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
>
[Figure 21]
Page: 172
[Figure 22]
Page: 175
[Figure 23]
Page: 178
[Figure 24]
Page: 181
[Figure 25]
Page: 184
[Figure 26]
Page: 187
[Figure 27]
Page: 190
[Figure 28]
Page: 349
[Figure 29]
Page: 352
[Figure 30]
Page: 355
[Figure 31]
Page: 358
[Figure 32]
Page: 361
[Figure 33]
Page: 364
[Figure 34]
Page: 367
[Figure 35]
Page: 370
[Figure 36]
Page: 373
[Figure 37]
Page: 376
[Figure 38]
Page: 379
[Figure 39]
Page: 382
[Figure 40]
Page: 385
<
1 - 30
31 - 40
>
page
|<
<
(105)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div399
"
type
="
section
"
level
="
1
"
n
="
42
">
<
pb
o
="
105
"
file
="
0283
"
n
="
298
"/>
</
div
>
<
div
xml:id
="
echoid-div434
"
type
="
section
"
level
="
1
"
n
="
43
">
<
head
xml:id
="
echoid-head46
"
xml:space
="
preserve
">
<
emph
style
="
sc
">Lect</
emph
>
. XII.</
head
>
<
p
>
<
s
xml:id
="
echoid-s13930
"
xml:space
="
preserve
">IN ſuſcepto negotio progredimur; </
s
>
<
s
xml:id
="
echoid-s13931
"
xml:space
="
preserve
">quod ut (quatenus licet) decurte-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0283-01
"
xlink:href
="
note-0283-01a
"
xml:space
="
preserve
">_Praparati@_
<
lb
/>
_Communis_.</
note
>
mus, verbíſque parcamus; </
s
>
<
s
xml:id
="
echoid-s13932
"
xml:space
="
preserve
">obſervetur, in ſequentibus ubique _line-_
<
lb
/>
_am_ AB _curvam_ eſſe (quales tractamus) quampiam; </
s
>
<
s
xml:id
="
echoid-s13933
"
xml:space
="
preserve
">cujus _Axis_ AD;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s13934
"
xml:space
="
preserve
">huic applicatas omnes rectas BD, CA, MF, NG perpendiculares; </
s
>
<
s
xml:id
="
echoid-s13935
"
xml:space
="
preserve
">
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s13936
"
xml:space
="
preserve
">ME, NS, CB parallelas eſſe; </
s
>
<
s
xml:id
="
echoid-s13937
"
xml:space
="
preserve
">_punctum_ M liberè ſumi; </
s
>
<
s
xml:id
="
echoid-s13938
"
xml:space
="
preserve
">_arcum_
<
lb
/>
MN indefinitè parvum eſſe; </
s
>
<
s
xml:id
="
echoid-s13939
"
xml:space
="
preserve
">rectam α β curvæ VB, α μ curvæ AM,
<
lb
/>
μ ν _arcui_ MN æquales eſſe; </
s
>
<
s
xml:id
="
echoid-s13940
"
xml:space
="
preserve
">ad rectam α β applicatas ei perpendicu-
<
lb
/>
lares eſſe. </
s
>
<
s
xml:id
="
echoid-s13941
"
xml:space
="
preserve
">His præſtratis,</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s13942
"
xml:space
="
preserve
">I. </
s
>
<
s
xml:id
="
echoid-s13943
"
xml:space
="
preserve
">Sit MP curvæ AB perpendicularis; </
s
>
<
s
xml:id
="
echoid-s13944
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s13945
"
xml:space
="
preserve
">lineæ KZ L, α φ δta-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0283-02
"
xlink:href
="
note-0283-02a
"
xml:space
="
preserve
">Fig. 156,
<
lb
/>
157.</
note
>
les, ut FZ ipſi MP, & </
s
>
<
s
xml:id
="
echoid-s13946
