Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
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<
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46
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file
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0224
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n
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239
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rhead
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"/>
DH. </
s
>
<
s
xml:id
="
echoid-s9757
"
xml:space
="
preserve
">LN - HO:</
s
>
<
s
xml:id
="
echoid-s9758
"
xml:space
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">: LH. </
s
>
<
s
xml:id
="
echoid-s9759
"
xml:space
="
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">LB:</
s
>
<
s
xml:id
="
echoid-s9760
"
xml:space
="
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">:) LH. </
s
>
<
s
xml:id
="
echoid-s9761
"
xml:space
="
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">HK. </
s
>
<
s
xml:id
="
echoid-s9762
"
xml:space
="
preserve
">erit DH x HK =
<
lb
/>
HO x LH; </
s
>
<
s
xml:id
="
echoid-s9763
"
xml:space
="
preserve
">hoc eſt DL x HK - LH x HK = KO x LH - HK
<
lb
/>
x LH. </
s
>
<
s
xml:id
="
echoid-s9764
"
xml:space
="
preserve
">unde erit DL x HK = KO x LH. </
s
>
<
s
xml:id
="
echoid-s9765
"
xml:space
="
preserve
">vel ZL x LD = ZK
<
lb
/>
x KO. </
s
>
<
s
xml:id
="
echoid-s9766
"
xml:space
="
preserve
">ergò conſtat lineam ODO eſſe _Hyperbolen_, cujus _Aſymptoti_
<
lb
/>
ZA, ZS. </
s
>
<
s
xml:id
="
echoid-s9767
"
xml:space
="
preserve
">Breviùs hoc oſtendi poſſet, producendo rectam NDS.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9768
"
xml:space
="
preserve
">Nam eſt DS = DM = DO ± OM = NM ± OM = ON. </
s
>
<
s
xml:id
="
echoid-s9769
"
xml:space
="
preserve
">Simi-
<
lb
/>
ter quartam & </
s
>
<
s
xml:id
="
echoid-s9770
"
xml:space
="
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">nonam breviùs demonſtres licet.</
s
>
<
s
xml:id
="
echoid-s9771
"
xml:space
="
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"/>
</
p
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<
p
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<
s
xml:id
="
echoid-s9772
"
xml:space
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">Quinimò ſi MN ad DO quamvis eandem perpetuò rationem pona-
<
lb
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<
note
position
="
left
"
xlink:label
="
note-0224-01
"
xlink:href
="
note-0224-01a
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xml:space
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">Fig. 38.</
note
>
tur habere (puta datam R ad S) etiam linea ODO _Hyperbola_ erit;
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9773
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xml:space
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">Nempe ſi tum fiat R. </
s
>
<
s
xml:id
="
echoid-s9774
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xml:space
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">S:</
s
>
<
s
xml:id
="
echoid-s9775
"
xml:space
="
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">: LB. </
s
>
<
s
xml:id
="
echoid-s9776
"
xml:space
="
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">LZ; </
s
>
<
s
xml:id
="
echoid-s9777
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s9778
"
xml:space
="
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">R. </
s
>
<
s
xml:id
="
echoid-s9779
"
xml:space
="
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">S:</
s
>
<
s
xml:id
="
echoid-s9780
"
xml:space
="
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">: DL. </
s
>
<
s
xml:id
="
echoid-s9781
"
xml:space
="
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">DE; </
s
>
<
s
xml:id
="
echoid-s9782
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s9783
"
xml:space
="
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">per
<
lb
/>
Z ducatur ZS ad BC; </
s
>
<
s
xml:id
="
echoid-s9784
"
xml:space
="
preserve
">ac per E tranſeat RE ad ZA parallela, cum
<
lb
/>
ZS conveniens in Y; </
s
>
<
s
xml:id
="
echoid-s9785
"
xml:space
="
preserve
">erunt YR, YS dictæ _Hyperbolæ aſymptoti_
<
lb
/>
quod jam ſufficerit innuiſſe.</
s
>
<
s
xml:id
="
echoid-s9786
"
xml:space
="
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"/>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s9787
"
xml:space
="
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">Hinc in tranſcurſu noto facilè confici _Problema (quo problematum_
<
lb
/>
_confectiones iſtæ Arcbimedeæ, ac Vieteæ ope primæ Conchoidis peractæ_,
<
lb
/>
_ad Sectiones conicas rediguntur_) Per datum punctum D rectam lineam
<
lb
/>
ducere, ſic ut anguli dati ABC lateribus intercepta ductæ rectæ pars
<
lb
/>
æquetur datæ T. </
s
>
<
s
xml:id
="
echoid-s9788
"
xml:space
="
preserve
">Nam deſcriptâ hyperbolâ ODO; </
s
>
<
s
xml:id
="
echoid-s9789
"
xml:space
="
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">centro D, in-
<
lb
/>
tervallo datam T æquante deſcribatur circulus POQ _hyperbolam_ in-
<
lb
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terſecans in O; </
s
>
<
s
xml:id
="
echoid-s9790
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s9791
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xml:space
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">producatur DON; </
s
>
<
s
xml:id
="
echoid-s9792
"
xml:space
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">fiétq; </
s
>
<
s
xml:id
="
echoid-s9793
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xml:space
="
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">MN = DO = T.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s9794
"
xml:space
="
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">Modus autem hic generalior eſt, & </
s
>
<
s
xml:id
="
echoid-s9795
"
xml:space
="
preserve
">concinnior eo, quem in _Opticis_
<
lb
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tradidimus.</
s
>
<
s
xml:id
="
echoid-s9796
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xml:space
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"/>
</
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<
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<
s
xml:id
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echoid-s9797
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xml:space
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">IV. </
s
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<
s
xml:id
="
echoid-s9798
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xml:space
="
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">Sit angulus ABC, et punctum datum D; </
s
>
<
s
xml:id
="
echoid-s9799
"
xml:space
="
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">ſit etiam linea O
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0224-02
"
xlink:href
="
note-0224-02a
