Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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ad ipſam EC parallelæ ducantur rectæ RT, SV; </
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<
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minatum punctum X inter limites T, V conſiſtere (nam extra TV
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punctum quodlibet L accipiendo, & </
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<
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">indè ducendo LI P ad CE paralle-
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lam, erit CL, hoc eft LP, major quàm LI, unde à C ad rectam LI,
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nulla duci recta poteſt æqualis ipſi LI). </
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<
s
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xml:space
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">Jam autem dico, quòd
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punctum Z ad ellipſin exiſtit, cujus axis TV, focus C. </
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<
s
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xml:space
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">Nam biſe-
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cetur TV in K; </
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<
s
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">fiat VD = TC; </
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<
s
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xml:space
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">ducatur KH ad CE parallela;
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</
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<
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xml:space
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">per H ducatur HN ad CK parallela. </
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<
s
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xml:space
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">Eſtque KH = {TR + VS/2} =
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{CT + CV/2} = KT = KV. </
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<
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xml:space
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">Et quoniam AV. </
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<
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<
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xml:space
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TR (hoc eſt) :</
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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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">erit per rationis con-
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vcrſionem AV. </
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<
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<
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">: CV. </
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<
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">CD. </
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<
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xml:space
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">vel, conſequentes ſubduplando,
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AV. </
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<
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">KV :</
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<
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<
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">CK. </
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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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AK. </
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<
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<
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<
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">CK. </
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<
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">hoc eſt HN. </
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<
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">NG :</
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<
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xml:space
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<
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">CK. </
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<
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xml:space
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">quare
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KH x NG = CK x HN = CK x KX. </
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<
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">atqui eſt CZq = XGq
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= KHq + NGq + 2 KH x NG. </
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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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">CXq = CKq + KXq
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+ 2 CK x KX = CKq + KXq + 2 KH x NG. </
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<
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xml:space
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KHq + NGq - CKq - KXq = CZq - CXq = XZq. </
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Ad alteras biſegmenti K partes ſumatur K ξ = KX, ducatúrque ξν ad
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KH parallela, ſecans curvam TEZV in ζ, & </
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<
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">rectam AH in γ, ac
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ipſam NH in ν erit quoque, ſimili ex diſcurſu, ξζq = KHq +
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νγq - CKq - Kξq; </
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<
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">unde liquet fore ξζ = XZ; </
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proinde rectis Cζ, Dζ, erit Dζ = CZ; </
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<
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<
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">Cζ + CZ = ξγ +
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XG = 2 KH = TV. </
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<
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xml:space
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">ergò Cζ + Dζ (vel DZ + CZ) = TV. </
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unde perſpicitur _curvam TζZV eſſe ellipſin_, cujus _axis_ TV; </
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<
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C, D.</
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</
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<
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">III. </
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<
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<
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note
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&</
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<
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<
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">CE) dico punctum Z ad oppoſitas hyperbolas, conſimili modo
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determinabiles, exiſtere. </
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<
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partem) angulis ſemirectis ACP; </
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<
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<
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">(ab ipſarum CP cum AE
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occurſibus) ductis rectis RT, SV ad CE parallelis, punctum X
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extra limites TV neceſſariò conſiſtet (etenim ubivis intra TV ductâ
<
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LIP ad CE parallelâ, erit LI &</
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<
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<
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angulo AL I ſubtendi poteſt; </
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<
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">id quod extra terminos hoſce nil pro-
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hibet fieri) erit jam TV axis, & </
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<
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<
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enim omnia, quæ in caſu præcedente; </
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<
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">erítque rurſus hîc KH =
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KV. </
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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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">DV; </
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<
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<
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