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
|<
<
(55)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div222
"
type
="
section
"
level
="
1
"
n
="
31
">
<
p
>
<
s
xml:id
="
echoid-s10466
"
xml:space
="
preserve
">
<
pb
o
="
55
"
file
="
0233
"
n
="
248
"
rhead
="
"/>
item PO ad TE parallela. </
s
>
<
s
xml:id
="
echoid-s10467
"
xml:space
="
preserve
">Eſtque EFq = EOq (CPq) + OFq
<
lb
/>
+ 2 EO x OF (+ 2 CP x OF). </
s
>
<
s
xml:id
="
echoid-s10468
"
xml:space
="
preserve
">Verùm ob CP. </
s
>
<
s
xml:id
="
echoid-s10469
"
xml:space
="
preserve
">CA :</
s
>
<
s
xml:id
="
echoid-s10470
"
xml:space
="
preserve
">: OP.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10471
"
xml:space
="
preserve
">OF :</
s
>
<
s
xml:id
="
echoid-s10472
"
xml:space
="
preserve
">: CE. </
s
>
<
s
xml:id
="
echoid-s10473
"
xml:space
="
preserve
">OF; </
s
>
<
s
xml:id
="
echoid-s10474
"
xml:space
="
preserve
">eſt CP x OF = CA x CE; </
s
>
<
s
xml:id
="
echoid-s10475
"
xml:space
="
preserve
">ergò EFq =
<
lb
/>
CPq + OFq + 2 CA x CE. </
s
>
<
s
xml:id
="
echoid-s10476
"
xml:space
="
preserve
">item eſt AEq = CEq +
<
lb
/>
CAq - 2 CA x CE; </
s
>
<
s
xml:id
="
echoid-s10477
"
xml:space
="
preserve
">quapropter eſt EFq + AEq = CPq +
<
lb
/>
CAq + OFq + CEq. </
s
>
<
s
xml:id
="
echoid-s10478
"
xml:space
="
preserve
">hoc eſt EGq = (APq + PFq = )
<
lb
/>
CVq + PFq. </
s
>
<
s
xml:id
="
echoid-s10479
"
xml:space
="
preserve
">vel EGq - PFq = CVq. </
s
>
<
s
xml:id
="
echoid-s10480
"
xml:space
="
preserve
">Verùm eſt CE. </
s
>
<
s
xml:id
="
echoid-s10481
"
xml:space
="
preserve
">
<
lb
/>
(PO). </
s
>
<
s
xml:id
="
echoid-s10482
"
xml:space
="
preserve
">PF :</
s
>
<
s
xml:id
="
echoid-s10483
"
xml:space
="
preserve
">: CP.</
s
>
<
s
xml:id
="
echoid-s10484
"
xml:space
="
preserve
">AP :</
s
>
<
s
xml:id
="
echoid-s10485
"
xml:space
="
preserve
">: CP.</
s
>
<
s
xml:id
="
echoid-s10486
"
xml:space
="
preserve
">CV; </
s
>
<
s
xml:id
="
echoid-s10487
"
xml:space
="
preserve
">unde EGq - {CVq/CPq} CEq
<
lb
/>
= CVq; </
s
>
<
s
xml:id
="
echoid-s10488
"
xml:space
="
preserve
">adeóque linea GVG eſt _hyperbola_, cujus centrum C; </
s
>
<
s
xml:id
="
echoid-s10489
"
xml:space
="
preserve
">ſe-
<
lb
/>
miaxes CV, CP.</
s
>
<
s
xml:id
="
echoid-s10490
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10491
"
xml:space
="
preserve
">Not. </
s
>
<
s
xml:id
="
echoid-s10492
"
xml:space
="
preserve
">Ductà rectâ FQ ad TH perpendiculari, ſumptáque QR =
<
lb
/>
AE; </
s
>
<
s
xml:id
="
echoid-s10493
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s10494
"
xml:space
="
preserve
">connexâ GR; </
s
>
<
s
xml:id
="
echoid-s10495
"
xml:space
="
preserve
">erit GR _hyperbolæ_ VGG perpendicularis;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10496
"
xml:space
="
preserve
">mihi præſta sîs ſidem; </
s
>
<
s
xml:id
="
echoid-s10497
"
xml:space
="
preserve
">aut ipſe rem ad Calculum exige; </
s
>
<
s
xml:id
="
echoid-s10498
"
xml:space
="
preserve
">eò verba
<
lb
/>
non proſundam.</
s
>
<
s
xml:id
="
echoid-s10499
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10500
"
xml:space
="
preserve
">XXVI. </
s
>
<
s
xml:id
="
echoid-s10501
"
xml:space
="
preserve
">Poſitione datæ ſint rectæ AC, BD (ſe interſecantes in X)
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0233-01
"
xlink:href
="
note-0233-01a
"
xml:space
="
preserve
">Fig. 59.</
note
>
qnas decuſſet recta A B; </
s
>
<
s
xml:id
="
echoid-s10502
"
xml:space
="
preserve
">tum ductâ utcunque rectâ PKL ad AB
<
lb
/>
parallelâ, (quæ rectas AC, BD ſecet punctis P, K) ſit PL æqua-
<
lb
/>
