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
331
138
332
139
333
140
334
141
335
142
336
143
337
144
338
145
339
146
340
147
341
342
149
343
150
344
151
345
346
347
348
349
1
350
351
352
2
353
354
355
3
356
357
358
4
359
360
<
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
|<
<
(144)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div575
"
type
="
section
"
level
="
1
"
n
="
98
">
<
pb
o
="
144
"
file
="
0322
"
n
="
337
"
rhead
="
"/>
<
p
>
<
s
xml:id
="
echoid-s15903
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s15904
"
xml:space
="
preserve
">Curva HLLI eſt _ſemicirculus_; </
s
>
<
s
xml:id
="
echoid-s15905
"
xml:space
="
preserve
">reliquas itidem oſtentat
<
lb
/>
Schema.</
s
>
<
s
xml:id
="
echoid-s15906
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15907
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s15908
"
xml:space
="
preserve
">Si A ζ = {_cc_/_b_}; </
s
>
<
s
xml:id
="
echoid-s15909
"
xml:space
="
preserve
">A Ψ = {_b_/4} - √ {_bb_/16} - {_cc_/2}; </
s
>
<
s
xml:id
="
echoid-s15910
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s15911
"
xml:space
="
preserve
">A φ = {_b_/4} +
<
lb
/>
√ {_bb_/16} - {_cc_/2}; </
s
>
<
s
xml:id
="
echoid-s15912
"
xml:space
="
preserve
">ordinentúrque rectæ ζ V, ψ X, φ Y; </
s
>
<
s
xml:id
="
echoid-s15913
"
xml:space
="
preserve
">erunt puncta V,
<
lb
/>
X, Y _nodi_ curvarum (ſi _b_ &</
s
>
<
s
xml:id
="
echoid-s15914
"
xml:space
="
preserve
">lt; </
s
>
<
s
xml:id
="
echoid-s15915
"
xml:space
="
preserve
">√ 8 _c c_, deerunt _nodi_ X, Y; </
s
>
<
s
xml:id
="
echoid-s15916
"
xml:space
="
preserve
">ſi _b_ = √
<
lb
/>
8 _c c_; </
s
>
<
s
xml:id
="
echoid-s15917
"
xml:space
="
preserve
">ii coaleſcent).</
s
>
<
s
xml:id
="
echoid-s15918
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15919
"
xml:space
="
preserve
">5. </
s
>
<
s
xml:id
="
echoid-s15920
"
xml:space
="
preserve
">Ordinatarum ad curvam CL H _maxima_ eſt ipſa AC ; </
s
>
<
s
xml:id
="
echoid-s15921
"
xml:space
="
preserve
">ſin AP
<
lb
/>
= {_b_/3} - √ {_bb_/9} - {_cc_/3}, & </
s
>
<
s
xml:id
="
echoid-s15922
"
xml:space
="
preserve
">ordinetur P γ ad curvam AM H; </
s
>
<
s
xml:id
="
echoid-s15923
"
xml:space
="
preserve
">erit
<
lb
/>
P γ _maxima_; </
s
>
<
s
xml:id
="
echoid-s15924
"
xml:space
="
preserve
">item ſi AQ = {3/8} _b_ - √ {@9/64} _b b_ - {_cc_/2}; </
s
>
<
s
xml:id
="
echoid-s15925
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s15926
"
xml:space
="
preserve
">ordinetur
<
lb
/>
Q δ ad curvam AN H, erit Q δ _maxima_.</
s
>
<
s
xml:id
="
echoid-s15927
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15928
"
xml:space
="
preserve
">6. </
s
>
<
s
xml:id
="
echoid-s15929
"
xml:space
="
preserve
">Ordinatarum ad curvam HLLI _maxima_ eſt ipſa OT ; </
s
>
<
s
xml:id
="
echoid-s15930
"
xml:space
="
preserve
">ſin AP
<
lb
/>
= {_b_/3} + √ {_bb_/9} - {_cc_/3}, & </
s
>
<
s
xml:id
="
echoid-s15931
"
xml:space
="
preserve
">ad curvam HM I ordinetur _p g_, erit _p g_
<
lb
/>
_maxima_; </
s
>
<
s
xml:id
="
echoid-s15932
"
xml:space
="
preserve
">item ſi A q = {3/8} _b_ + √ {9/64} _b b_ - {_cc_/2}; </
s
>
<
s
xml:id
="
echoid-s15933
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s15934
"
xml:space
="
preserve
">ordinetur _q d_
<
lb
/>
