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
page
|<
<
(116)
of 393
>
>|
<
echo
version
="
1.0RC
">
<
text
xml:lang
="
la
"
type
="
free
">
<
div
xml:id
="
echoid-div189
"
type
="
section
"
level
="
1
"
n
="
23
">
<
pb
o
="
116
"
file
="
0134
"
n
="
134
"
rhead
="
"/>
<
p
>
<
s
xml:id
="
echoid-s7585
"
xml:space
="
preserve
">XVI. </
s
>
<
s
xml:id
="
echoid-s7586
"
xml:space
="
preserve
">Addiametrum CO deſcribatur circulus CFH; </
s
>
<
s
xml:id
="
echoid-s7587
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7588
"
xml:space
="
preserve
">ab O
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0134-01
"
xlink:href
="
note-0134-01a
"
xml:space
="
preserve
">Fig. 187.</
note
>
radiusincidat talis, ut cum ejus reflexus ſit DS, contingat fore DS
<
lb
/>
= {1/2} DH, vel {1/2} DI; </
s
>
<
s
xml:id
="
echoid-s7589
"
xml:space
="
preserve
">poſitâ CI ad DS perpendiculari (talis autem
<
lb
/>
radius facilè duci poſſe concipiatur; </
s
>
<
s
xml:id
="
echoid-s7590
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7591
"
xml:space
="
preserve
">per curvam appropriatam re-
<
lb
/>
verà ſtatim determinetur; </
s
>
<
s
xml:id
="
echoid-s7592
"
xml:space
="
preserve
">id proinde nos non diſtinebit). </
s
>
<
s
xml:id
="
echoid-s7593
"
xml:space
="
preserve
">Erit tum
<
lb
/>
puncti Simago, puta σ, à puncto D infinitè disjuncta; </
s
>
<
s
xml:id
="
echoid-s7594
"
xml:space
="
preserve
">quoniam (id
<
lb
/>
quod fieri nequit, niſi H σ, σ D ſint infinitæ) eſt H σ. </
s
>
<
s
xml:id
="
echoid-s7595
"
xml:space
="
preserve
">σ D :</
s
>
<
s
xml:id
="
echoid-s7596
"
xml:space
="
preserve
">: IS.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7597
"
xml:space
="
preserve
">SD. </
s
>
<
s
xml:id
="
echoid-s7598
"
xml:space
="
preserve
">Jam in arcum DB cadat utcunque radius OM, cujus reflexus
<
lb
/>
ſit MA E; </
s
>
<
s
xml:id
="
echoid-s7599
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7600
"
xml:space
="
preserve
">in hac ſumatur ME = MF; </
s
>
<
s
xml:id
="
echoid-s7601
"
xml:space
="
preserve
">tum in OM producta
<
lb
/>
capiatur punctum α, ut ſit F α. </
s
>
<
s
xml:id
="
echoid-s7602
"
xml:space
="
preserve
">α M :</
s
>
<
s
xml:id
="
echoid-s7603
"
xml:space
="
preserve
">: EA. </
s
>
<
s
xml:id
="
echoid-s7604
"
xml:space
="
preserve
">AM; </
s
>
<
s
xml:id
="
echoid-s7605
"
xml:space
="
preserve
">erit α puncti A
<
lb
/>
imago. </
s
>
<
s
xml:id
="
echoid-s7606
"
xml:space
="
preserve
">ſimili methodo reperiatur ρ puncti R imago; </
s
>
<
s
xml:id
="
echoid-s7607
"
xml:space
="
preserve
">neque non reliqua
<
lb
/>
totius R ρασ, ipſam BS referentis, puncta.</
s
>
<
s
xml:id
="
echoid-s7608
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7609
"
xml:space
="
preserve
">XVII. </
s
>
<
s
xml:id
="
echoid-s7610
"
xml:space
="
preserve
">In harc verò conſtructionem quædam veniunt adnotanda.</
s
>
<
s
xml:id
="
echoid-s7611
"
xml:space
="
preserve
"/>
</
p
>
<
note
position
="
left
"
xml:space
="
preserve
">Fig. 187,
<
lb
/>
188.</
note
>
<
p
>
<
s
xml:id
="
echoid-s7612
"
xml:space
="
preserve
">1. </
s
>
<
s
xml:id
="
echoid-s7613
"
xml:space
="
preserve
">Quòd CS &</
s
>
<
s
xml:id
="
echoid-s7614
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7615
"
xml:space
="
preserve
">CZ. </
s
>
<
s
xml:id
="
echoid-s7616
"
xml:space
="
preserve
">Nam 4 CZq = CBq = 3 SDq +
<
lb
/>
CSq. </
s
>
<
s
xml:id
="
echoid-s7617
"
