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
>
41
(23)
42
(24)
43
(25)
44
(26)
45
(27)
46
(28)
47
(29)
48
(30)
49
(31)
50
(32)
<
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
|<
<
(25)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div22
"
type
="
section
"
level
="
1
"
n
="
11
">
<
p
>
<
s
xml:id
="
echoid-s943
"
xml:space
="
preserve
">
<
pb
o
="
25
"
file
="
0043
"
n
="
43
"
rhead
="
"/>
obliquiùs quàm DB.) </
s
>
<
s
xml:id
="
echoid-s944
"
xml:space
="
preserve
">Horum verò refracti ſint B _a_, Bδ; </
s
>
<
s
xml:id
="
echoid-s945
"
xml:space
="
preserve
">dico an-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0043-01
"
xlink:href
="
note-0043-01a
"
xml:space
="
preserve
">Fig. 21.</
note
>
gulum β B _a_ majorem eſſe angulo HB δ. </
s
>
<
s
xml:id
="
echoid-s946
"
xml:space
="
preserve
">Nam ad BP in perpendicu-
<
lb
/>
lari liberè ſumptam diametrum conſtituatur ſemicirculus BGP; </
s
>
<
s
xml:id
="
echoid-s947
"
xml:space
="
preserve
">cui
<
lb
/>
occurrant ipſæ AB, DB protractæ ad G, H; </
s
>
<
s
xml:id
="
echoid-s948
"
xml:space
="
preserve
">nec non ipſæ B _a_, B δ
<
lb
/>
punctis _a_, δ. </
s
>
<
s
xml:id
="
echoid-s949
"
xml:space
="
preserve
">Fiat autem angulus GBK æqualis angulo HBδ, vel
<
lb
/>
arcus GK arcui Hδ; </
s
>
<
s
xml:id
="
echoid-s950
"
xml:space
="
preserve
">connectatur etiam rècta δ G, ſecans ipſam PK
<
lb
/>
in X; </
s
>
<
s
xml:id
="
echoid-s951
"
xml:space
="
preserve
">ducatnurque denuò ſubtenſæ G δ, H δ. </
s
>
<
s
xml:id
="
echoid-s952
"
xml:space
="
preserve
">Jam ob angulos PG δ,
<
lb
/>
PH δ pares (arcui quippe P δ inſiſtentes ambos) & </
s
>
<
s
xml:id
="
echoid-s953
"
xml:space
="
preserve
">angulos GPK,
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0043-02
"
xlink:href
="
note-0043-02a
"
xml:space
="
preserve
">Fig. 22.</
note
>
HP δ ex conſtructione quoque pares, erunt triangula GPX,
<
lb
/>
HP δ inter ſe ſimilia. </
s
>
<
s
xml:id
="
echoid-s954
"
xml:space
="
preserve
">Quapropter erit PG. </
s
>
<
s
xml:id
="
echoid-s955
"
xml:space
="
preserve
">PX :</
s
>
<
s
xml:id
="
echoid-s956
"
xml:space
="
preserve
">: PH. </
s
>
<
s
xml:id
="
echoid-s957
"
xml:space
="
preserve
">P δ. </
s
>
<
s
xml:id
="
echoid-s958
"
xml:space
="
preserve
">eſt
<
lb
/>
autem, è lege refractionum PH. </
s
>
<
s
xml:id
="
echoid-s959
"
xml:space
="
preserve
">P δ :</
s
>
<
s
xml:id
="
echoid-s960
"
xml:space
="
preserve
">: PG. </
s
>
<
s
xml:id
="
echoid-s961
"
xml:space
="
preserve
">P _a_. </
s
>
<
s
xml:id
="
echoid-s962
"
xml:space
="
preserve
">quare PG. </
s
>
<
s
xml:id
="
echoid-s963
"
xml:space
="
preserve
">PX :</
s
>
<
s
xml:id
="
echoid-s964
"
xml:space
="
preserve
">:
<
lb
/>
PG. </
s
>
<
s
xml:id
="
echoid-s965
"
xml:space
="
preserve
">P _a_: </
s
>
<
s
xml:id
="
echoid-s966
"
xml:space
="
preserve
">unde PX = P _a_. </
s
>
<
s
xml:id
="
echoid-s967
"
xml:space
="
preserve
">eſt autem PX minor quàm PK (quia
<
lb
/>
tota ſubtenſa G δ intra circulum jacet.) </
s
>
<
s
xml:id
="
echoid-s968
"
xml:space
="
preserve
">Quare P _a_ minor eſt quàm
<
lb
/>
PK; </
s
>
<
s
xml:id
="
echoid-s969
"
xml:space
="
preserve
">adeóque PK ſecabit angulum GP _a_. </
s
>
<
s
xml:id
="
echoid-s970
"
xml:space
="
preserve
">quamobrem arcùs G _a_ ma-
<
lb
/>
jor erit arcu GK, hoc eſt arcu H δ. </
s
>
<
s
xml:id
="
echoid-s971
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s972
"
xml:space
="
preserve
">idcircò major erit angulus
<
lb
/>
GB _a_ angulo HB δ: </
s
>
<
s
xml:id
="
echoid-s973
"
xml:space
="
preserve
">Q. </
s
>
<
s
xml:id
="
echoid-s974
"
xml:space
="
preserve
">E. </
s
>
<
s
xml:id
="
echoid-s975
"
xml:space
="
preserve
">D.</
s
>
<
s
xml:id
="
echoid-s976
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s977
"
xml:space
="
preserve
">Procedit hæc demonſtratio quoad caſum, ubi I &</
s
>
<
s
xml:id
="
echoid-s978
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s979
"
xml:space
="
preserve
">R (vel cùm ra-
<
lb
