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
|<
<
(73)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div331
"
type
="
section
"
level
="
1
"
n
="
34
">
<
p
>
<
s
xml:id
="
echoid-s11687
"
xml:space
="
preserve
">
<
pb
o
="
73
"
file
="
0251
"
n
="
266
"
rhead
="
"/>
DEF concurrentes punctis S, T; </
s
>
<
s
xml:id
="
echoid-s11688
"
xml:space
="
preserve
">erit ſemper DT = 2 DS. </
s
>
<
s
xml:id
="
echoid-s11689
"
xml:space
="
preserve
">Quòd
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0251-01
"
xlink:href
="
note-0251-01a
"
xml:space
="
preserve
">Fig. 99.</
note
>
ſi DE ſunt ut cubi ipſarum DF, erit ſemper DT = 3 DS; </
s
>
<
s
xml:id
="
echoid-s11690
"
xml:space
="
preserve
">ac ſi-
<
lb
/>
mili deinceps modo.</
s
>
<
s
xml:id
="
echoid-s11691
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11692
"
xml:space
="
preserve
">X. </
s
>
<
s
xml:id
="
echoid-s11693
"
xml:space
="
preserve
">Sint rectæ VD, TB concurrentes in T, quas decuſſet poſnio-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0251-02
"
xlink:href
="
note-0251-02a
"
xml:space
="
preserve
">Fig. 100</
note
>
ne data recta DB; </
s
>
<
s
xml:id
="
echoid-s11694
"
xml:space
="
preserve
">tranſeant etiam per B lineæ EBE, FBF tales,
<
lb
/>
ut ductâ quâcunque PG ad DB parallelâ, ſit perpetuò PF eodem or-
<
lb
/>
dine media Arithmeticè inter PG, PE; </
s
>
<
s
xml:id
="
echoid-s11695
"
xml:space
="
preserve
">tangat autem BR curvam
<
lb
/>
EBE, opertet lineæ FBF tangentem ad B determinare.</
s
>
<
s
xml:id
="
echoid-s11696
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11697
"
xml:space
="
preserve
">Sumptis NM (ordinum in quibus ſunt PF, PE exponentibus)
<
lb
/>
fiat N x TD + M \\ - N} x RD. </
s
>
<
s
xml:id
="
echoid-s11698
"
xml:space
="
preserve
">M x TD:</
s
>
<
s
xml:id
="
echoid-s11699
"
xml:space
="
preserve
">: RD. </
s
>
<
s
xml:id
="
echoid-s11700
"
xml:space
="
preserve
">SD; </
s
>
<
s
xml:id
="
echoid-s11701
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s11702
"
xml:space
="
preserve
">connecta-
<
lb
/>
tur BS; </
s
>
<
s
xml:id
="
echoid-s11703
"
xml:space
="
preserve
">hæc curvam FBF continget.</
s
>
<
s
xml:id
="
echoid-s11704
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11705
"
xml:space
="
preserve
">Nam utcunque ducta ſit PG, dictas lineas ſecans ut vides. </
s
>
<
s
xml:id
="
echoid-s11706
"
xml:space
="
preserve
">Eſtque
<
lb
/>
EG. </
s
>
<
s
xml:id
="
echoid-s11707
"
xml:space
="
preserve
">FG:</
s
>
<
s
xml:id
="
echoid-s11708
"
xml:space
="
preserve
">: M. </
s
>
<
s
xml:id
="
echoid-s11709
"
xml:space
="
preserve
">N. </
s
>
<
s
xml:id
="
echoid-s11710
"
xml:space
="
preserve
">ergò FG x TD. </
s
>
<
s
xml:id
="
echoid-s11711
"
xml:space
="
preserve
">EG x TD:</
s
>
<
s
xml:id
="
echoid-s11712
"
xml:space
="
preserve
">: N x TD.</
s
>
<
s
xml:id
="
echoid-s11713
"
xml:space
="
preserve
"> M x TD. </
s
>
<
s
xml:id
="
echoid-s11714
"
xml:space
="
preserve
">Item EF x RD. </
s
>
<
s
xml:id
="
echoid-s11715
"
xml:space
="
preserve
">EG x TD:</
s
>
<
s
xml:id
="
echoid-s11716
"
xml:space
="
preserve
">: M - N x RD. </
s
>
<
s
xml:id
="
echoid-s11717
"
xml:space
="
preserve
">M x
<
lb
/>
<
note
symbol
="
(_a_)
"
position
="
right
"
xlink:label
="
note-0251-03
"
xlink:href
="
note-0251-03a
"
xml:space
="
preserve
">11. Lect.