xml:space
="
preserve
">ergò quum ſit CZ &</
s
>
<
s
xml:id
="
echoid-s7618
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7619
"
xml:space
="
preserve
">SD; </
s
>
<
s
xml:id
="
echoid-s7620
"
xml:space
="
preserve
">erit CS &</
s
>
<
s
xml:id
="
echoid-s7621
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7622
"
xml:space
="
preserve
">CZ.</
s
>
<
s
xml:id
="
echoid-s7623
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7624
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s7625
"
xml:space
="
preserve
">Quod CA &</
s
>
<
s
xml:id
="
echoid-s7626
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7627
"
xml:space
="
preserve
">CS. </
s
>
<
s
xml:id
="
echoid-s7628
"
xml:space
="
preserve
">Nam (è ſuprà monſtratis) ſi ducatur
<
lb
/>
recta M ψ ad DO parallela, ejuſce reflexa (puta M ξ) ſecabit ipſam
<
lb
/>
DS, verſus I, puta ad ξ. </
s
>
<
s
xml:id
="
echoid-s7629
"
xml:space
="
preserve
">ergò M ξ ipſam CB ſecabit ſupra punctum S,
<
lb
/>
velut ad φ. </
s
>
<
s
xml:id
="
echoid-s7630
"
xml:space
="
preserve
">atqui quoniam ang. </
s
>
<
s
xml:id
="
echoid-s7631
"
xml:space
="
preserve
">CMO &</
s
>
<
s
xml:id
="
echoid-s7632
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7633
"
xml:space
="
preserve
">CMψ, ſeu ang. </
s
>
<
s
xml:id
="
echoid-s7634
"
xml:space
="
preserve
">CMA
<
lb
/>
&</
s
>
<
s
xml:id
="
echoid-s7635
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7636
"
xml:space
="
preserve
">CMφ, eſt CA &</
s
>
<
s
xml:id
="
echoid-s7637
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7638
"
xml:space
="
preserve
">C φ; </
s
>
<
s
xml:id
="
echoid-s7639
"
xml:space
="
preserve
">adeóque magìs eſt CA &</
s
>
<
s
xml:id
="
echoid-s7640
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7641
"
xml:space
="
preserve
">CS.</
s
>
<
s
xml:id
="
echoid-s7642
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7643
"
xml:space
="
preserve
">3. </
s
>
<
s
xml:id
="
echoid-s7644
"
xml:space
="
preserve
">Quòd EA &</
s
>
<
s
xml:id
="
echoid-s7645
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7646
"
xml:space
="
preserve
">AM. </
s
>
<
s
xml:id
="
echoid-s7647
"
xml:space
="
preserve
">cùm enim ſit EM (vel FM) &</
s
>
<
s
xml:id
="
echoid-s7648
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7649
"
xml:space
="
preserve
">HD,
<
lb
/>
atque DS &</
s
>
<
s
xml:id
="
echoid-s7650
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7651
"
xml:space
="
preserve
">MA; </
s
>
<
s
xml:id
="
echoid-s7652
"
xml:space
="
preserve
">erit EM. </
s
>
<
s
xml:id
="
echoid-s7653
"
xml:space
="
preserve
">MA &</
s
>
<
s
xml:id
="
echoid-s7654
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7655
"
xml:space
="
preserve
">FD. </
s
>
<
s
xml:id
="
echoid-s7656
"
xml:space
="
preserve
">DS :</
s
>
<
s
xml:id
="
echoid-s7657
"
xml:space
="
preserve
">: 2. </
s
>
<
s
xml:id
="
echoid-s7658
"
xml:space
="
preserve
">1.</
s
>
<
s
xml:id
="
echoid-s7659
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7660
"
xml:space
="
preserve
">4. </
s
>
<
s
xml:id
="
echoid-s7661
"
xml:space
="
preserve
">Hinc denuò liquebit totam lineam B ρασ ultra rectam CBL
<
lb
/>
jacere. </
s
>
<
s
xml:id
="
echoid-s7662
"
xml:space
="
preserve
">nam ducatur FQ ad AM parallela eſt hîc ang FCA &</
s
>
<
s
xml:id
="
echoid-s7663
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7664
"
xml:space
="
preserve
">ang
<
lb
/>
ACE. </
s
>
<
