Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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centrum C) datáque ſint duo puncta A, X; </
s
>
<
s
xml:id
="
echoid-s3994
"
xml:space
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">reperiendum eſt in
<
lb
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circumferentia punctum aliquod; </
s
>
<
s
xml:id
="
echoid-s3995
"
xml:space
="
preserve
">à quo ductæ ad A, X rectæ, altera ſit
<
lb
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alterius reflexa. </
s
>
<
s
xml:id
="
echoid-s3996
"
xml:space
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">‖ Hocità perficimus:</
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>
<
s
xml:id
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echoid-s3997
"
xml:space
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"/>
</
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<
p
>
<
s
xml:id
="
echoid-s3998
"
xml:space
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">Conjungantur rectæ AC, XC; </
s
>
<
s
xml:id
="
echoid-s3999
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s4000
"
xml:space
="
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">fiat (ſeorſim) ang. </
s
>
<
s
xml:id
="
echoid-s4001
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xml:space
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">δ = {1/2} ang.
<
lb
/>
</
s
>
<
s
xml:id
="
echoid-s4002
"
xml:space
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preserve
">
<
note
position
="
left
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xlink:label
="
note-0084-01
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xlink:href
="
note-0084-01a
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xml:space
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">Fig. 92, 93.</
note
>
AC X. </
s
>
<
s
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echoid-s4003
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xml:space
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">& </
s
>
<
s
xml:id
="
echoid-s4004
"
xml:space
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">in ξ δ crure anguli δ ſumpto liberè puncto π ducatur π V
<
lb
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ad ξ δ perpendicularis alterum crus ſecans in V; </
s
>
<
s
xml:id
="
echoid-s4005
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s4006
"
xml:space
="
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">in V π protracta
<
lb
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capiatur π γ = π V; </
s
>
<
s
xml:id
="
echoid-s4007
"
xml:space
="
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">tum dividatur γ V in φ, ut ſit γ φ. </
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>
<
s
xml:id
="
echoid-s4008
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xml:space
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">φ V:</
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<
s
xml:id
="
echoid-s4009
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xml:space
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">: XC. </
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>
<
s
xml:id
="
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xml:space
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">CA;
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</
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>
<
s
xml:id
="
echoid-s4011
"
xml:space
="
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">perque punctum φ trajiciatur κ ξ ſic ut ſit κξ. </
s
>
<
s
xml:id
="
echoid-s4012
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xml:space
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">κ v:</
s
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<
s
xml:id
="
echoid-s4013
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xml:space
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">: CX. </
s
>
<
s
xml:id
="
echoid-s4014
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xml:space
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">CN. </
s
>
<
s
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="
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xml:space
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">denique
<
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<
note
position
="
left
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xlink:label
="
note-0084-02
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xlink:href
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xml:space
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">L@m. pr@ced.</
note
>
fiat angulus XCNæ qualis angulo ξ κ v; </
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>
<
s
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="
echoid-s4016
"
xml:space
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">erit punctum N quale deſi-
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deramus. </
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<
s
xml:id
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xml:space
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">Nam ducantur XN, ξ v; </
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<
s
xml:id
="
echoid-s4018
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xml:space
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">& </
s
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<
s
xml:id
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echoid-s4019
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xml:space
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">fiat ang. </
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<
s
xml:id
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echoid-s4020
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xml:space
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">CNG = ang.
