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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<
s
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xml:space
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">V. </
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<
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xml:space
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">Horum caſuum primus ad unum duntaxat ab una axis parte radi-
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um pertinet, qui reliquos aliis caſibus convenientes medius diſterminat.
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</
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<
s
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xml:space
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<
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position
="
left
"
xlink:label
="
note-0088-01
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xlink:href
="
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xml:space
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">Fig. 101.</
note
>
de poſteribus itaque duobus ſeparatim paullò diſpiciamus, Sit jam
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itaque primò AC = AG = A γ; </
s
>
<
s
xml:id
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"
xml:space
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">unde quilibet incidens cavo GB γ
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radius (ut AN) major erit quam AC; </
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>
<
s
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xml:space
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">hujus itaque reflexus axem
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ſecet puncto K; </
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<
s
xml:id
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"
xml:space
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">dico, ſi ſemidiameter CB dividatur in Z; </
s
>
<
s
xml:id
="
echoid-s4312
"
xml:space
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">ut ſit CZ.
<
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</
s
>
<
s
xml:id
="
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"
xml:space
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">ZB:</
s
>
<
s
xml:id
="
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"
xml:space
="
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">: AC. </
s
>
<
s
xml:id
="
echoid-s4315
"
xml:space
="
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">AB; </
s
>
<
s
xml:id
="
echoid-s4316
"
xml:space
="
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">fore CK &</
s
>
<
s
xml:id
="
echoid-s4317
"
xml:space
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">gt; </
s
>
<
s
xml:id
="
echoid-s4318
"
xml:space
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">CZ. </
s
>
<
s
xml:id
="
echoid-s4319
"
xml:space
="
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">etenim ob angulum ANK
<
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<
note
position
="
left
"
xlink:label
="
note-0088-02
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xlink:href
="
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xml:space
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">Fig. 100.</
note
>
biſectum, erit AC. </
s
>
<
s
xml:id
="
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xml:space
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">CK:</
s
>
<
s
xml:id
="
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"
xml:space
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">: AN. </
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<
s
xml:id
="
echoid-s4322
"
xml:space
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">NK. </
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>
<
s
xml:id
="
echoid-s4323
"
xml:space
="
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">vel permutando AC. </
s
>
<
s
xml:id
="
echoid-s4324
"
xml:space
="
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">AN
<
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:</
s
>
<
s
xml:id
="
echoid-s4325
"
xml:space
="
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">: CK. </
s
>
<
s
xml:id
="
echoid-s4326
"
xml:space
="
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">NK. </
s
>
<
s
xml:id
="
echoid-s4327
"
xml:space
="
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">eſt autem AC. </
s
>
<
s
xml:id
="
echoid-s4328
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xml:space
="
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">AB &</
s
>
<
s
xml:id
="
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xml:space
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">lt; </
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>
<
s
xml:id
="
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xml:space
="
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">AC. </
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>
<
s
xml:id
="
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xml:space
="
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">AN ergo AC. </
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<
s
xml:id
="
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xml:space
="
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">AB
<
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&</
s
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<
s
xml:id
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xml:space
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<
s
xml:id
="
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xml:space
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">CK. </
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>
<
s
xml:id
="
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xml:space
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">NK &</
s
>
<
s
xml:id
="
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xml:space
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">lt; </
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>
<
s
xml:id
="
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xml:space
="
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">CK. </
s
>
<
s
xml:id
="
echoid-s4338
"
xml:space
="
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">BK. </
s
>
<
s
xml:id
="
echoid-s4339
"
xml:space
="
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">ergo cùm ſit, ex hypotheſi, CZ. </
s
>
<
s
xml:id
="
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xml:space
="
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">ZB
<
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/>
:</
s
>
<
s
xml:id
="
echoid-s4341
"
xml:space
="
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">: AC. </
s
>
<
s
xml:id
="
echoid-s4342
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xml:space
="
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">AB; </
s
>
<
s
xml:id
="
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xml:space
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">erit CZ. </
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>
<
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xml:id
="
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xml:space
="
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">ZB &</
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>
<
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xml:id
="
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xml:space
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">lt; </
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<
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xml:id
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xml:space
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">CK. </
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>
<
s
xml:id
="
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xml:space
="
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">BK. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">componendóque CB.