<
lb
/>
VII.</
note
>
TD. </
s
>
<
s
xml:id
="
echoid-s11718
"
xml:space
="
preserve
">Quapropter (antecedentes conjungendo) erit FG x TD +
<
lb
/>
EF x RD. </
s
>
<
s
xml:id
="
echoid-s11719
"
xml:space
="
preserve
">EG x TD:</
s
>
<
s
xml:id
="
echoid-s11720
"
xml:space
="
preserve
">: N x TD + M - N x RD. </
s
>
<
s
xml:id
="
echoid-s11721
"
xml:space
="
preserve
">M x TD;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s11722
"
xml:space
="
preserve
">(hoc eſt):</
s
>
<
s
xml:id
="
echoid-s11723
"
xml:space
="
preserve
">: RD. </
s
>
<
s
xml:id
="
echoid-s11724
"
xml:space
="
preserve
">SD. </
s
>
<
s
xml:id
="
echoid-s11725
"
xml:space
="
preserve
"> Eſt antem LG x TD + KL x RD.</
s
>
<
s
xml:id
="
echoid-s11726
"
xml:space
="
preserve
">
<
note
symbol
="
(_b_)
"
position
="
right
"
xlink:label
="
note-0251-04
"
xlink:href
="
note-0251-04a
"
xml:space
="
preserve
">_Conſtr._</
note
>
<
note
symbol
="
(_c_)
"
position
="
right
"
xlink:label
="
note-0251-05
"
xlink:href
="
note-0251-05a
"
xml:space
="
preserve
">4. Lect.
<
lb
/>
VII.</
note
>
KG x TD:</
s
>
<
s
xml:id
="
echoid-s11727
"
xml:space
="
preserve
">: RD. </
s
>
<
s
xml:id
="
echoid-s11728
"
xml:space
="
preserve
">SD. </
s
>
<
s
xml:id
="
echoid-s11729
"
xml:space
="
preserve
">quare FG x TD + EF x RD. </
s
>
<
s
xml:id
="
echoid-s11730
"
xml:space
="
preserve
">EG x
<
lb
/>
TD:</
s
>
<
s
xml:id
="
echoid-s11731
"
xml:space
="
preserve
">: LG x TD + KL x RD. </
s
>
<
s
xml:id
="
echoid-s11732
"
xml:space
="
preserve
">KG x TD. </
s
>
<
s
xml:id
="
echoid-s11733
"
xml:space
="
preserve
">hinc, cùm ſit EG
<
note
symbol
="
(_d_)
"
position
="
right
"
xlink:label
="
note-0251-06
"
xlink:href
="
note-0251-06a
"
xml:space
="
preserve
">_Hyp_</
note
>
&</
s
>
<
s
xml:id
="
echoid-s11734
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s11735
"
xml:space
="
preserve
">KG; </
s
>
<
s
xml:id
="
echoid-s11736
"
xml:space
="
preserve
">erit FG x TD + EF x RD &</
s
>
<
s
xml:id
="
echoid-s11737
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s11738
"
xml:space
="
preserve
">LG x TD + KL x RD;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s11739
"
xml:space
="
preserve
">vel FG. </
s
>
<
s
xml:id
="
echoid-s11740
"
xml:space
="
preserve
">EF + TD. </
s
>
<
s
xml:id
="
echoid-s11741
"
xml:space
="
preserve
">RD &</
s
>
<
s
xml:id
="
echoid-s11742
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s11743
"
xml:space
="
preserve
">LG. </
s
>
<
s
xml:id
="
echoid-s11744
"
xml:space
="
preserve
">KL + TD. </
s
>
<
s
xml:id
="
echoid-s11745
"
xml:space
="
preserve
">RD; </
s
>
<
s
xml:id
="
echoid-s11746
"
xml:space
="
preserve
">ſeu (dem-
<
lb
/>
ptâ communi ratione) FG. </
s
>
<
s
xml:id
="
echoid-s11747
"
xml:space
="
preserve
">EF &</
s
>
<
s
xml:id
="
echoid-s11748
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s11749
"
xml:space
="
preserve
">LG. </
s
>
<
s
xml:id
="
echoid-s11750
"
xml:space
="
preserve
">KL. </
s
>
<
s
xml:id
="
echoid-s11751
"
xml:space
="
preserve
">vel componendo
<
lb
/>
EG. </
s
>
<
s
xml:id
="
