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
>
51
(33)
52
(34)
53
(35)
54
(36)
55
(37)
56
(38)
57
(39)
58
(40)
59
(41)
60
(42)
<
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
|<
<
(34)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div41
"
type
="
section
"
level
="
1
"
n
="
13
">
<
pb
o
="
34
"
file
="
0052
"
n
="
52
"
rhead
="
"/>
<
p
>
<
s
xml:id
="
echoid-s1668
"
xml:space
="
preserve
">XI _corol_. </
s
>
<
s
xml:id
="
echoid-s1669
"
xml:space
="
preserve
">I. </
s
>
<
s
xml:id
="
echoid-s1670
"
xml:space
="
preserve
">Hinc ſi duo reſracti M _a_, N _a_ cum Axe AB conve-
<
lb
/>
niant in I, K; </
s
>
<
s
xml:id
="
echoid-s1671
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1672
"
xml:space
="
preserve
">à puncto Y ad incidentias ducantur rectæ YM, YN;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1673
"
xml:space
="
preserve
">erit KB. </
s
>
<
s
xml:id
="
echoid-s1674
"
xml:space
="
preserve
">IB :</
s
>
<
s
xml:id
="
echoid-s1675
"
xml:space
="
preserve
">: YN. </
s
>
<
s
xml:id
="
echoid-s1676
"
xml:space
="
preserve
">YM. </
s
>
<
s
xml:id
="
echoid-s1677
"
xml:space
="
preserve
">Nam KBq. </
s
>
<
s
xml:id
="
echoid-s1678
"
xml:space
="
preserve
">YNq :</
s
>
<
s
xml:id
="
echoid-s1679
"
xml:space
="
preserve
">: Iq - Rq. </
s
>
<
s
xml:id
="
echoid-s1680
"
xml:space
="
preserve
">
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0052-01
"
xlink:href
="
note-0052-01a
"
xml:space
="
preserve
">Fig. 40.</
note
>
Rq :</
s
>
<
s
xml:id
="
echoid-s1681
"
xml:space
="
preserve
">: IBq. </
s
>
<
s
xml:id
="
echoid-s1682
"
xml:space
="
preserve
">YMq. </
s
>
<
s
xml:id
="
echoid-s1683
"
xml:space
="
preserve
">quare permutatim KBq. </
s
>
<
s
xml:id
="
echoid-s1684
"
xml:space
="
preserve
">IBq :</
s
>
<
s
xml:id
="
echoid-s1685
"
xml:space
="
preserve
">: YNq.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1686
"
xml:space
="
preserve
">YM q.</
s
>
<
s
xml:id
="
echoid-s1687
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1688
"
xml:space
="
preserve
">XII. </
s
>
<
s
xml:id
="
echoid-s1689
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s1690
"
xml:space
="
preserve
">Hinc etiam ſi refracti M I, NK conveniant in X; </
s
>
<
s
xml:id
="
echoid-s1691
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1692
"
xml:space
="
preserve
">de-
<
lb
/>
mìttatur XP ad AB parallela; </
s
>
<
s
xml:id
="
echoid-s1693
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1694
"
xml:space
="
preserve
">huic protractæ MY, NY occur-
<
lb
/>
rant in R, S; </
s
>
<
s
xml:id
="
echoid-s1695
"
xml:space
="
preserve
">erit NS = MR Nam X P. </
s
>
<
s
xml:id
="
echoid-s1696
"
xml:space
="
preserve
">SN :</
s
>
<
s
xml:id
="
echoid-s1697
"
xml:space
="
preserve
">: KB. </
s
>
<
s
xml:id
="
echoid-s1698
"
xml:space
