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 figures
<
1 - 30
31 - 40
[out of range]
>
<
1 - 30
31 - 40
[out of range]
>
page
|<
<
(65)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div301
"
type
="
section
"
level
="
1
"
n
="
33
">
<
pb
o
="
65
"
file
="
0243
"
n
="
258
"
rhead
="
"/>
<
p
>
<
s
xml:id
="
echoid-s11164
"
xml:space
="
preserve
">Nam (facto ut priùs) erit IL. </
s
>
<
s
xml:id
="
echoid-s11165
"
xml:space
="
preserve
">IK :</
s
>
<
s
xml:id
="
echoid-s11166
"
xml:space
="
preserve
">: EG. </
s
>
<
s
xml:id
="
echoid-s11167
"
xml:space
="
preserve
">EF :</
s
>
<
s
xml:id
="
echoid-s11168
"
xml:space
="
preserve
">: MO. </
s
>
<
s
xml:id
="
echoid-s11169
"
xml:space
="
preserve
">MN.</
s
>
<
s
xml:id
="
echoid-s11170
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11171
"
xml:space
="
preserve
">* quapropter erit punctum K extra curvam YFN.</
s
>
<
s
xml:id
="
echoid-s11172
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
right
"
xml:space
="
preserve
">* 2. Lect. VII.</
note
>
<
p
>
<
s
xml:id
="
echoid-s11173
"
xml:space
="
preserve
">Poſſit hæc, ut præceden@, aliter oſtendi; </
s
>
<
s
xml:id
="
echoid-s11174
"
xml:space
="
preserve
">ſed verbis pluribus.</
s
>
<
s
xml:id
="
echoid-s11175
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11176
"
xml:space
="
preserve
">Curvas ità ſitas concipe quales figura monſtrat. </
s
>
<
s
xml:id
="
echoid-s11177
"
xml:space
="
preserve
">nam {στ}ενολχίαν} ego
<
lb
/>
ac{αδολεοιαν} fugitans caſus præ cæteris obvios ac faciles arripiens pro-
<
lb
/>
pono. </
s
>
<
s
xml:id
="
echoid-s11178
"
xml:space
="
preserve
">Hoc ubique ſubnotatum velim.</
s
>
<
s
xml:id
="
echoid-s11179
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11180
"
xml:space
="
preserve
">VII. </
s
>
<
s
xml:id
="
echoid-s11181
"
xml:space
="
preserve
">Sit punctum datum D, curvæque duæ XEM, YFN, ità
<
lb
/>
relatæ, ut à D projectâ quacunque rectâ DEF, habeant ad ſe rectæ
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0243-02
"
xlink:href
="
note-0243-02a
"
xml:space
="
preserve
">Fig. 81.</
note
>
DE, DF rationem ſemper eandem; </
s
>
<
s
xml:id
="
echoid-s11182
"
xml:space
="
preserve
">unam verò YFN tangat recta
<
lb
/>
FS; </
s
>
<
s
xml:id
="
echoid-s11183
"
xml:space
="
preserve
">cui parallela ſit ER; </
s
>
<
s
xml:id
="
echoid-s11184
"
xml:space
="
preserve
">tanget recta ER curvam XEM.</
s
>
<
s
xml:id
="
echoid-s11185
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11186
"
xml:space
="
preserve
">Nam à D utcunque projiciatur recta DK _(_ lineas interſecans, ut
<
lb
/>
vides). </
s
>
<
s
xml:id
="
echoid-s11187
"
xml:space
="
preserve
">Eſtque DK. </
s
>
<
s
xml:id
="
echoid-s11188
"
xml:space
="
preserve
">DI :</
s
>
<
s
xml:id
="
echoid-s11189
"
xml:space
="
preserve
">: DF. </
s
>
<
s
xml:id
="
echoid-s11190
"
xml:space
="
preserve
">DE :</
s
>
<
s
xml:id
="
echoid-s11191
"
xml:space
="
preserve
">: DN. </
s
>
<
s
xml:id
="
echoid-s11192
"
xml:space
="
preserve
">DM; </
s
>
<
s
xml:id
="
echoid-s11193
"
xml:space
="
preserve
">ergò quum ſit
<
lb
/>
DK &</
s
>
<
s
xml:id
="
echoid-s11194
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s11195
"
xml:space
="
preserve
">DN; </
s
>
<
s
xml:id
="
echoid-s11196
"
xml:space
="
preserve
">erit DI &</
s
>
<
s
xml:id
="
echoid-s11197
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s11198
"
xml:space
="
preserve
">DM; </
s
>
<
s
xml:id
="
echoid-s11199
"
xml:space
="
preserve
">quare tota recta RE extra curvam
<
lb
/>
XEM cadit.</
s
>
<
s
xml:id
="
echoid-s11200
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11201
"
xml:space
="
preserve
">Rectæ NK, MI rationem ſemper eandem obtinent; </
s
>
<
s
xml:id
="
echoid-s11202
"
xml:space
="
preserve
">unde res ali-
<
lb
/>