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</
s
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<
s
xml:id
="
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xml:space
="
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">ZB. </
s
>
<
s
xml:id
="
echoid-s4350
"
xml:space
="
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">&</
s
>
<
s
xml:id
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xml:space
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">lt; </
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>
<
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xml:id
="
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xml:space
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">CB. </
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<
s
xml:id
="
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xml:space
="
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">KB. </
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>
<
s
xml:id
="
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xml:space
="
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">unde ZB &</
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>
<
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="
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<
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xml:space
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">KB; </
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<
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="
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">ſeu CZ &</
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>
<
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xml:space
="
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">lt; </
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>
<
s
xml:id
="
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xml:space
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">CK; </
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<
s
xml:id
="
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xml:space
="
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">Q. </
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<
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E. </
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<
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xml:space
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<
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</
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<
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<
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">VI. </
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<
s
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xml:space
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">Hinc punctum Z eſt limes infra quem, Verſus centrum, nullus
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reflexus axem interſecat.</
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<
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<
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">_Coroll._ </
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<
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">Hinc ſi puncta Z, ζ ſint limites punctorum A, _a_ (quorum
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A remotius) erit CZ &</
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<
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<
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</
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<
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<
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<
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<
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<
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<
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<
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xml:space
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">componendóque AB. </
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<
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xml:id
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xml:space
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>
<
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xml:id
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xml:space
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</
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<
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xml:space
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">_a_ B. </
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<
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">_a_ C. </
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<
s
xml:id
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xml:space
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">hoc eſt ZB. </
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<
s
xml:id
="
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xml:space
="
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>
<
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xml:id
="
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xml:space
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">lt; </
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<
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xml:id
="
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xml:space
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">ζ B. </
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<
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">ζ C. </
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>
<
s
xml:id
="
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"
xml:space
="
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">vel compoſitè CB. </
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>
<
s
xml:id
="
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"
xml:space
="
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">ZC
<
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/>
&</
s
>
<
s
xml:id
="
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"
xml:space
="
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">lt; </
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>
<
s
xml:id
="
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xml:space
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">CB. </
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<
s
xml:id
="
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xml:space
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">ζ C. </
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<
s
xml:id
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xml:space
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">ergò ZC &</
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<
s
xml:id
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xml:space
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<
s
xml:id
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xml:space
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">ζ C.</
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<
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</
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<
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<
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">VII. </
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<
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xml:space
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">Quinetiam erit in hoc caſu; </
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<
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<
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xml:space
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">CNq:</
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>
<
s
xml:id
="
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xml:space
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<
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AC. </
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<
s
xml:id
="
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xml:space
="
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">CK. </
s
>
<
s
xml:id
="
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"
xml:space
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">Nam ducatur KH ad CN parallela, protractæ AN
<
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occurrens in H; </
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>
<
s
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xml:space
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">& </
s
>
<
s
xml:id
="
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">connectatur CP; </
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>
<
s
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="
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xml:space
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">& </
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>
<
s
xml:id
="
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"
xml:space
="
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">eodem planè modo quo ſu-
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periùs (in iis quæ circa convexas partes attigimus) oſtendetur fore
<
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AN x NP. </
s
>
<
s
xml:id
="
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xml:space
="
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">CNq:</
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>
<
s
xml:id
="
echoid-s4408
"
xml:space
="
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">: AK. </
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>
<
s
xml:id
="
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xml:space
="
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">CK. </
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>
<
s
xml:id
="
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"
xml:space
="
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">unde diviſim erit AN x NP -
<
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CNq. </
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>
<
s
xml:id
="
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xml:space
="
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">CNq:</
s
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<
s
xml:id
="
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xml:space
="
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">: AC. </
s
>
<
s
xml:id
="
echoid-s4413
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xml:space
="
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">CK. </
s
>
<
s
xml:id
="
echoid-s4414
"
xml:space
="
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">eſt autem AN x NP = ANq -
<
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AN x AP = ANq -: </
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>
<
s
xml:id
="
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"
xml:space
="
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">ACq - CNq = ANq - ACq +
<
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CNq; </
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>
<
s
xml:id
="
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"
xml:space
="
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">adeóque AN x NP - CNq = ANq - ACq. </
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>
<
s
xml:id
="
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xml:space
="
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">ergò
<
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demum erit ANq - ACq. </
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>
<
s
xml:id
="
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xml:space
="
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">CNq:</
s
>
<
s
xml:id
="
echoid-s4419
"
xml:space
="
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">: AC. </
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>
<
s
xml:id
="
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xml:space
="
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">CK: </
s
>
<
s
xml:id
="
echoid-s4421
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xml:space
="
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">Q. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">E. </
s
>
<
s
xml:id
="
echoid-s4423
"
xml:space
="
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">D.</
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>
<
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xml:id
="
echoid-s4424
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="
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"/>
</
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>
<
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>
<
s
xml:id
="
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="
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">Notetur; </
s
>
<
s
xml:id
="
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xml:space
="
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">ſi fuerit AC minor ſemiſſe ſemidiametri circuli re-
<
lb
/>
flectentis, quòd punctum A duos focos habebit ad eaſdem centri par-
<
lb
/>
tes, quorum alter ad partes D, alter ad B pertinebit; </
s
>
<
s
xml:id
="
echoid-s4427
"
xml:space
="
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">ſin AC major
<
lb
/>
fuerit iſtâ Semiſſe, focis qui ad diverſos vertices B, & </
s
>
<
s
xml:id
="
echoid-s4428
"
xml:space
="
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">D pertinent,
<
lb
/>
centrum C interjacebit.</
s
>
<
s
xml:id
="
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="
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"/>
</
p
>
<
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>
<
s
xml:id
="
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xml:space
="
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">VIII. </
s
>
<
s
xml:id
="
echoid-s4431
"
xml:space
="
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">Etiam hoc interſeram _Theorema_, præmiſſis conforme: </
s
>
<
s
xml:id
="
echoid-s4432
"
xml:space
="
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">Si
<
lb
/>
fiat 2 CK. </
s
>
<
s
xml:id
="
echoid-s4433
"
xml:space
="
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">CN:</
s
>
<
s
xml:id
="
echoid-s4434
"
xml:space
="
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">: CN. </
s
>
<
s
xml:id
="
echoid-s4435
"
xml:space
="
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">F; </
s
>
<
s
xml:id
="
echoid-s4436
"
xml:space
="
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">itémque 2 CA. </
s
>
<
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xml:id
="
echoid-s4437
"
xml:space
="
preserve
">CN:</
s
>
<
s
xml:id
="
echoid-s4438
"
xml:space
="
preserve
">: CN. </
s
>
<
s
xml:id
="
echoid-s4439
"
xml:space
="
preserve
">E;</
s
>
<
s
xml:id
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echoid-s4440
"
xml:space
="
preserve
"/>
</
p
>
</
div
>
</
text
>
</
echo
>