="
preserve
">YN :</
s
>
<
s
xml:id
="
echoid-s1699
"
xml:space
="
preserve
">:
<
lb
/>
IB. </
s
>
<
s
xml:id
="
echoid-s1700
"
xml:space
="
preserve
">YM :</
s
>
<
s
xml:id
="
echoid-s1701
"
xml:space
="
preserve
">: XP. </
s
>
<
s
xml:id
="
echoid-s1702
"
xml:space
="
preserve
">RM. </
s
>
<
s
xml:id
="
echoid-s1703
"
xml:space
="
preserve
">cum itaque ſit X P. </
s
>
<
s
xml:id
="
echoid-s1704
"
xml:space
="
preserve
">SN :</
s
>
<
s
xml:id
="
echoid-s1705
"
xml:space
="
preserve
">: XP . </
s
>
<
s
xml:id
="
echoid-s1706
"
xml:space
="
preserve
">RM;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1707
"
xml:space
="
preserve
">erìt SN = RM.</
s
>
<
s
xml:id
="
echoid-s1708
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1709
"
xml:space
="
preserve
">XIII. </
s
>
<
s
xml:id
="
echoid-s1710
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s1711
"
xml:space
="
preserve
">In ſecundo caſu ; </
s
>
<
s
xml:id
="
echoid-s1712
"
xml:space
="
preserve
">ſit cujuſvis incidentis AN refractus
<
lb
/>
KN _a_ & </
s
>
<
s
xml:id
="
echoid-s1713
"
xml:space
="
preserve
">fiat YBq. </
s
>
<
s
xml:id
="
echoid-s1714
"
xml:space
="
preserve
">KBq :</
s
>
<
s
xml:id
="
echoid-s1715
"
xml:space
="
preserve
">: Rq. </
s
>
<
s
xml:id
="
echoid-s1716
"
xml:space
="
preserve
">Rq - Iq; </
s
>
<
s
xml:id
="
echoid-s1717
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1718
"
xml:space
="
preserve
">connectatur YN;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1719
"
xml:space
="
preserve
">erit ABq. </
s
>
<
s
xml:id
="
echoid-s1720
"
xml:space
="
preserve
">YNq :</
s
>
<
s
xml:id
="
echoid-s1721
"
xml:space
="
preserve
">: Rq - Iq. </
s
>
<
s
xml:id
="
echoid-s1722
"
xml:space
="
preserve
">Iq.</
s
>
<
s
xml:id
="
echoid-s1723
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1724
"
xml:space
="
preserve
">Nam quia KBq = KNq - BNq = KNq - YNq + YBq; </
s
>
<
s
xml:id
="
echoid-s1725
"
xml:space
="
preserve
">erit
<
lb
/>
(hypotheſin perſequendo) YBq. </
s
>
<
s
xml:id
="
echoid-s1726
"
xml:space
="
preserve
">KNq + YBq - YNq :</
s
>
<
s
xml:id
="
echoid-s1727
"
xml:space
="
preserve
">: Rq.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1728
"
xml:space
="
preserve
">Rq - Iq :</
s
>
<
s
xml:id
="
echoid-s1729
"
xml:space
="
preserve
">: ANq. </
s
>
<
s
xml:id
="
echoid-s1730
"
xml:space
="
preserve
">ANq - KNq. </
s
>
<
s
xml:id
="
echoid-s1731
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1732
"
xml:space
="
preserve
">per rationis converſionem
<
lb
/>
YBq. </
s
>
<
s
xml:id
="
echoid-s1733
"
xml:space
="
preserve
">YNq - KNq :</
s
>
<
s
xml:id
="
echoid-s1734
"
xml:space
="
preserve
">: ANq. </
s
>
<
s
xml:id
="
echoid-s1735
"
xml:space
="
preserve
">KNq. </
s
>
<
s
xml:id
="
echoid-s1736
"
xml:space
="
preserve
">(eſt autem YBq =
