Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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">Sit curva AEG (cnjus Axis AD) proprietate talis, ut ſi à quo-
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cunque puncto in ipſa ſumpto E, ducatur recta EPad AD normalis;
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">Fig. 182.</
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connectatúrque AE, ſit AEinter deſignatam AR, & </
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<
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">APpropor-
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tione media, ſecundum ordinem, cujus exponens ſit {_n_/_m_}; </
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<
s
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curva AMB, quam tangat TMad AEparallela.</
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</
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<
s
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xml:space
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">De curva AMadnoto fore _n. </
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<
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<
s
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xml:space
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">: AE. </
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<
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">arc. </
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<
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xml:space
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">AM.</
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<
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</
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<
s
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xml:space
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">Si {_n_/_m_} = {1/2} (vel AEſit inter AR, AP ſimpliciter media) erit
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AEG circulus, & </
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<
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xml:space
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">AMB _Ciclois primaria_; </
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<
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xml:space
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">hujus igitur dimenſio è
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lege generali habetur.</
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<
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xml:space
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">Hæc etiam ex adjuncto _Problemate_ magis ccomprehenſivo pera-
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guntur.</
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<
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<
s
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">Curva deſignetur, puta AMB, cujus _axis_ AD, ità ut in hac
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ſumpto puncto quopiam M, & </
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poſito rectam MT ipſam tangere, habeant TP, PM relationem aſ-
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ſignatam.</
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<
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">Accipiatur recta quæpiam R, & </
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<
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">fiat ut TPad PM (quam utique
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rationem aſſignatâ dabit relatio) ità R ad PY (quæ nempe ſumatur
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in recta PM, & </
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xml:space
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">ad axem ADordinetur) ſic ut per ejuſmodi puncta
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Y tranſeat curva YYK; </
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<
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xml:space
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">tum ſi ſiat PM = {ſpat. </
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">APY/R}; </
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<
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xml:space
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">de curvæ
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AMB indè conſtabit natura.</
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">& </
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<
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habere debeat TPad PM rationem eandem quam habet R ad arcum
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AE; </
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rit PY = arc. </
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<
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