s9967
"
xml:space
="
preserve
">ſumantur DM, & </
s
>
<
s
xml:id
="
echoid-s9968
"
xml:space
="
preserve
">DO (hinc indè) pares ipſi _m_;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9969
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s9970
"
xml:space
="
preserve
">per M ducatur M L@ad IK parallela, factóq; </
s
>
<
s
xml:id
="
echoid-s9971
"
xml:space
="
preserve
">_b. </
s
>
<
s
xml:id
="
echoid-s9972
"
xml:space
="
preserve
">m_:</
s
>
<
s
xml:id
="
echoid-s9973
"
xml:space
="
preserve
">: _m_. </
s
>
<
s
xml:id
="
echoid-s9974
"
xml:space
="
preserve
">MQ; </
s
>
<
s
xml:id
="
echoid-s9975
"
xml:space
="
preserve
">ſit
<
lb
/>
MZ = 2 MQ = {2_mm_;</
s
>
<
s
xml:id
="
echoid-s9976
"
xml:space
="
preserve
">/_b_} tum per Z, O traducatur recta ZT; </
s
>
<
s
xml:id
="
echoid-s9977
"
xml:space
="
preserve
">erunt
<
lb
/>
ZM, ZT aſymptoti.</
s
>
<
s
xml:id
="
echoid-s9978
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s9979
"
xml:space
="
preserve
">Ducatur enim ZS ad MO parallela, cui occurrat N Gin R (quæ
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s9980
"
xml:space
="
preserve
">ipſam ZT ſect in P). </
s
>
<
s
xml:id
="
echoid-s9981
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s9982
"
xml:space
="
preserve
">connectatur DQ. </
s
>
<
s
xml:id
="
echoid-s9983
"
xml:space
="
preserve
">Eſt ergò PN = RG
<
lb
/>
+ GN - RP. </
s
>
<
s
xml:id
="
echoid-s9984
"
xml:space
="
preserve
">Verùm eſt MD. </
s
>
<
s
xml:id
="
echoid-s9985
"
xml:space
="
preserve
">MQ:</
s
>
<
s
xml:id
="
echoid-s9986
"
xml:space
="
preserve
">: ZR (MG). </
s
>
<
s
xml:id
="
echoid-s9987
"
xml:space
="
preserve
">RP; </
s
>
<
s
xml:id
="
echoid-s9988
"
xml:space
="
preserve
">hoc
<
lb
/>
eſt _m_. </
s
>
<
s
xml:id
="
echoid-s9989
"
xml:space
="
preserve
">{_mm_/_b_}:</
s
>
<
s
xml:id
="
echoid-s9990
"
xml:space
="
preserve
">: _m_ + _x_. </
s
>
<
s
xml:id
="
echoid-s9991
"
xml:space
="
preserve
">RP = {_mm_/_b_} + {_mx._</
s
>
<
s
xml:id
="
echoid-s9992
"
xml:space
="
preserve
">/_b_} adeóq; </
s
>
<
s
xml:id
="
echoid-s9993
"
xml:space
="
preserve
">RG - RP
<
lb
/>
= {_mm_/_b_} - {_mx._</
s
>
<
s
xml:id
="
echoid-s9994
"
xml:space
="
preserve
">/_b_} ergò PN = {_mm_ - _mx_/_b_} + _y_. </
s
>
<
s
xml:id
="
echoid-s9995
"
xml:space
="
preserve
">Unde PN x MG
<
lb
/>
= {_m_
<
emph
style
="
sub
">3</
emph
>
/_b_} + _my_ + _xy_ - {_mxx._</
s
>
<
s
xml:id
="
echoid-s9996
"
xml:space
="
preserve
">/_b_} Verùm (ex hypotheſi) eſt _m </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>