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</
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<
s
xml:id
="
echoid-s4021
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xml:space
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">κ v γ. </
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<
s
xml:id
="
echoid-s4022
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xml:space
="
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">adſumatúrque PG = PN; </
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>
<
s
xml:id
="
echoid-s4023
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xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s4024
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xml:space
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">connectatur XG. </
s
>
<
s
xml:id
="
echoid-s4025
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xml:space
="
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">liquet jam
<
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trangula XCN, ξ κ v ſimilia fore; </
s
>
<
s
xml:id
="
echoid-s4026
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xml:space
="
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">nec non ipſa CNF, κ v φ; </
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<
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="
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& </
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<
s
xml:id
="
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">ipſa XP F, ξ π φ; </
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<
s
xml:id
="
echoid-s4029
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xml:space
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">ipsáque demùm XFN, ξ φ v aſſimilari. </
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<
s
xml:id
="
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xml:space
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">quare
<
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PF. </
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<
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xml:id
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">XF:</
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<
s
xml:id
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">: π φ. </
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<
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">ξ φ. </
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<
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">& </
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<
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xml:id
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">XF. </
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<
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">FN:</
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<
s
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<
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">φ V. </
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<
s
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xml:space
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">& </
s
>
<
s
xml:id
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xml:space
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">ex æquo PF. </
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<
s
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<
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FN:</
s
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<
s
xml:id
="
echoid-s4042
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xml:space
="
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">: π φ. </
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<
s
xml:id
="
echoid-s4043
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xml:space
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">φ V. </
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>
<
s
xml:id
="
echoid-s4044
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xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s4045
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xml:space
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">antecedentes duplando 2 PF. </
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<
s
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echoid-s4046
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xml:space
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">FN :</
s
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<
s
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xml:space
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">: 2 π φ. </
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<
s
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">φ V. </
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<
s
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<
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componendóque 2 PF + FN. </
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<
s
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">FN:</
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<
s
xml:id
="
echoid-s4051
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xml:space
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">: 2 π φ + φ V. </
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<
s
xml:id
="
echoid-s4052
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xml:space
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">φ V. </
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<
s
xml:id
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xml:space
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">hoc eſt
<
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GF. </
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<
s
xml:id
="
echoid-s4054
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xml:space
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">FN:</
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<
s
xml:id
="
echoid-s4055
"
xml:space
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">: γ φ. </
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>
<
s
xml:id
="
echoid-s4056
"
xml:space
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">φ V (hoc eſt):</
s
>
<
s
xml:id
="
echoid-s4057
"
xml:space
="
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">: XC. </
s
>
<
s
xml:id
="
echoid-s4058
"
xml:space
="
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">CA. </
s
>
<
s
xml:id
="
echoid-s4059
"
xml:space
="
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">ducatur jam NL ad
<
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XG parailela; </
s
>
<
s
xml:id
="
echoid-s4060
"
xml:space
="
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">quare eſt ang. </
s
>
<
s
xml:id
="
echoid-s4061
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xml:space
="
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">ING = ang. </
s
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<
s
xml:id
="
echoid-s4062
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xml:space
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">G = ang. </
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<
s
xml:id
="
echoid-s4063
"
xml:space
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">XNG; </
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<
s
xml:id
="
echoid-s4064
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xml:space
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">
<
