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
>
271
(78)
272
(79)
273
(80)
274
(81)
275
(82)
276
(83)
277
(84)
278
(85)
279
(86)
280
(87)
<
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
|<
<
(89)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div381
"
type
="
section
"
level
="
1
"
n
="
41
">
<
p
>
<
s
xml:id
="
echoid-s12659
"
xml:space
="
preserve
">
<
pb
o
="
89
"
file
="
0267
"
n
="
282
"
rhead
="
"/>
CG = KL x LZ; </
s
>
<
s
xml:id
="
echoid-s12660
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12661
"
xml:space
="
preserve
">AB x BF = IK x KZ, & </
s
>
<
s
xml:id
="
echoid-s12662
"
xml:space
="
preserve
">VA x AE =
<
lb
/>
DI x IZ. </
s
>
<
s
xml:id
="
echoid-s12663
"
xml:space
="
preserve
">Verùm ſumma CD x DH + BC x CG + AB x
<
lb
/>
BF + VA x AE à ſpatio VDH minimè differt; </
s
>
<
s
xml:id
="
echoid-s12664
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12665
"
xml:space
="
preserve
">ſumma LH x
<
lb
/>
DO + KL x LZ + IK x KZ + DI x IZ à ſpatio DHO mi-
<
lb
/>
nimè differt. </
s
>
<
s
xml:id
="
echoid-s12666
"
xml:space
="
preserve
">itaque ſpatio VDH, DHO æquantur.</
s
>
<
s
xml:id
="
echoid-s12667
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12668
"
xml:space
="
preserve
">Hoc _perutile Theorema_ doctiſſimo Viro D. </
s
>
<
s
xml:id
="
echoid-s12669
"
xml:space
="
preserve
">_Gregorio Aberdonenſi_
<
lb
/>
debetur; </
s
>
<
s
xml:id
="
echoid-s12670
"
xml:space
="
preserve
">cui ſequentia ſubnectimus.</
s
>
<
s
xml:id
="
echoid-s12671
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12672
"
xml:space
="
preserve
">XI. </
s
>
<
s
xml:id
="
echoid-s12673
"
xml:space
="
preserve
">Iiſdem poſitis; </
s
>
<
s
xml:id
="
echoid-s12674
"
xml:space
="
preserve
">ſolidum ex ſpatio DHO circa axem VDR
<
lb
/>
rotato factum duplum erit ſolidi facti ex ſpatio VDH itidem circa ax-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0267-01
"
xlink:href
="
note-0267-01a
"
xml:space
="
preserve
">Fig. 125.</
note
>
em VD rotato.</
s
>
<
s
xml:id
="
echoid-s12675
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12676
"
xml:space
="
preserve
">Nam eſt HL. </
s
>
<
s
xml:id
="
echoid-s12677
"
xml:space
="
preserve
">LG:</
s
>
<
s
xml:id
="
echoid-s12678
"
xml:space
="
preserve
">: (DH. </
s
>
<
s
xml:id
="
echoid-s12679
"
xml:space
="
preserve
">DT:</
s
>
<
s
xml:id
="
echoid-s12680
"
xml:space
="
preserve
">: DH. </
s
>
<
s
xml:id
="
echoid-s12681
"
xml:space
="
preserve
">HO:</
s
>
<
s
xml:id
="
echoid-s12682
"
xml:space
="
preserve
">:) DHq.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s12683
"
xml:space
="
preserve
">DH x HO. </
s
>
<
s
xml:id
="
echoid-s12684
"
xml:space
="
preserve
">unde HL x DH x HO = LG x DHq = CD x
<
lb
/>
DHq. </
s
>
<
s
xml:id
="
echoid-s12685
"
xml:space
="
preserve
">Similíque diſcurſu ſunt LK x DL x LZ = BC x CGq. </
s
>
<
s
xml:id
="
echoid-s12686
"
xml:space
="
preserve
">
<
lb
/>
& </
s
>
<
s
xml:id
="
echoid-s12687
"
xml:space
="
preserve
">KI x DK x KZ = AB x BFq. </
s
>
<
s
xml:id
="
echoid-s12688
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12689
"
xml:space
="
preserve
">demum ID x DI x IZ =
<
lb
/>
VA x AEq. </
s
>
<
s
xml:id
="
echoid-s12690
"
xml:space
="
preserve
">Eſt autem (ut vulgò notatum habetur) ſumma CD
<
lb
/>
x DHq + BCB x CGq + AB x BFq + VA x AEq dupla
<
lb
/>
