Viviani, Vincenzo
,
De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei
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diuerſos vertices ſimul adſcriptæ, ipſæ, vel ad neutram partem ſe
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vnquam ſecabunt, vel ſi ad alteram partem occurrant, occurrent
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quoque ad aliam, punctaque occurſuum erunt extrema eiuſdem
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communis applicatæ, ac in ijſdem occurſibus ſe mutuò ſecabunt.</
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<
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xml:space
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uerſos vertices B, E ſimul adſcriptæ. </
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<
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xml:space
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nes ad alteram partium, vt ad A nunquam conueniunt, ad aliam quoque C
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nunquam conuenire.</
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partes C, quocunque puncto F, per ip-
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sũ ordinatim applicetur recta CFGDA,
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quæ vtrinque producta, vtrique ſectio-
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ni occurret (cum ipſæ ob Hypoteſim,
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ſint ſectiones in infinitam diſtantiam
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abeuntes ad inferiores partes) cumque
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in ſectione ABC ſit ſemi-applicata AG,
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æqualis GC, & </
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<
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">in ſectione DEF, ſemi-
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applicata DG, æqualis GF, ſitque ante-
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cedens AG maior antecedente DG (cum ad partes A nunquam cõueniant)
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erit etiam conſequens GC, maior conſequenti GF, quare punctum F, ſe-
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ctionis DEF cadit intra ABC, & </
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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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">Si verò ſectiones ad alteras partes, veluti ad A, & </
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<
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</
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<
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">Dico ipſas ad alias quoque partes ſimul occurrere ad extrema puncta eiuſ-
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de m applicatæ.</
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<
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<
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">Nam, ducta per H communi applicata HI, ipſa producatur ſecans ſectio-
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nem BC in L; </
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<
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xml:space
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IL, & </
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<
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<
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<
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que ſectionum puncta L, M in vnum conueniunt; </
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<
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xml:space
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">Quare cum ſectiones
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ABC, DEF non per vertices ſimul adſcriptæ ad alteram partem occurrunt,
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occurrent quoque ad aliam, punctaque occurſuum erunt extrema eiuſdem
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communis applicatæ.</
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<
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<
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<
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ſi huiuſmodi ſectiones tangerent ſe mutuò in occurſu H, ita vt ſectionis, ver-
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bi gratia, ED partes HO, HN cadant totæ intra ſectionem ABC: </
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<
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altera ipſarum partium, vt puta OH, quolibet puncto D, & </
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communi applicata ADGFG vtranque ſectionem ſecane
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, erunt in ſectione
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ABC rectæ AG, GC æquales, & </
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les, ſed eſt AG maior GD cum ponatur peripheria OH cadere intra BH, vn-
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de & </
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<
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<
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monſtrabitur de quolibet alio extremo puncto cuiuſcunque applicatæ inter
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O, & </
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