"
xml:space
="
preserve
">Fig. 39.</
note
>
BO talis, ut per D ductâ quâpiam rectâ DN, ſit anguli late-
<
lb
/>
ribus intercepta MN ad rectâ BC curvâque OBO interceptam
<
lb
/>
MO in eadem ſemper ratione (puta X ad Y;) </
s
>
<
s
xml:id
="
echoid-s9800
"
xml:space
="
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">erit linea OBO
<
lb
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_hyperbola_.</
s
>
<
s
xml:id
="
echoid-s9801
"
xml:space
="
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"/>
</
p
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<
p
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<
s
xml:id
="
echoid-s9802
"
xml:space
="
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">Ducatur enim recta DL ad CB parallela, ipſi AB occurrens
<
lb
/>
<
note
position
="
left
"
xlink:label
="
note-0224-03
"
xlink:href
="
note-0224-03a
"
xml:space
="
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">Fig. 39.</
note
>
in L; </
s
>
<
s
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echoid-s9803
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xml:space
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">ſecentúrque DL, BL punctis E, F, ut ſit DL. </
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<
s
xml:id
="
echoid-s9804
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xml:space
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s
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<
s
xml:id
="
echoid-s9805
"
xml:space
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<
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</
s
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<
s
xml:id
="
echoid-s9806
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xml:space
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s
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<
s
xml:id
="
echoid-s9807
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xml:space
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<
s
xml:id
="
echoid-s9808
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xml:space
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">BF; </
s
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<
s
xml:id
="
echoid-s9809
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xml:space
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">tum per E ducatur recta ER, ad BA; </
s
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<
s
xml:id
="
echoid-s9810
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xml:space
="
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">& </
s
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<
s
xml:id
="
echoid-s9811
"
xml:space
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<
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F recta FS ad BC parallela; </
s
>
<
s
xml:id
="
echoid-s9812
"
xml:space
="
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">concurrántque rectæ ER, FS pun-
<
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cto Z; </
s
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<
s
xml:id
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echoid-s9813
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xml:space
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">denuò per punctum O ducatur OH ad AB parallela. </
s
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<
s
xml:id
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echoid-s9814
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xml:space
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">Jam
<
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ob DL. </
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<
s
xml:id
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echoid-s9815
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xml:space
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">DH:</
s
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<
s
xml:id
="
echoid-s9816
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xml:space
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">: LN. </
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<
s
xml:id
="
echoid-s9817
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xml:space
="
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">HO:</
s
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<
s
xml:id
="
echoid-s9818
"
xml:space
="
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">: LB + BN. </
s
>
<
s
xml:id
="
echoid-s9819
"
xml:space
="
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">HO:</
s
>
<
s
xml:id
="
echoid-s9820
"
xml:space
="
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">: DE x LB
<
lb
/>
+ DE x BN. </
s
>
<
s
xml:id
="
echoid-s9821
"
xml:space
="
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">DE x HO. </
s
>
<
s
xml:id
="
echoid-s9822
"
xml:space
="
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">item DL x KO = DE x BN
<
lb
/>
(nam DL. </
s
>
<
s
xml:id
="
echoid-s9823
"
xml:space
="
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">DE:</
s
>
<
s
xml:id
="
echoid-s9824
"
xml:space
="
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">: MN. </
s
>
<
s
xml:id
="
echoid-s9825
"
xml:space
="
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">MO:</
s
>
<
s
xml:id
="
echoid-s9826
"
xml:space
="
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">: BN. </
s
>
<
s
xml:id
="
echoid-s9827
"
xml:space
="
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">KO) & </
s
>
<
s
xml:id
="
echoid-s9828
"
xml:space
="
preserve
">DE x LB = DL
<
lb
/>
x BF (ob DE. </
s
>
<
s
xml:id
="
echoid-s9829
"
xml:space
="
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">DL:</
s
>
<
s
xml:id
="
echoid-s9830
"
xml:space
="
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">: BF. </
s
>
<
s
xml:id
="
echoid-s9831
"
xml:space
="
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">LB;) </
s
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<
s
xml:id
="
echoid-s9832
"
xml:space
="
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">erit DL. </
s
>
<
s
xml:id
="
echoid-s9833
"
xml:space
="
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">DH:</
s
>
<
s
xml:id
="
echoid-s9834
"
xml:space
="
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">: DL x BF
<
lb
/>
+ DL x KO. </
s
>
<
s
xml:id
="
echoid-s9835
"
xml:space
="
preserve
">DE x HO; </
s
>
<
s
xml:id
="
echoid-s9836
"
xml:space
="
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">hoc eſt DL x BF + DL x
<
lb
/>
KO. </
s
>
<
s
xml:id
="
echoid-s9837
"
xml:space
="
preserve
">DH x BF + DH x KO:</
s
>
<
s
xml:id
="
echoid-s9838
"
xml:space
="
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">: DL x BF x DL x KO.</
s
>
<
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="
echoid-s9839
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