s
xml:id
="
echoid-s7665
"
xml:space
="
preserve
">& </
s
>
<
s
xml:id
="
echoid-s7666
"
xml:space
="
preserve
">ang FQA = ang CAE. </
s
>
<
s
xml:id
="
echoid-s7667
"
xml:space
="
preserve
">quapropter erit CF. </
s
>
<
s
xml:id
="
echoid-s7668
"
xml:space
="
preserve
">FQ
<
lb
/>
&</
s
>
<
s
xml:id
="
echoid-s7669
"
xml:space
="
preserve
">lt; </
s
>
<
s
xml:id
="
echoid-s7670
"
xml:space
="
preserve
">CE. </
s
>
<
s
xml:id
="
echoid-s7671
"
xml:space
="
preserve
">AE. </
s
>
<
s
xml:id
="
echoid-s7672
"
xml:space
="
preserve
">adeóque FQ &</
s
>
<
s
xml:id
="
echoid-s7673
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7674
"
xml:space
="
preserve
">AE. </
s
>
<
s
xml:id
="
echoid-s7675
"
xml:space
="
preserve
">acindè FQ. </
s
>
<
s
xml:id
="
echoid-s7676
"
xml:space
="
preserve
">AM &</
s
>
<
s
xml:id
="
echoid-s7677
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7678
"
xml:space
="
preserve
">AE.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s7679
"
xml:space
="
preserve
">AM; </
s
>
<
s
xml:id
="
echoid-s7680
"
xml:space
="
preserve
">hoc eſt FK, KM &</
s
>
<
s
xml:id
="
echoid-s7681
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7682
"
xml:space
="
preserve
">Fα. </
s
>
<
s
xml:id
="
echoid-s7683
"
xml:space
="
preserve
">αM. </
s
>
<
s
xml:id
="
echoid-s7684
"
xml:space
="
preserve
">dividendóque FM. </
s
>
<
s
xml:id
="
echoid-s7685
"
xml:space
="
preserve
">KM &</
s
>
<
s
xml:id
="
echoid-s7686
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7687
"
xml:space
="
preserve
">
<
lb
/>
FM. </
s
>
<
s
xml:id
="
echoid-s7688
"
xml:space
="
preserve
">αM. </
s
>
<
s
xml:id
="
echoid-s7689
"
xml:space
="
preserve
">quare α M &</
s
>
<
s
xml:id
="
echoid-s7690
"
xml:space
="
preserve
">gt; </
s
>
<
s
xml:id
="
echoid-s7691
"
xml:space
="
preserve
">KM. </
s
>
<
s
xml:id
="
echoid-s7692
"
xml:space
="
preserve
">adeóque punctum α ultra K in
<
lb
/>
recta OK protenſa jacet.</
s
>
<
s
xml:id
="
echoid-s7693
"
xml:space
="
preserve
"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s7694
"
xml:space
="
preserve
">XVIII. </
s
>
<
s
xml:id
="
echoid-s7695
"
xml:space
="
preserve
">Quòd ſiad partes alteras rectæ OD ducatur radius ON’
<
lb
/>
cujus reflexus NGT = NV; </
s
>
<
s
xml:id
="
echoid-s7696
"
xml:space
="
preserve
">ſitque TG. </
s
>
<
s
xml:id
="
echoid-s7697
"
xml:space
="
preserve
">GN &</
s
>
<
s
xml:id
="
echoid-s7698
"
xml:space
="
preserve
">lt; </
s
>
<
s
xml:id
="
echoid-s7699
"
xml:space
="
preserve
">2. </
s
>
<
s
xml:id
="
echoid-s7700
"
xml:space
="
preserve
">1; </
s
>
<
s
xml:id
="
echoid-s7701
"
xml:space
="
preserve
">ſtatuen-
<
lb
/>
da eſt puncti Gimago (puta γ) ad partes O. </
s
>
<
s
xml:id
="
echoid-s7702
"
xml:space
="
preserve
">quinimò cùm in hanc
<
lb
/>
rem plura ſubjici poſſent, ego jam _Specimina_ tantùm inſtituens
<
lb
/>
(quippe cùm operâ dignum haud arbitrer adeò tenuem materiam curi-
<
lb
/>
oſiùs proſequi) à minutiis abſtineo. </
s
>
<
s
xml:id
="
echoid-s7703
"
xml:space
="
preserve
">quo & </
s
>
<
s
xml:id
="
echoid-s7704
"
xml:space
="
preserve
">indè pronior ſum, quo-
<
lb
/>
niam in hac re copioſus videtur A. </
s
>
<
s
xml:id
="
echoid-s7705
"
xml:space
="
preserve
">_Tacquetus;_ </
s
>
<
s
xml:id
="
echoid-s7706
"
xml:space
="
preserve
">ſubinde quidem is,
<
lb
/>
ob admiſſum iſtud falſum principium, ceſpitans, at bene multa </
s
>
</
p
>
</
div
>
</
text
>
</
echo
>