lis ipſi BK; </
s
>
<
s
xml:id
="
echoid-s10503
"
xml:space
="
preserve
">erit linea ALL recta.</
s
>
<
s
xml:id
="
echoid-s10504
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10505
"
xml:space
="
preserve
">Nam, (ductâ XQ ad BA parallelâ, eſt AQ. </
s
>
<
s
xml:id
="
echoid-s10506
"
xml:space
="
preserve
">AP :</
s
>
<
s
xml:id
="
echoid-s10507
"
xml:space
="
preserve
">: (BX.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10508
"
xml:space
="
preserve
">BK :</
s
>
<
s
xml:id
="
echoid-s10509
"
xml:space
="
preserve
">: ) QX. </
s
>
<
s
xml:id
="
echoid-s10510
"
xml:space
="
preserve
">PL: </
s
>
<
s
xml:id
="
echoid-s10511
"
xml:space
="
preserve
">ergo linea ALL eſt recta.</
s
>
<
s
xml:id
="
echoid-s10512
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10513
"
xml:space
="
preserve
">XXVII. </
s
>
<
s
xml:id
="
echoid-s10514
"
xml:space
="
preserve
">Poſitione data ſit recta A X, & </
s
>
<
s
xml:id
="
echoid-s10515
"
xml:space
="
preserve
">punctum D; </
s
>
<
s
xml:id
="
echoid-s10516
"
xml:space
="
preserve
">neque non
<
lb
/>
linea DNN talis; </
s
>
<
s
xml:id
="
echoid-s10517
"
xml:space
="
preserve
">ut per D ductâ quâcunque rectâ MN (quæ re-
<
lb
/>
<
note
position
="
right
"
xlink:label
="
note-0233-02
"
xlink:href
="
note-0233-02a
"
xml:space
="
preserve
">Fig. 60.</
note
>
ctam AX ſecet in M, & </
s
>
<
s
xml:id
="
echoid-s10518
"
xml:space
="
preserve
">lineam DNN in N) ſit perpetim rectangu-
<
lb
/>
lum ex DM, DN æquale dato (puta quadrato ex Z); </
s
>
<
s
xml:id
="
echoid-s10519
"
xml:space
="
preserve
">erit linea
<
lb
/>
DNN circularis.</
s
>
<
s
xml:id
="
echoid-s10520
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10521
"
xml:space
="
preserve
">Nam ducatur DB ad AX perpendicularis; </
s
>
<
s
xml:id
="
echoid-s10522
"
xml:space
="
preserve
">ſitque DB. </
s
>
<
s
xml:id
="
echoid-s10523
"
xml:space
="
preserve
">Z :</
s
>
<
s
xml:id
="
echoid-s10524
"
xml:space
="
preserve
">: Z.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s10525
"
xml:space
="
preserve
">DE; </
s
>
<
s
xml:id
="
echoid-s10526
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s10527
"
xml:space
="
preserve
">connectatur NE; </
s
>
<
s
xml:id
="
echoid-s10528
"
xml:space
="
preserve
">Eſt jam DM x DN = Zq = DB x
<
lb
/>
DE; </
s
>
<
s
xml:id
="
echoid-s10529
"
xml:space
="
preserve
">quare DM. </
s
>
<
s
xml:id
="
echoid-s10530
"
xml:space
="
preserve
">DB :</
s
>
<
s
xml:id
="
echoid-s10531
"
xml:space
="
preserve
">: DE. </
s
>
<
s
xml:id
="
echoid-s10532
"
xml:space
="
preserve
">DN. </
s
>
<
s
xml:id
="
echoid-s10533
"
xml:space
="
preserve
">ergò triangula DBM, DNE
<
lb
/>
ſimilia ſunt; </
s
>
<
s
xml:id
="
echoid-s10534
"
xml:space
="
preserve
">quapropter angulus DNE rectus eſt; </
s
>
<
s
xml:id
="
echoid-s10535
"
xml:space
="
preserve
">itaque linea DNN
<
lb
/>
eſt circularis: </
s
>
<
s
xml:id
="
echoid-s10536
"
xml:space
="
preserve
">(ad circulum pertinens, _c@jus Diameter_ DE).</
s
>
<
s
xml:id
="
echoid-s10537
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s10538
"
xml:space
="
preserve
">Vides nedum rectam & </
s
>
<
s
xml:id
="
echoid-s10539
"
xml:space
="
preserve
">_hyperbolam_; </
s
>
<
s
xml:id
="
echoid-s10540
"
xml:space
="
preserve
">ſed & </
s
>
<
s
xml:id
="
echoid-s10541
"
xml:space
="
preserve
">ſuo modo rectam ac
<
lb
/>
_circulum_ ſibi lineas eſſe reciprocas. </
s
>
<
s
xml:id
="
echoid-s10542
"
xml:space
="
preserve
">Verùm hîc, etſi præludiis no-
<
lb
/>
ſtris nondum abſolutis, paulùm ſubſiſtamus.</
s
>
<
s
xml:id
="
echoid-s10543
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>