"
xml:space
="
preserve
">μ φ ipſi M Fæquentur; </
s
>
<
s
xml:id
="
echoid-s13947
"
xml:space
="
preserve
">erît _ſpatium_ α β δ ipſi
<
lb
/>
AD LK æquale.</
s
>
<
s
xml:id
="
echoid-s13948
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s13949
"
xml:space
="
preserve
">Nam _Triangula_ MRN, PFM ſimilia ſunt, adeoque MN. </
s
>
<
s
xml:id
="
echoid-s13950
"
xml:space
="
preserve
">NR
<
lb
/>
:</
s
>
<
s
xml:id
="
echoid-s13951
"
xml:space
="
preserve
">: PM. </
s
>
<
s
xml:id
="
echoid-s13952
"
xml:space
="
preserve
">MF. </
s
>
<
s
xml:id
="
echoid-s13953
"
xml:space
="
preserve
">unde MN x MF = NR x PM, hoc eſt (ſubſtitutis
<
lb
/>
æqualibus) μ ν x μ φ = FG x FZ; </
s
>
<
s
xml:id
="
echoid-s13954
"
xml:space
="
preserve
">ſeu rectang. </
s
>
<
s
xml:id
="
echoid-s13955
"
xml:space
="
preserve
">μ θ = rectang. </
s
>
<
s
xml:id
="
echoid-s13956
"
xml:space
="
preserve
">FH;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s13957
"
xml:space
="
preserve
">ſpatium verò α β δ minimè differt ab indeſinitè multis rectangulis,
<
lb
/>
qualia μθ & </
s
>
<
s
xml:id
="
echoid-s13958
"
xml:space
="
preserve
">ſpatium AD LK totidem rectangulis, qualia FH, æ-
<
lb
/>
quivalet. </
s
>
<
s
xml:id
="
echoid-s13959
"
xml:space
="
preserve
">unde liquet Propoſitum.</
s
>
<
s
xml:id
="
echoid-s13960
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s13961
"
xml:space
="
preserve
">II. </
s
>
<
s
xml:id
="
echoid-s13962
"
xml:space
="
preserve
">Hinc, ſi curva AMB circa axem AD rotetur, habebit ſe _pro._
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s13963
"
xml:space
="
preserve
">_ducta ſuperficies_ ad _ſpatium_ AD LK, ut _Circumferentia circuli Ad ra-_
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0283-03
"
xlink:href
="
note-0283-03a
"
xml:space
="
preserve
">Fig. 156.</
note
>
_dium_; </
s
>
<
s
xml:id
="
echoid-s13964
"
xml:space
="
preserve
">unde noto ſpatio AD LK cognoſcetur dicta _ſuperficies._ </
s
>
<
s
xml:id
="
echoid-s13965
"
xml:space
="
preserve
">Con-
<
lb
/>
ſequentiæ rationem jam anteà pridem aſſignavimus.</
s
>
<
s
xml:id
="
echoid-s13966
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s13967
"
xml:space
="
preserve
">III. </
s
>
<
s
xml:id
="
echoid-s13968
"
xml:space
="
preserve
">Exhinc _Spbæræ, Spbæroidis_ utriuſque, _Conidúmque ſuperficies_
<
lb
/>
_dimenſionem_ accipiunt; </
s
>
<
s
xml:id
="
echoid-s13969
"
xml:space
="
preserve
">nam ſi AD ſit conicæ ſectionis, à qua iſtæ
<
lb
/>
figuræ oriuntur, axis; </
s
>
<
s
xml:id
="
echoid-s13970
"
xml:space
="
preserve
">linea KZL ſemper aliqua conicarum exiſtet,
<
lb
/>
haud difficili negotio determinabilis. </
s
>
<
s
xml:id
="
echoid-s13971
"
xml:space
="
preserve
">Hoc ſuggero tantùm, quoniam
<
lb
/>
nunc evulgatum habet ur.</
s
>
<
s
xml:id
="
echoid-s13972
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>