Barrow, Isaac
,
Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur
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nihilominùs gravatim admittuntur; </
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<
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xml:space
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">iſtâ tantummodò raptim inſinua-
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tâ, ſubnectemus alìam ab illorum guſtu non abhorrentem; </
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<
s
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xml:space
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">illam
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nempe (quando ſcilicet haud alia melior, ut varias pertentans analyſes,
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& </
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<
s
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xml:space
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">hoc in alia complura _Problemata_ transformans exiſtimari poſſum,
<
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facilè poſſit excogitari; </
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<
s
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xml:space
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">quum & </
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<
s
xml:id
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xml:space
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">operæ meæ ſatìs alioquin exerci-
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tatæ nonnunquam videatur parcendum) quam olim _Alhazenus Arabs_
<
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ſcriptis commendavit; </
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<
s
xml:id
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xml:space
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">ab horribili tamen illâ prolixitate ſimul ac
<
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obſcuritate; </
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<
s
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xml:space
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">neque non ab incondita ſermonis barbarie nonnihil re-
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purgatam. </
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<
s
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xml:space
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">quorſum hoc præmittimus _Lemmaticum Problema._</
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<
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<
s
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">VI. </
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<
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xml:space
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">Trianguli DPNangulus ad P rectus ſit; </
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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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">in hujus uno cru-
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<
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xml:space
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">Fig. 91.</
note
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re PN adſignetur punctum F; </
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<
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xml:space
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">per F recta ducenda eſt, quæ reli-
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quum latus DP (protractam nempe) ac hypotenuſam DN ità ſecet,
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ut ab illis intercepta ad ſegmentum hypotenuſæ lateri primò contermi-
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num datam obtineat proportionem R ad S.</
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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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">Hoc ità peragatur licet. </
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<
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xml:space
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">Ducatur FH ad PD parallela. </
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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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">Dia-
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metro HN deſcribatur Circulus HFN(is nempe per F tranſibit, ob
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angulum HFNrectum) tum connectatur DF; </
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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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">fiat angulus
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FHI = ang. </
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<
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">FD N. </
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<
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">ſit etiam R. </
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<
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<
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xml:space
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">: DF. </
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<
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xml:space
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">T & </
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<
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xml:space
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">a puncto I duca-
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tur recta ILKdiametrum HN interſecans ad L, & </
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<
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">circulo occurrens
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in K, ità quidem ut ſit intercepta LK = T (hoc autem quomodò
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præſtetur in ſuperioribus oſtenſum) denuo per puncta KF trajiciatur
<
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recta CF, ipſam DP ſecans in X. </
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<
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xml:space
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">Dico factum, vel ipſe CX.
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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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">& </
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<
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<
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(vel FH I) = FDN, erit triangulum FDCſimile triangulo
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LK C; </
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<
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</
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<
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<
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">erunt triangula XDC, NKCſibi quoque
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ſimilia, proindéque DC. </
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<
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<
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<
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æquali FD. </
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<
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C N; </
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<
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<
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erat.</
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<
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<
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indefinitè protenſa variè ſtatui poteſt; </
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<
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N; </
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<
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ſingulo quoque recta IK (conditione gaudens præſtitutâ) plurifa-
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riàm duci poteſt; </
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<
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<
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tiones. </
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<
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">at quoad omnes caſus perſimilis erit conſtructio, nec ferè di-
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verſa demonſtratio. </
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<
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