Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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diſcurſu eſt DM x TD - DM x RD = MO x RD. </
s
>
<
s
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xml:space
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">quapropter
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note-0235-01
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xml:space
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">Fig. 63.</
note
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erit MN x SD. </
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<
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<
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xml:space
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<
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echoid-s10637
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xml:space
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<
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xml:space
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LG x SD. </
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<
s
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echoid-s10639
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xml:space
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">KG x RD :</
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<
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xml:space
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<
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">TD - RD; </
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<
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xml:space
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">vel (ad æqua-
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tionem redigendo) LG x SD x TD - LG x SD x RD = KG x
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RD x TD - KG x RD x SD; </
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<
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xml:space
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">tranſponendóque LG x SD x
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TD + KG x RD x SD - LG x SD x RD = KG x RD x TD.
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</
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<
s
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xml:space
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">hoc eſt LG x SD x TD + KL x SD x RD = KG x RD x TD. </
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<
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vel (ad analogiſmum reducendo) LG x TD + KL x RD. </
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<
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xml:space
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">KG x
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TD :</
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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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xml:space
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">Quòd ſi puncta T, R non ad eaſdem puncti D partes ſita ſint,
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xml:space
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">Fig. 64.</
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erit LG x RD - KL x TD. </
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<
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xml:space
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<
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xml:space
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<
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">SD.</
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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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">Simili conſtabit id diſcurſu; </
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<
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<
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xml:space
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">Sint quatuor continuè proportionalium ſeries æquinumeræ (qua-
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les adſcriptas cernis) quarum cùm antecedentes primi, tum ultimi conſe-
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quentes inter ſe proportionales ſint(A. </
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xml:space
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xml:space
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">& </
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<
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<
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crunt ejuſdem ordinis quilibet accepti quatuor etiam inter ſe proportio-
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nales (puta nempe, D. </
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A. # B. # C. # D. # E. # F.
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α. # β. # γ. # δ. # @. # φ
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M. # N. # O. # P. # R. # S.
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μ. # ν. # ο. # π. # ς. # σ.
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<
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tionales.</
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</
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<
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xml:space
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">Cùm igitur ſit Aμ, = αM; </
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<
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xml:space
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">Fσ = φ S, liquidum eſt ſore D π
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= σ P; </
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<
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<
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(tam Arithmeticam quàm Geometricam) æquè ſpectat hæc Con-
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cluſio.</
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<
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<
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BD; </
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recta PG ad DB parallelâ; </
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portionalis inter PG, PE; </
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punctum E tranſeat HE ipſis AB, CD parallela, sítque alia curva
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KEK talis, ut ductâ utcunque QL itidem ad DB parallelâ, ſit </
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