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
|<
<
(88)
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-s12603
"
xml:space
="
preserve
">
<
pb
o
="
88
"
file
="
0266
"
n
="
281
"
rhead
="
"/>
_ſpatio_ VDψ φ _circa axem_ VD _rotato ſubduplnm ſolidi ex ſpatio_
<
lb
/>
DRSH, _itidem circa axem_ VD _rotato, confecti._</
s
>
<
s
xml:id
="
echoid-s12604
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12605
"
xml:space
="
preserve
">Nam ob HL. </
s
>
<
s
xml:id
="
echoid-s12606
"
xml:space
="
preserve
">LG:</
s
>
<
s
xml:id
="
echoid-s12607
"
xml:space
="
preserve
">: PD. </
s
>
<
s
xml:id
="
echoid-s12608
"
xml:space
="
preserve
">DH:</
s
>
<
s
xml:id
="
echoid-s12609
"
xml:space
="
preserve
">: Dψ. </
s
>
<
s
xml:id
="
echoid-s12610
"
xml:space
="
preserve
">DH:</
s
>
<
s
xml:id
="
echoid-s12611
"
xml:space
="
preserve
">: Dψ_q_. </
s
>
<
s
xml:id
="
echoid-s12612
"
xml:space
="
preserve
">Dψ x
<
lb
/>
DH:</
s
>
<
s
xml:id
="
echoid-s12613
"
xml:space
="
preserve
">: Dψ_q_. </
s
>
<
s
xml:id
="
echoid-s12614
"
xml:space
="
preserve
">HS x DH; </
s
>
<
s
xml:id
="
echoid-s12615
"
xml:space
="
preserve
">erit HL x HS x DH = LG x Dψ_q_.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s12616
"
xml:space
="
preserve
"> = DC x Dψ_q_. </
s
>
<
s
xml:id
="
echoid-s12617
"
xml:space
="
preserve
">Simili planè diſcurſu erit LK x LX x DL =
<
lb
/>
CB x CZ_q_; </
s
>
<
s
xml:id
="
echoid-s12618
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12619
"
xml:space
="
preserve
">KI x KX x DK = BA x BZ_q_, &</
s
>
<
s
xml:id
="
echoid-s12620
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12621
"
xml:space
="
preserve
">atqui ſoli-
<
lb
/>
dum pt
<
unsure
/>
ius eſt {ῶ/δ}: </
s
>
<
s
xml:id
="
echoid-s12622
"
xml:space
="
preserve
">AZ_q_ + BZ_q_ + CZ_q_, &</
s
>
<
s
xml:id
="
echoid-s12623
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12624
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12625
"
xml:space
="
preserve
">ſolidum poſte-
<
lb
/>
rius eſt {2 ῶ/δ}: </
s
>
<
s
xml:id
="
echoid-s12626
"
xml:space
="
preserve
">DI x IX + DK x KX + DL x LX, &</
s
>
<
s
xml:id
="
echoid-s12627
"
xml:space
="
preserve
">c. </
s
>
<
s
xml:id
="
echoid-s12628
"
xml:space
="
preserve
">itaque
<
lb
/>
conſtat Propoſitum.</
s
>
<
s
xml:id
="
echoid-s12629
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12630
"
xml:space
="
preserve
">IX. </
s
>
<
s
xml:id
="
echoid-s12631
"
xml:space
="
preserve
">Hæc itidem omnia ſimili ratione vera ſunt, etiam ſi curva VEH
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0266-01
"
xlink:href
="
note-0266-01a
"
xml:space
="
preserve
">Fig. 124.</
note
>
rectæ VD convexas ſuas partes obvertat; </
s
>
<
s
xml:id
="
echoid-s12632
"
xml:space
="
preserve
">nempe quovis in curva ac-
<
lb
/>
cepto puncto E; </
s
>
<
s
xml:id
="
echoid-s12633
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12634
"
xml:space
="
preserve
">per hoc ductâ EP ad curvam VEH perpendicu-
<