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& </
s
>
<
s
xml:id
="
echoid-s4065
"
xml:space
="
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">XG (XN). </
s
>
<
s
xml:id
="
echoid-s4066
"
xml:space
="
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">NL:</
s
>
<
s
xml:id
="
echoid-s4067
"
xml:space
="
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">: GF. </
s
>
<
s
xml:id
="
echoid-s4068
"
xml:space
="
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">FN:</
s
>
<
s
xml:id
="
echoid-s4069
"
xml:space
="
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">: XC. </
s
>
<
s
xml:id
="
echoid-s4070
"
xml:space
="
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">CA. </
s
>
<
s
xml:id
="
echoid-s4071
"
xml:space
="
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">porro fiàt ang. </
s
>
<
s
xml:id
="
echoid-s4072
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xml:space
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">
<
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LNH = ang. </
s
>
<
s
xml:id
="
echoid-s4073
"
xml:space
="
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">XCA; </
s
>
<
s
xml:id
="
echoid-s4074
"
xml:space
="
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">& </
s
>
<
s
xml:id
="
echoid-s4075
"
xml:space
="
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">HN protracta ipſi CA occurrat in M; </
s
>
<
s
xml:id
="
echoid-s4076
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xml:space
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<
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cſtque proptereà triangulum HNLſimile triangulo HCM; </
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>
<
s
xml:id
="
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xml:space
="
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">idcir-
<
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cóque HC. </
s
>
<
s
xml:id
="
echoid-s4078
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xml:space
="
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">CM:</
s
>
<
s
xml:id
="
echoid-s4079
"
xml:space
="
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">: HN. </
s
>
<
s
xml:id
="
echoid-s4080
"
xml:space
="
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">NL. </
s
>
<
s
xml:id
="
echoid-s4081
"
xml:space
="
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">ducatur denuò tangens NQ; </
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>
<
s
xml:id
="
echoid-s4082
"
xml:space
="
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">eſt-
<
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que tum ang. </
s
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<
s
xml:id
="
echoid-s4083
"
xml:space
="
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">PNQ = rect - CNP = rect - κ V π = ang. </
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>
<
s
xml:id
="
echoid-s4084
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xml:space
="
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">
<
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δ = {1/2} XC A; </
s
>
<
s
xml:id
="
echoid-s4085
"
xml:space
="
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">vel 2 ang. </
s
>
<
s
xml:id
="
echoid-s4086
"
xml:space
="
preserve
">PNQ = ang XCA = ang LNH. </
s
>
<
s
xml:id
="
echoid-s4087
"
xml:space
="
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">
<
lb
/>
verùm erat priùs 2 ang. </
s
>
<
s
xml:id
="
echoid-s4088
"
xml:space
="
preserve
">XNF = ang. </
s
>
<
s
xml:id
="
echoid-s4089
"
xml:space
="
preserve
">XNL. </
s
>
<
s
xml:id
="
echoid-s4090
"
xml:space
="
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">ergo 2 ang XNF
<
lb
/>
- 2 ang PNQ = ang XNL- ang. </
s
>
<
s
xml:id
="
echoid-s4091
"
xml:space
="
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">LNH. </
s
>
<
s
xml:id
="
echoid-s4092
"
xml:space
="
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">hoc eſt 2 ang XNQ
<
lb
/>
= ang. </
s
>
<
s
xml:id
="
echoid-s4093
"
xml:space
="
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">XNH. </
s
>
<
s
xml:id
="
echoid-s4094
"
xml:space
="
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">ergo tangens NQ biſecat angulum XNH; </
s
>
<
s
xml:id
="
echoid-s4095
"
xml:space
="
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">indéque
<
lb
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conſectatur fore rectam HM ipſius XN reflexam; </
s
>
<
s
xml:id
="
echoid-s4096
"
xml:space
="
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">ac ideò eſſe XC. </
s
>
<
s
xml:id
="
echoid-s4097
"
xml:space
="
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">
<
lb
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HC:</
s
>
<
s
xml:id
="
echoid-s4098
"
xml:space
="
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">: XN. </
s
>
<
s
xml:id
="
echoid-s4099
"
xml:space
="
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">HN. </
s
>
<
s
xml:id
="
echoid-s4100
"
xml:space
="
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">atqui fuit priùs HC. </
s
>
<
s
xml:id
="
echoid-s4101
"
xml:space
="
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">CM:</
s
>
<
s
xml:id
="
echoid-s4102
"
xml:space
="
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">: HN. </
s
>
<
s
xml:id
="
echoid-s4103
"
xml:space
="
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">NL quare
<
lb
/>
jam erit ex æquo XC. </
s
>
<
s
xml:id
="
echoid-s4104
"
xml:space
="
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">CM:</
s
>
<
s
xml:id
="
echoid-s4105
"
xml:space
="
preserve
">: XN. </
s
>
<
s
xml:id
="
echoid-s4106
"
xml:space
="
preserve
">NL (h@c eſt etiam è præmon-
<
lb
/>
ſtratis):</
s
>
<
s
xml:id
="
echoid-s4107
"
xml:space
="
preserve
">: XC. </
s
>
<
s
xml:id
="
echoid-s4108
"
xml:space
="
preserve
">CA. </
s
>
<
s
xml:id
="
echoid-s4109
"
xml:space
="
preserve
">unde CM = CA. </
s
>
<
s
xml:id
="
echoid-s4110
"
xml:space
="
preserve
">quapropter HM, ipſius
<
lb
/>
XN reflexa tranſit per A: </
s
>
<
s
xml:id
="
echoid-s4111
"
xml:space
="
preserve
">Quod propoſitum erat efficere.</
s
>
<
s
xml:id
="
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"
xml:space
="
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">‖</
s
>
</
p
>
<
p
>
<
s
xml:id
="
echoid-s4113
"
xml:space
="
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">VIII. </
s
>
<
s
xml:id
="
echoid-s4114
"
xml:space
="
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">Hujuſce _Problematis_ ità generaliùs propoſiti varii quidem
<
lb
/>
caſus ſunt (etenim vel data puncta jacent ambo extra circuh@ re-
<
lb
/>
flectentem; </
s
>
<
s
xml:id
="
echoid-s4115
"
xml:space
="
preserve
">vel utrumque poſitum eſt intra circulum; </
s
>
<
s
xml:id
="
echoid-s4116
"
xml:space
="
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">vel unum intra
<
lb
/>
jacet, alterum extra; </
s
>
<
s
xml:id
="
echoid-s4117
"
xml:space
="
preserve
">quinetiam in horum caſuum unoquoque pluries
<
lb
/>
conficitur negotium) aſt ubique non abſimilis erit conſtructio; </
s
>
<
s
xml:id
="
echoid-s4118
"
xml:space
="
preserve
">ſanè
<
lb
/>
nimius eſſem; </
s
>
<
s
xml:id
="
echoid-s4119
"
xml:space
="
preserve
">meámque pariter ac veſtram patientiam macerarem
<
lb
/>
omnes intricati _Problematis_ nodos evolvendo; </
s
>
<
s
xml:id
="
echoid-s4120
"
xml:space
="
preserve
">ſuffecerit ejuſce ſpeci-
<
lb
/>
men aliquod protuliſſe.</
s
>
<
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="
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xml:space
="
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</
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