Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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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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">pro ſingulo trium ſerierum gradu tan-
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tùm unam adhibendo lineam) explicantur iſtæ præcedaneæ æquatio-
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nes, hoc pacto:</
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<
s
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">Sit AH recta indefinitè protenſa, & </
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<
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<
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<
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210.</
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qua ſumatur AB = _n_, & </
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lineæ LXL, MXM, NXN tales
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, ut ſumpto in AH quocunque
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puncto G, & </
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<
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">ductâ GK ad AD parallelâ, ſit in proportione AG ad
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GK (vel AB) proportione _tertia_ GL, _quarta_ GM, _quinta_ GN; </
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<
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lineæ propoſitarum æquationum naturæ explicandæ inſervient.</
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<
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<
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xml:space
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">Nam ſumpta AE = _b_ (ſumatur autem AE ob primam ſeriem
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ad partes I, ob ſecundam & </
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<
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gulus FEH ſemirectus (iſte quidem pro prima & </
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rie inclinans verſus H, pro tertia reclinans ab H, ut Schema ſatis
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monſtrat) tum rectæ EF cum expoſitis lineis interſectiones reſpectivæ
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radices a determinabunt; </
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perpendiculares(LG, MG, NG) erunt interceptæ AG radicibus _a_
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æquales reſpectivè.</
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<
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cedentibus ipſa _n_.</
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<
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unica.</
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<
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<
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(vel _a_) = _n_.</
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<
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ſcilicet EF curvas bis ſecat) nonnunquam una tantùm (cùm EF ip-
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ſarum aliquam contingat; </
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a = {_b_/2}; </
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">in quarto cùm a = {3/4}_b_) aliquando
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nulla, cùm EF infra tangentes cadit, & </
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rit.</
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<
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quarum communes _aſymptoti_ ſunt rectæ AH, AD.</
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