echoid-s11752
"
xml:space
="
preserve
">EF &</
s
>
<
s
xml:id
="
echoid-s11753
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s11754
"
xml:space
="
preserve
">KG. </
s
>
<
s
xml:id
="
echoid-s11755
"
xml:space
="
preserve
">KL &</
s
>
<
s
xml:id
="
echoid-s11756
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s11757
"
xml:space
="
preserve
">EG. </
s
>
<
s
xml:id
="
echoid-s11758
"
xml:space
="
preserve
">EL. </
s
>
<
s
xml:id
="
echoid-s11759
"
xml:space
="
preserve
">unde eſt EF &</
s
>
<
s
xml:id
="
echoid-s11760
"
xml:space
="
preserve
">lt; </
s
>
<
s
xml:id
="
echoid-s11761
"
xml:space
="
preserve
">EL.</
s
>
<
s
xml:id
="
echoid-s11762
"
xml:space
="
preserve
">
<
note
symbol
="
(_e_)
"
position
="
right
"
xlink:label
="
note-0251-07
"
xlink:href
="
note-0251-07a
"
xml:space
="
preserve
">1. Lect.
<
lb
/>
VII.</
note
>
itaque punctum L extra curvam FBF ſitum eſt; </
s
>
<
s
xml:id
="
echoid-s11763
"
xml:space
="
preserve
">adeoque liquet
<
lb
/>
Propoſitum.</
s
>
<
s
xml:id
="
echoid-s11764
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11765
"
xml:space
="
preserve
">XI. </
s
>
<
s
xml:id
="
echoid-s11766
"
xml:space
="
preserve
">Quinetiam, reliquis ſtantibus iiſdem, ſi PF ſupponatur ejuſ-
<
lb
/>
dem ordinis Geometricè media liquet (planè ſicut in modò præceden-
<
lb
/>
tibus) eandem BS curvam FBF contingere.</
s
>
<
s
xml:id
="
echoid-s11767
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11768
"
xml:space
="
preserve
">_Exemplnum._ </
s
>
<
s
xml:id
="
echoid-s11769
"
xml:space
="
preserve
">Si PF ſit è ſex mediis tertia, ſeu M = 7; </
s
>
<
s
xml:id
="
echoid-s11770
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s11771
"
xml:space
="
preserve
">N = 3;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s11772
"
xml:space
="
preserve
">erit 3 TD + 4 RD. </
s
>
<
s
xml:id
="
echoid-s11773
"
xml:space
="
preserve
">7 MD:</
s
>
<
s
xml:id
="
echoid-s11774
"
xml:space
="
preserve
">: RD. </
s
>
<
s
xml:id
="
echoid-s11775
"
xml:space
="
preserve
">SD; </
s
>
<
s
xml:id
="
echoid-s11776
"
xml:space
="
preserve
">vel SD = {7 MD x RD/3 TD + 4 RD.</
s
>
<
s
xml:id
="
echoid-s11777
"
xml:space
="
preserve
">}</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s11778
"
xml:space
="
preserve
">XII. </
s
>
<
s
xml:id
="
echoid-s11779
"
xml:space
="
preserve
">Patet etiam, accepto quolibet in curva FBF puncto (ceu F)
<
lb
/>
rectam ad hoc tangentem conſimili pacto deſignari. </
s
>
<
s
xml:id
="
echoid-s11780
"
xml:space
="
preserve
">Nempe per F
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0251-08
"
xlink:href
="
note-0251-08a
"
xml:space
="
preserve
">Fig. 101.</
note
>
ducatur recta PG ad DB parallela, ſecans curvam EBE ad E; </
s
>
<
s
xml:id
="
echoid-s11781
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s11782
"
xml:space
="
preserve
">
<
lb
/>
per E ducatur ER curvam EBE tangens; </
s
>
<
s
xml:id
="
echoid-s11783
"
xml:space
="
preserve
">fiátque N x TP + M/- N} x RP.</
s
>
<
s
xml:id
="
echoid-s11784
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>