lb
/>
lari, & </
s
>
<
s
xml:id
="
echoid-s12635
"
xml:space
="
preserve
">EAY ad rectam VD normali, factáque AZ = AP; </
s
>
<
s
xml:id
="
echoid-s12636
"
xml:space
="
preserve
">erit
<
lb
/>
ſpatium VDψ = {DH_q_;</
s
>
<
s
xml:id
="
echoid-s12637
"
xml:space
="
preserve
">/2} Sin quoque fiat AY = VP; </
s
>
<
s
xml:id
="
echoid-s12638
"
xml:space
="
preserve
">erit ſpati-
<
lb
/>
um VD ψ = {VH_q_;</
s
>
<
s
xml:id
="
echoid-s12639
"
xml:space
="
preserve
">/2} Et pariter quoad cætera.</
s
>
<
s
xml:id
="
echoid-s12640
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12641
"
xml:space
="
preserve
">Ex his verò _Theorematis quam innumerarum magnitudinum_ (ex
<
lb
/>
ipſarum immediatè conſtructione) _dimenſiones innoteſcant_, ab expe-
<
lb
/>
rientia facilè comperietur.</
s
>
<
s
xml:id
="
echoid-s12642
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12643
"
xml:space
="
preserve
">X. </
s
>
<
s
xml:id
="
echoid-s12644
"
xml:space
="
preserve
">Sit rurſus curva quæpiam VH (cujus axis VD, baſis DH)
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0266-02
"
xlink:href
="
note-0266-02a
"
xml:space
="
preserve
">Fig. 125.</
note
>
& </
s
>
<
s
xml:id
="
echoid-s12645
"
xml:space
="
preserve
">linea DZZO talis, ut a curvæ puncto quopiam, cen E, ductâ
<
lb
/>
rectâ ET, quæ curvam tangat, & </
s
>
<
s
xml:id
="
echoid-s12646
"
xml:space
="
preserve
">recta EIZ ad baſin parallelâ, ſit
<
lb
/>
qerpetuò IZ æqualis ipſi AT; </
s
>
<
s
xml:id
="
echoid-s12647
"
xml:space
="
preserve
">dico _ſpatium_ DHO _ſpatio_ VDH
<
lb
/>
_æquari_.</
s
>
<
s
xml:id
="
echoid-s12648
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s12649
"
xml:space
="
preserve
">Æquiſecetur enim recta DH indefinitè, punctis I, K, L, per quæ
<
lb
/>
ducantur rectæ EIZ, FKZ, GLZ ad VD parallelæ, curvæque oc-
<
lb
/>
currentes ad E, F, G, unde ducantur rectæ EA, FB, GC ad HD
<
lb
/>
parallelæ, rectæque ET, FT, GT (ut & </
s
>
<
s
xml:id
="
echoid-s12650
"
xml:space
="
preserve
">HT) _curvam tangentes;_
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s12651
"
xml:space
="
preserve
">lineæ verò ſe, ut Schema monſtrat, interſecent. </
s
>
<
s
xml:id
="
echoid-s12652
"
xml:space
="
preserve
">Eſtque jam triangu-
<
lb
/>
lum GLH ſimile triangulo TDH (nam ob diviſionem iſtam indefi-
<
lb
/>
nitam arculus GH rectæ inſtar cenſeri poteſt, eatenus tangenti HT
<
lb
/>
coincidens) quare LG. </
s
>
<
s
xml:id
="
echoid-s12653
"
xml:space
="
preserve
">LH:</
s
>
<
s
xml:id
="
echoid-s12654
"
xml:space
="
preserve
">: TD. </
s
>
<
s
xml:id
="
echoid-s12655
"
xml:space
="
preserve
">DH; </
s
>
<
s
xml:id
="
echoid-s12656
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s12657
"
xml:space
="
preserve
">LG x DH = LH
<
lb
/>
x TD; </
s
>
<
s
xml:id
="
echoid-s12658
"
xml:space
="
preserve
">ſeu CD x DH = LH x HO. </
s
>
<
s
xml:id
="
echoid-s12659
"
xml:space
="
preserve
">ſimili ratiocinio eſt BC </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>