ad curvam HN I, erit _q d maxima_.</
s
>
<
s
xml:id
="
echoid-s15935
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15936
"
xml:space
="
preserve
">7. </
s
>
<
s
xml:id
="
echoid-s15937
"
xml:space
="
preserve
">Hinc radicum limites dignoſcentur, ut innuitur in iis, quæ ad
<
lb
/>
octavam ſeriem animadverſa ſunt.</
s
>
<
s
xml:id
="
echoid-s15938
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15939
"
xml:space
="
preserve
">8. </
s
>
<
s
xml:id
="
echoid-s15940
"
xml:space
="
preserve
">Patet in Serie duodecima nunc tres, modo duas, ſemper unam
<
lb
/>
radicem haberi; </
s
>
<
s
xml:id
="
echoid-s15941
"
xml:space
="
preserve
">in decima tertia verò ſubinde duas, aliquando tantùm
<
lb
/>
unam, interdum nullam haberi.</
s
>
<
s
xml:id
="
echoid-s15942
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15943
"
xml:space
="
preserve
">9. </
s
>
<
s
xml:id
="
echoid-s15944
"
xml:space
="
preserve
">Et hæc quidem conſtant poſito fore {_b_/2}&</
s
>
<
s
xml:id
="
echoid-s15945
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s15946
"
xml:space
="
preserve
">_c_; </
s
>
<
s
xml:id
="
echoid-s15947
"
xml:space
="
preserve
">at ſi {_b_/2} = β;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s15948
"
xml:space
="
preserve
">evaneſcet Series decima tertia; </
s
>
<
s
xml:id
="
echoid-s15949
"
xml:space
="
preserve
">coaleſcent puncta H, O, I; </
s
>
<
s
xml:id
="
echoid-s15950
"
xml:space
="
preserve
">recta AB
<
lb
/>
_byperbolam_ KK K tanget; </
s
>
<
s
xml:id
="
echoid-s15951
"
xml:space
="
preserve
">curvæque CL H, IL λ in rectas lineas
<
lb
/>
degenerabunt.</
s
>
<
s
xml:id
="
echoid-s15952
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s15953
"
xml:space
="
preserve
">10. </
s
>
<
s
xml:id
="
echoid-s15954
"
xml:space
="
preserve
">Sin {_b_/2} &</
s
>
<
s
xml:id
="
echoid-s15955
"
xml:space
="
preserve
">lt; </
s
>
<
s
xml:id
="
echoid-s15956
"
xml:space
="
preserve
">_c_; </
s
>
<
s
xml:id
="
echoid-s15957
"
xml:space
="
preserve
">etiam evaneſcit Series decima tertia; </
s
>
<
s
xml:id
="
echoid-s15958
"
xml:space
="
preserve
">_byperbola_ KKK
<
lb
/>
tota infra rectam AB jacente; </
s
>
<
s
xml:id
="
echoid-s15959
"
xml:space
="
preserve
">quo caſu curva CL L erit hyperbola
<
lb
/>
æquilatera, habens centrum O, ſemiaxem (ipſi AB perpendicula-
<
lb
/>
rem) OT = √ AC q - AO q; </
s
>
<
s
xml:id
="
echoid-s15960
"
xml:space
="
preserve
">tunc & </
s
>
<
s
xml:id
="
echoid-s15961
"
xml:space
="
preserve
">curvæ AM M, AN N
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0322-01
"
xlink:href
="
note-0322-01a
"
xml:space
="
preserve
">Fig. 218.</
note
>
ad infinitum procurrent, ſic ut æquationes, quæ in Serie duodecima,
<
lb
/>
unam ſemper, & </
s
>
<
s
xml:id
="
echoid-s15962
"
xml:space
="
preserve
">unicam radicem obtineant. </
s
>
<
s
xml:id
="
echoid-s15963
"
xml:space
="
preserve
">Hæc ſuffecerit inſinu-
<
lb
/>
âſſe; </
s
>
<
s
xml:id
="
echoid-s15964
"
xml:space
="
preserve
">quin & </
s
>
<
s
xml:id
="
echoid-s15965
"
xml:space
="
preserve
">rem totam hactenus particulatim attigiſſe. </
s
>
<
s
xml:id
="
echoid-s15966
"
xml:space
="
preserve
">Subnecte-
<
lb
/>
mus autem notas quaſdam magìs generales.</
s
>
<
s
xml:id
="
echoid-s15967
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>