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; </
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<
s
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circumferentia punctum aliquod; </
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<
s
xml:id
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"
xml:space
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">à quo ductæ ad A, X rectæ, altera ſit
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alterius reflexa. </
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<
s
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xml:space
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<
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</
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<
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<
s
xml:id
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xml:space
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">Conjungantur rectæ AC, XC; </
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>
<
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xml:space
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">& </
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>
<
s
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xml:space
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">fiat (ſeorſim) ang. </
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<
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xml:space
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</
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<
s
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<
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xlink:label
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note-0084-01
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xlink:href
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xml:space
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">Fig. 92, 93.</
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AC X. </
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<
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">& </
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<
s
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xml:space
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">in ξ δ crure anguli δ ſumpto liberè puncto π ducatur π V
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ad ξ δ perpendicularis alterum crus ſecans in V; </
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<
s
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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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">in V π protracta
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capiatur π γ = π V; </
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<
s
xml:id
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xml:space
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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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xml:space
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<
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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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xlink:label
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fiat angulus XCNæ qualis angulo ξ κ v; </
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<
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deramus. </
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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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trangula XCN, ξ κ v ſimilia fore; </
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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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PF. </
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<
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<
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<
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FN:</
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<
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<
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<
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">& </
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<
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">antecedentes duplando 2 PF. </
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<
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<
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<
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<
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componendóque 2 PF + FN. </
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<
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<
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<
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<
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GF. </
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<
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<
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<
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<
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">CA. </
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<
s
xml:id
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xml:space
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XG parailela; </
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<
s
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<
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xml:space
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<
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">G = ang. </
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<
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<
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& </
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<
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<
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<
s
xml:id
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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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<
s
xml:id
="
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xml:space
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">CA. </
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<
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xml:id
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<
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LNH = ang. </
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<
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<
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">& </
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<
s
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xml:space
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">HN protracta ipſi CA occurrat in M; </
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<
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cſtque proptereà triangulum HNLſimile triangulo HCM; </
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<
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cóque HC. </
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<
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<
s
xml:id
="
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xml:space
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<
s
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<
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">ducatur denuò tangens NQ; </
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<
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que tum ang. </
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<
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xml:space
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">PNQ = rect - CNP = rect - κ V π = ang. </
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<
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δ = {1/2} XC A; </
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<
s
xml:id
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xml:space
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">vel 2 ang. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">PNQ = ang XCA = ang LNH. </
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<
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="
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<
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verùm erat priùs 2 ang. </
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<
s
xml:id
="
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xml:space
="
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">XNF = ang. </
s
>
<
s
xml:id
="
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xml:space
="
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">XNL. </
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<
s
xml:id
="
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xml:space
="
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">ergo 2 ang XNF
<
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- 2 ang PNQ = ang XNL- ang. </
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<
s
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xml:space
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">LNH. </
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<
s
xml:id
="
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xml:space
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">hoc eſt 2 ang XNQ
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= ang. </
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<
s
xml:id
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xml:space
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">XNH. </
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<
s
xml:id
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"
xml:space
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">ergo tangens NQ biſecat angulum XNH; </
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<
s
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xml:space
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">indéque
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conſectatur fore rectam HM ipſius XN reflexam; </
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<
s
xml:id
="
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xml:space
="
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">ac ideò eſſe XC. </
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<
s
xml:id
="
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<
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HC:</
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>
<
s
xml:id
="
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xml:space
="
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">: XN. </
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<
s
xml:id
="
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xml:space
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">HN. </
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>
<
s
xml:id
="
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xml:space
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">atqui fuit priùs HC. </
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>
<
s
xml:id
="
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xml:space
="
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">CM:</
s
>
<
s
xml:id
="
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xml:space
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">: HN. </
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>
<
s
xml:id
="
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xml:space
="
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">NL quare
<
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jam erit ex æquo XC. </
s
>
<
s
xml:id
="
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xml:space
="
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">CM:</
s
>
<
s
xml:id
="
echoid-s4105
"
xml:space
="
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">: XN. </
s
>
<
s
xml:id
="
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xml:space
="
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">NL (h@c eſt etiam è præmon-
<
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ſtratis):</
s
>
<
s
xml:id
="
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xml:space
="
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">: XC. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">CA. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">unde CM = CA. </
s
>
<
s
xml:id
="
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"
xml:space
="
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">quapropter HM, ipſius
<
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XN reflexa tranſit per A: </
s
>
<
s
xml:id
="
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"
xml:space
="
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">Quod propoſitum erat efficere.</
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>
<
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">‖</
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</
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<
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>
<
s
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xml:space
="
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">VIII. </
s
>
<
s
xml:id
="
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xml:space
="
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">Hujuſce _Problematis_ ità generaliùs propoſiti varii quidem
<
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/>
caſus ſunt (etenim vel data puncta jacent ambo extra circuh@ re-
<
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flectentem; </
s
>
<
s
xml:id
="
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"
xml:space
="
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">vel utrumque poſitum eſt intra circulum; </
s
>
<
s
xml:id
="
echoid-s4116
"
xml:space
="
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">vel unum intra
<
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jacet, alterum extra; </
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>
<
s
xml:id
="
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"
xml:space
="
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">quinetiam in horum caſuum unoquoque pluries
<
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conficitur negotium) aſt ubique non abſimilis erit conſtructio; </
s
>
<
s
xml:id
="
echoid-s4118
"
xml:space
="
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">ſanè
<
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nimius eſſem; </
s
>
<
s
xml:id
="
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"
xml:space
="
preserve
">meámque pariter ac veſtram patientiam macerarem
<
lb
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omnes intricati _Problematis_ nodos evolvendo; </
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>
<
s
xml:id
="
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"
xml:space
="
preserve
">ſuffecerit ejuſce ſpeci-
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men aliquod protuliſſe.</
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>
<
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