Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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<
s
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xml:space
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">{_cc_/_a_} - _b_ - _a_ = _n_.</
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<
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<
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<
s
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xml:space
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">_cc_ - _ba_ - _aa_ = _nn_.</
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<
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</
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<
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<
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">_cca_ - _baa_ - _a_
<
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>
= _n_
<
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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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">_ccaa_ - _ba_
<
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- _a_
<
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= _n_
<
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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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">In recta BAH ſumatur BA = _b_; </
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<
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">& </
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<
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xml:space
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">in AD ad AH perpendi-
<
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">Fig. 216.</
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culari ſit AC = _c_; </
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<
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<
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utcunque ductâ GK ξ ad AH perpendiculari (quæ ipſam BS
<
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ſecet in ξ; </
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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
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xml:space
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">per K intra _aſymptotos_
<
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VD, VS deſcribatur _hyperbola_ KYHK; </
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<
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xml:space
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">ſint demum curvæ CLHLλ,
<
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AMHMμ, ANHNν tales, ut inter AG (vel GZ) & </
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<
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xml:space
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">GK ſint _me_-
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_dia_ GL, _bimedia_ GM, _trimedia_ GN; </
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<
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">hæ propoſito ſervient. </
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<
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quod conſtat, ut in præcedentibus.</
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</
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<
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">Not.</
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<
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">1. </
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<
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">Curvæ HLλ, HMμ, HNν ad decimam ſeriem pertinent;
<
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</
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<
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xml:space
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">reliquæ CLH, AMH, ANH ad undecimam.</
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<
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</
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<
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<
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">2. </
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<
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<
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">curva CLH _circula_-
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_ris circumferentiæ_ pars; </
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<
s
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xml:space
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">utriuſque commune centrum eſt O, ipſam AB
<
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biſecans (unde AH = √{_bb_/4} + _cc_: </
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<
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</
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<
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">3. </
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<
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">In decima ſerie radix una ſemper habetur, & </
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<
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<
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ma nunc duæ, nunc una, ſubinde nulla.</
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<
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">4. </
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<
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xml:space
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">Aφ = {_cc_/_b_}; </
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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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">Aψ = √{_bb_/16} + {_cc_/2}: </
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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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<
s
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φ Y, ψ X; </
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<
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<
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xml:space
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">In undecimæ ſecundo gradu ordinata AC eſt maxìma; </
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<
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<
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= √{_bb_/9} + {_cc_/3}: </
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<
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xml:space
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">- {_b_/3}; </
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<
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<
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xml:space
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">à P ad curvam AMH ordinetur Pγ,
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hæc maxima erit; </
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<
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xml:id
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xml:space
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">item ſi AQ = √{9_bb_/64} + {_cc_/2}: </
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<
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xml:id
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xml:space
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">- {3_b_/8}; </
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