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0052-02
"
xlink:href
="
note-0052-02a
"
xml:space
="
preserve
">Fig. 41.</
note
>
YNq - BNq = YNq - ANq + ABq) ergò YNq - ANq
<
lb
/>
+ ABq. </
s
>
<
s
xml:id
="
echoid-s1737
"
xml:space
="
preserve
">YNq - KNq :</
s
>
<
s
xml:id
="
echoid-s1738
"
xml:space
="
preserve
">: ANq. </
s
>
<
s
xml:id
="
echoid-s1739
"
xml:space
="
preserve
">KNq (hoc eſt, anteceden-
<
lb
/>
tes & </
s
>
<
s
xml:id
="
echoid-s1740
"
xml:space
="
preserve
">conſequentes adjungendo) :</
s
>
<
s
xml:id
="
echoid-s1741
"
xml:space
="
preserve
">: YNq + ABq. </
s
>
<
s
xml:id
="
echoid-s1742
"
xml:space
="
preserve
">YNq. </
s
>
<
s
xml:id
="
echoid-s1743
"
xml:space
="
preserve
">quare
<
lb
/>
dividendo ANq - KNq. </
s
>
<
s
xml:id
="
echoid-s1744
"
xml:space
="
preserve
">KNq :</
s
>
<
s
xml:id
="
echoid-s1745
"
xml:space
="
preserve
">: ABq. </
s
>
<
s
xml:id
="
echoid-s1746
"
xml:space
="
preserve
">YNq hoc eſt Rq -
<
lb
/>
Iq. </
s
>
<
s
xml:id
="
echoid-s1747
"
xml:space
="
preserve
">Iq :</
s
>
<
s
xml:id
="
echoid-s1748
"
xml:space
="
preserve
">: ABq. </
s
>
<
s
xml:id
="
echoid-s1749
"
xml:space
="
preserve
">YNq: </
s
>
<
s
xml:id
="
echoid-s1750
"
xml:space
="
preserve
">Q. </
s
>
<
s
xml:id
="
echoid-s1751
"
xml:space
="
preserve
">E. </
s
>
<
s
xml:id
="
echoid-s1752
"
xml:space
="
preserve
">D.</
s
>
<
s
xml:id
="
echoid-s1753
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1754
"
xml:space
="
preserve
">XIV. </
s
>
<
s
xml:id
="
echoid-s1755
"
xml:space
="
preserve
">_Corol_. </
s
>
<
s
xml:id
="
echoid-s1756
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s1757
"
xml:space
="
preserve
">Hinc rurſus, ſi duo reſracti M _a_, N _a_ ſecent axem punctis
<
lb
/>
I, K; </
s
>
<
s
xml:id
="
echoid-s1758
"
xml:space
="
preserve
">ipſos autem ſe decuſſent puncto X; </
s
>
<
s
xml:id
="
echoid-s1759
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1760
"
xml:space
="
preserve
">ſiat YP. </
s
>
<
s
xml:id
="
echoid-s1761
"
xml:space
="
preserve
">XP :</
s
>
<
s
xml:id
="
echoid-s1762
"
xml:space
="
preserve
">: R. </
s
>
<
s
xml:id
="
echoid-s1763
"
xml:space
="
preserve
">√
<
lb
/>
Rq - Iq. </
s
>
<
s
xml:id
="
echoid-s1764
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1765
"
xml:space
="
preserve
">per Y ducantur MY R, NY S; </
s
>
<
s
xml:id
="
echoid-s1766
"
xml:space
="
preserve
">erit NS = MR.</
s
>
<
s
xml:id
="
echoid-s1767
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1768
"
xml:space
="
preserve
">Nam SB. </
s
>
<
s
xml:id
="
echoid-s1769
"
xml:space
="
preserve
">KB :</
s
>
<
s
xml:id
="
echoid-s1770
"
xml:space
="
preserve
">: YP. </
s
>
<
s
xml:id
="
echoid-s1771
"
xml:space
="
preserve
">XP :</
s
>
<
s
xml:id
="
echoid-s1772
"
xml:space
="
preserve
">: R. </
s
>
<
s