ter conſtat.</
s
>
<
s
xml:id
="
echoid-s11203
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11204
"
xml:space
="
preserve
">VIII. </
s
>
<
s
xml:id
="
echoid-s11205
"
xml:space
="
preserve
">Sint tres curvæ XEM, YFN, ZG O tales, ut ſi ab aſſig-
<
lb
/>
nato puncto D projiciatur utcunque recta DEFG, habeant interceptæ
<
lb
/>
EG, EF rationem ſemper eandem (puta quam R ad _S_) tangant au-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0243-03
"
xlink:href
="
note-0243-03a
"
xml:space
="
preserve
">Fig. 82.</
note
>
tem rectæ ET, GT curvarum duas (puta XEM, ZGO) in E, G;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s11206
"
xml:space
="
preserve
">oportet curvæ YFN tangentem ad F deſignare.</
s
>
<
s
xml:id
="
echoid-s11207
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11208
"
xml:space
="
preserve
">Concipiatur curva TFV talis, ut à D utcunque projectâ rectâ
<
lb
/>
DM K L, (quæ ſecet rectas TE, TG punctis I, L, & </
s
>
<
s
xml:id
="
echoid-s11209
"
xml:space
="
preserve
">iſtam cur-
<
lb
/>
vam in K) habeant ſemper interceptæ IL, IK rationem eandem datæ
<
lb
/>
R ad S; </
s
>
<
s
xml:id
="
echoid-s11210
"
xml:space
="
preserve
"> eſt igitur IK &</
s
>
<
s
xml:id
="
echoid-s11211
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s11212
"
xml:space
="
preserve
">I N; </
s
>
<
s
xml:id
="
echoid-s11213
"
xml:space
="
preserve
">quare curva TFK curvam
<
note
position
="
right
"
xlink:label
="
note-0243-04
"
xlink:href
="
note-0243-04a
"
xml:space
="
preserve
">(_a_) 2 Lect.
<
lb
/>
VIII.</
note
>
tangit; </
s
>
<
s
xml:id
="
echoid-s11214
"
xml:space
="
preserve
"> eſt antem curva TFK _hyperbola_; </
s
>
<
s
xml:id
="
echoid-s11215
"
xml:space
="
preserve
">hanc tangat FS; </
s
>
<
s
xml:id
="
echoid-s11216
"
xml:space
="
preserve
">
<
note
position
="
right
"
xlink:label
="
note-0243-05
"
xlink:href
="
note-0243-05a
"
xml:space
="
preserve
">(_b_) 4 Lect. VI.</
note
>
<
note
position
="
right
"
xlink:label
="
note-0243-06
"
xlink:href
="
note-0243-06a
"
xml:space
="
preserve
">(_c_) 2. _hujus
<
unsure
/>
_</
note
>
illa quoque curvam YFN tanget.</
s
>
<
s
xml:id
="
echoid-s11217
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11218
"
xml:space
="
preserve
">Quoniam _hyperbolam_ tangentis hîc primum injecta eſt mentio; </
s
>
<
s
xml:id
="
echoid-s11219
"
xml:space
="
preserve
">hu-
<
lb
/>
jus ( unà cum aliarum omnium conſimili ratione procreatarum ſeu _re_-
<
lb
/>
_cipr ocarum linearum tangentibus_) _tangentem_ ità definiemus.</
s
>
<
s
xml:id
="
echoid-s11220
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11221
"
xml:space
="
preserve
">IX. </
s
>
<
s
xml:id
="
echoid-s11222
"
xml:space
="
preserve
">Sint VD recta linea, duæque curvæ XEM, YFN ità re-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0243-07
"
xlink:href
="
note-0243-07a
"
xml:space
="
preserve
">Fig. 83.</
note
>
latæ, ut ductâ liberè rectâ EDF ad poſitione datam parallelâ, ſit
<
lb
/>
ſemper _rectangulum_ ex DE, DF par eidem alicui ſpatio; </
s
>
<
s
xml:id
="
echoid-s11223
"
xml:space
="
preserve
">tangat au-
<
lb
/>
tem recta ET curvam XEM in E, cum recta VD concurrens in T;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s11224
"
xml:space
="
preserve
">ſumatúrque DS = DT; </
s
>
<
s
xml:id
="
echoid-s11225
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s11226
"
xml:space
="
preserve
">connectatur F S; </
s
>
<
s
xml:id
="
echoid-s11227
"
xml:space
="
preserve
">hæc curvam YFN
<
lb
/>
tanget ad F.</
s
>
<
s
xml:id
="
echoid-s11228
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11229
"
xml:space
="
preserve
">Nam utcunque ducatur IN ad EF parallela; </
s
>
<
s
xml:id
="
echoid-s11230
"
xml:space
="
preserve
">lineas expoſitas </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>