/>
dius è medio rariori denſius ingreditur) at exinde quoad alterum quo-
<
lb
/>
que caſum facilè deducitur concluſio. </
s
>
<
s
xml:id
="
echoid-s980
"
xml:space
="
preserve
">Nam ſi viciſſim _a_ B, δ B con-
<
lb
/>
cipiantur incidentes, erunt ipſæ BA, BD earum refractæ; </
s
>
<
s
xml:id
="
echoid-s981
"
xml:space
="
preserve
">ac etiam-
<
lb
/>
num anguli _a_ BG, δ BH erunt anguli refracti.</
s
>
<
s
xml:id
="
echoid-s982
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s983
"
xml:space
="
preserve
">Hujuſce Theorematis apud _Herigonium_ habetur alia demonſtra-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0043-03
"
xlink:href
="
note-0043-03a
"
xml:space
="
preserve
">_Diopt
<
unsure
/>
. Prop@.4_.</
note
>
tio. </
s
>
<
s
xml:id
="
echoid-s984
"
xml:space
="
preserve
">Confer ſodes, & </
s
>
<
s
xml:id
="
echoid-s985
"
xml:space
="
preserve
">utramvis elige. </
s
>
<
s
xml:id
="
echoid-s986
"
xml:space
="
preserve
">No3 quam res obtulit
<
lb
/>
poſuimus.</
s
>
<
s
xml:id
="
echoid-s987
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s988
"
xml:space
="
preserve
">VII. </
s
>
<
s
xml:id
="
echoid-s989
"
xml:space
="
preserve
">In iſto refractionis caſu, quum I minor eſt quàm R, ſi anguli
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0043-04
"
xlink:href
="
note-0043-04a
"
xml:space
="
preserve
">Fig. 23.</
note
>
incidentiæ, puta anguli DBQ, rectus ſinus PH, ad ſinum totum ſe
<
lb
/>
habeat ut I ad R; </
s
>
<
s
xml:id
="
echoid-s990
"
xml:space
="
preserve
">nullus incidente DB obliquior radius medium EF
<
lb
/>
refractus ingredietur, aut penetrabit.</
s
>
<
s
xml:id
="
echoid-s991
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s992
"
xml:space
="
preserve
">Nam penerret (ſi fieri poteſt) obliquioris alicujus ABG refractus
<
lb
/>
B _a_. </
s
>
<
s
xml:id
="
echoid-s993
"
xml:space
="
preserve
">Erit ergo PG. </
s
>
<
s
xml:id
="
echoid-s994
"
xml:space
="
preserve
">P _a_ :</
s
>
<
s
xml:id
="
echoid-s995
"
xml:space
="
preserve
">: (I. </
s
>
<
s
xml:id
="
echoid-s996
"
xml:space
="
preserve
">R :</
s
>
<
s
xml:id
="
echoid-s997
"
xml:space
="
preserve
">: ) *PH. </
s
>
<
s
xml:id
="
echoid-s998
"
xml:space
="
preserve
">PB. </
s
>
<
s
xml:id
="
echoid-s999
"
xml:space
="
preserve
">eſt autem PG
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0043-05
"
xlink:href
="
note-0043-05a
"
xml:space
="
preserve
">*_Hypotb_.</
note
>
major quàm PH. </
s
>
<
s
xml:id
="
echoid-s1000
"
xml:space
="
preserve
">ergo P _a_ major erit quam PB. </
s
>
<
s
xml:id
="
echoid-s1001
"
xml:space
="
preserve
">quod planè
<
lb
/>
fieri nequit. </
s
>
<
s
xml:id
="
echoid-s1002
"
xml:space
="
preserve
">Ergò AB non refringetur in medium ipſi EF ſub-
<
lb
/>
jectum.</
s
>
<
s
xml:id
="
echoid-s1003
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1004
"
xml:space
="
preserve
">VIII. </
s
>
<
s
xml:id
="
echoid-s1005
"
xml:space
="
preserve
">Angulus incidentiæ major ad angulum ſuum refractum ma-
<
lb
/>
jorem habet rationem, quam angulus incidentiæ minor ad refra-
<
lb
/>
ctum fuum.</
s
>
<
s
xml:id
="
echoid-s1006
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s1007
"
xml:space
="
preserve
">Erit ſcilicet (in figura numeri Sexti, cujus huc apparatus transfe-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0043-06
"
xlink:href
="
note-0043-06a
"
xml:space
="
preserve
">Fig. 27, 22.</
note
>
ratur) ang. </
s
>
<
s
xml:id
="
echoid-s1008
"
xml:space
="
preserve
">GBP. </
s
>
<
s
xml:id
="
echoid-s1009
"
xml:space
="
preserve
">_a_ BP. </
s
>
<
s
xml:id
="
echoid-s1010
"
xml:space
="
preserve
">&</
s
>
<
s
xml:id
="
echoid-s1011
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s1012
"
xml:space
="
preserve
">ang. </
s
>
<
s
xml:id
="
echoid-s1013
"
xml:space
="
preserve
">HBP. </
s
>
<
s
xml:id
="
echoid-s1014
"
xml:space
="
preserve
">δ BP. </
s
>
<
s
xml:id
="
echoid-s1015
"
xml:space
="
preserve
">Nam </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>