ſummæ DI x IE + DK x KF + DL x LG, &</
s
>
<
s
xml:id
="
echoid-s12691
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12692
"
xml:space
="
preserve
">Quare ſolidum
<
lb
/>
ex ſpatio HDO circa axem DR converſo factum duplum eſt ſolidi,
<
lb
/>
quod è ſpatio VDH circa VD converſo producitur.</
s
>
<
s
xml:id
="
echoid-s12693
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12694
"
xml:space
="
preserve
">XII. </
s
>
<
s
xml:id
="
echoid-s12695
"
xml:space
="
preserve
">Hinc, ſumma DI x IZ + DK x KZ + DL x LZ, &</
s
>
<
s
xml:id
="
echoid-s12696
"
xml:space
="
preserve
">c.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s12697
"
xml:space
="
preserve
">æquatur ſummæ quadratorum ex applicatis ad VD; </
s
>
<
s
xml:id
="
echoid-s12698
"
xml:space
="
preserve
">ſcilicet ipſis AEq
<
lb
/>
+ BFq + CGq, &</
s
>
<
s
xml:id
="
echoid-s12699
"
xml:space
="
preserve
">c.</
s
>
<
s
xml:id
="
echoid-s12700
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12701
"
xml:space
="
preserve
">XIII. </
s
>
<
s
xml:id
="
echoid-s12702
"
xml:space
="
preserve
">Simili ratiocinio conſtabit ſummam DIq x IZ + DKq x
<
lb
/>
KZ + DLq x LZ, &</
s
>
<
s
xml:id
="
echoid-s12703
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12704
"
xml:space
="
preserve
">triplam eſſe ſummæ DIq x IE + DKq
<
lb
/>
x KF + DLq x LG, &</
s
>
<
s
xml:id
="
echoid-s12705
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12706
"
xml:space
="
preserve
">hòc eſt æqualem ſummæ cuborum ab
<
lb
/>
omnibus AE, BF, CG, &</
s
>
<
s
xml:id
="
echoid-s12707
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12708
"
xml:space
="
preserve
">ad VD applicatis. </
s
>
<
s
xml:id
="
echoid-s12709
"
xml:space
="
preserve
">Idem quoad _re-_
<
lb
/>
_liquas poteſtates_ obſervabilis eſt Concluſionum tenor.</
s
>
<
s
xml:id
="
echoid-s12710
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12711
"
xml:space
="
preserve
">XIV. </
s
>
<
s
xml:id
="
echoid-s12712
"
xml:space
="
preserve
">Iiſdem poſitis; </
s
>
<
s
xml:id
="
echoid-s12713
"
xml:space
="
preserve
">ſi DXH ſit linea talis, ut quævis ad DH
<
lb
/>
o
<
unsure
/>
rdinata, ceu IX, ſit media proportionalis inter ſibi congruas ordi-
<
lb
/>
natas IE, IZ; </
s
>
<
s
xml:id
="
echoid-s12714
"
xml:space
="
preserve
">erìt ſolidum ex ſpatio VDH circa axem DH rotato
<
lb
/>
duplum ſolidi ex ſpatio DXH circa eundem axem DH converſo pro-
<
lb
/>
creati.</
s
>
<
s
xml:id
="
echoid-s12715
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12716
"
xml:space
="
preserve
">Nam ob VA x AE = DI x IZ, erit VA x AE x EI = DI x IZ x IE = ID x
<
lb
/>
IXq. </
s
>
<
s
xml:id
="
echoid-s12717
"
xml:space
="
preserve
">Similíque de cauſa AB x BF x FK = IK x KXq; </
s
>
<
s
xml:id
="
echoid-s12718
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12719
"
xml:space
="
preserve
">BC
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0267-02
"
xlink:href
="
note-0267-02a
"
xml:space
="
preserve
">In 10. hujus.</
note
>
x CG x GL = KL x LXq, &</
s
>
<
s
xml:id
="
echoid-s12720
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12721
"
xml:space
="
preserve
">Eſt autem ſumma VA x AE
<
lb
/>
x EI + AB x BF x FK + BC x CG x GL, &</
s
>
<
s
xml:id
="
echoid-s12722
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12723
"
xml:space
="
preserve
">Subdupla </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>