xml:id
="
echoid-s1773
"
xml:space
="
preserve
">√ Rq - Iq. </
s
>
<
s
xml:id
="
echoid-s1774
"
xml:space
="
preserve
">quare AB.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1775
"
xml:space
="
preserve
">SN :</
s
>
<
s
xml:id
="
echoid-s1776
"
xml:space
="
preserve
">: √ Rq - Iq. </
s
>
<
s
xml:id
="
echoid-s1777
"
xml:space
="
preserve
">I. </
s
>
<
s
xml:id
="
echoid-s1778
"
xml:space
="
preserve
">item RB. </
s
>
<
s
xml:id
="
echoid-s1779
"
xml:space
="
preserve
">IB :</
s
>
<
s
xml:id
="
echoid-s1780
"
xml:space
="
preserve
">: YP. </
s
>
<
s
xml:id
="
echoid-s1781
"
xml:space
="
preserve
">XP :</
s
>
<
s
xml:id
="
echoid-s1782
"
xml:space
="
preserve
">: R. </
s
>
<
s
xml:id
="
echoid-s1783
"
xml:space
="
preserve
">√ Rq -
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0052-03
"
xlink:href
="
note-0052-03a
"
xml:space
="
preserve
">Fig. 42.</
note
>
Iq. </
s
>
<
s
xml:id
="
echoid-s1784
"
xml:space
="
preserve
">quare AB. </
s
>
<
s
xml:id
="
echoid-s1785
"
xml:space
="
preserve
">RM :</
s
>
<
s
xml:id
="
echoid-s1786
"
xml:space
="
preserve
">: √ Rq - Iq. </
s
>
<
s
xml:id
="
echoid-s1787
"
xml:space
="
preserve
">I. </
s
>
<
s
xml:id
="
echoid-s1788
"
xml:space
="
preserve
">ergò AB. </
s
>
<
s
xml:id
="
echoid-s1789
"
xml:space
="
preserve
">SN :</
s
>
<
s
xml:id
="
echoid-s1790
"
xml:space
="
preserve
">: AB.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s1791
"
xml:space
="
preserve
">RM. </
s
>
<
s
xml:id
="
echoid-s1792
"
xml:space
="
preserve
">quare SN = RM.</
s
>
<
s
xml:id
="
echoid-s1793
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1794
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s1795
"
xml:space
="
preserve
">Hinc SB. </
s
>
<
s
xml:id
="
echoid-s1796
"
xml:space
="
preserve
">RB :</
s
>
<
s
xml:id
="
echoid-s1797
"
xml:space
="
preserve
">: KB. </
s
>
<
s
xml:id
="
echoid-s1798
"
xml:space
="
preserve
">IB.</
s
>
<
s
xml:id
="
echoid-s1799
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1800
"
xml:space
="
preserve
">XV. </
s
>
<
s
xml:id
="
echoid-s1801
"
xml:space
="
preserve
">Porrò, notandum eſt quò radii ab A manantes axi viciniores
<
lb
/>
f
<
unsure
/>
unt eò refractos ipſorum ſpiſſiùs incedere; </
s
>
<
s
xml:id
="
echoid-s1802
"
xml:space
="
preserve
">ſeu minora fore concur-
<
lb
/>
ſuum interſtitia; </
s
>
<
s
xml:id
="
echoid-s1803
"
xml:space
="
preserve
">ut nempe ſi in refringente EF ſumantur æqualia
<
lb
/>
intervalla MN, NO; </
s
>
<
s
xml:id
="
echoid-s1804
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s1805
"
xml:space
="
preserve
">radiorum punctis M, N, O incidentium
<
lb
/>
refracti M _a_, N _a_, O_a_ cum axe concurrant punctis I, K, L ; </
s
>
<
s
xml:id
="
echoid-s1806
"
xml:space
="
preserve
">erit </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>