"313696" . "1"^^ . "P\u00E1t\u00E1 a \u0161est\u00E1 kniha Eukleidov\u00FDch Z\u00E1klad\u016F pojedn\u00E1v\u00E1 o pom\u011Brech veli\u010Din, p\u0159edev\u0161\u00EDm d\u00E9lek \u00FAse\u010Dek a plo\u0161n\u00FDch obsah\u016F triangulovateln\u00FDch \u00FAtvar\u016F. P\u0159itom v\u00FDsledky p\u00E1t\u00E9 knihy jsou snadno odvoditeln\u00FDmi rovnostmi \u010Di nerovnostmi p\u0159\u00EDslu\u0161n\u00E9ho form\u00E1ln\u00EDho algebraick\u00E9ho kalkulu, kter\u00FD ov\u0161em v dob\u011BEukleidov\u011B nebyl zn\u00E1m. Podobn\u011B n\u011Bkter\u00E9 v\u00FDsledky obsa\u017Een\u00E9 v \u0161est\u00E9 knize, ale i \u0159adu dal\u0161\u00EDch, nav\u00EDc obt\u00ED\u017En\u011B dosa\u017Eiteln\u00FDch v n\u00E1zorn\u00E9 geometrii, lze snadno obdr\u017Eet Descartovou metodou (viz odd\u00EDl Dixit Cartesius v knize Al-Chv\u00E1rizm\u00ED: Aritmetick\u00FD a algebraick\u00FD trakt\u00E1t, OPS, Nymburk 2008). Autorem koment\u00E1\u0159\u016F a text\u016F dopl\u0148uj\u00EDc\u00EDch Heibergovo (a tedy i \u010Desk\u00E9 Serv\u00EDtovo) vyd\u00E1n\u00ED Z\u00E1klad\u016F je Petr Vop\u011Bnka." . . "Eukleides Z\u00E1klady. Knihy V-VI"@cs . . . . . "The fifth and sixth book of Elements by Euclid talks about the ratios of quantities, primarily the lengths of abscissae and areas of figures that can be triangulated. The results of the fifth book are easily deducible equalities or inequalities of the given formal algebraic calculation, which, however, was not known in the time of Euclid. Similarly, some results included in the sixth book as well as a number of other results which can only be achieved in solid geometry with difficulty, can easily be obtained by the Descartes method (see section Dixit Cartesius in book of Al-Chv\u00E1rizm\u00ED: Arithmetic and Algebraic Tract, OPS, Nymburk 2008). The author of commentaries and texts complementing Heiberg?s edition (and consequently also the Czech edition of Serv\u00EDt) is Petr Vop\u011Bnka."@en . . "Prameny evropsk\u00E9 vzd\u011Blanosti,3" . "RIV/49777513:23330/09:00502398" . "Eukleides Elements. Books V-VI"@en . "Nymburk" . . "Eukleides Z\u00E1klady. Knihy V-VI" . "130"^^ . "Eukleides Z\u00E1klady. Knihy V-VI"@cs . . . . . "Vop\u011Bnka, Petr" . "O" . "OPS" . "Eukleides Z\u00E1klady. Knihy V-VI" . . "P\u00E1t\u00E1 a \u0161est\u00E1 kniha Eukleidov\u00FDch Z\u00E1klad\u016F pojedn\u00E1v\u00E1 o pom\u011Brech veli\u010Din, p\u0159edev\u0161\u00EDm d\u00E9lek \u00FAse\u010Dek a plo\u0161n\u00FDch obsah\u016F triangulovateln\u00FDch \u00FAtvar\u016F. P\u0159itom v\u00FDsledky p\u00E1t\u00E9 knihy jsou snadno odvoditeln\u00FDmi rovnostmi \u010Di nerovnostmi p\u0159\u00EDslu\u0161n\u00E9ho form\u00E1ln\u00EDho algebraick\u00E9ho kalkulu, kter\u00FD ov\u0161em v dob\u011BEukleidov\u011B nebyl zn\u00E1m. Podobn\u011B n\u011Bkter\u00E9 v\u00FDsledky obsa\u017Een\u00E9 v \u0161est\u00E9 knize, ale i \u0159adu dal\u0161\u00EDch, nav\u00EDc obt\u00ED\u017En\u011B dosa\u017Eiteln\u00FDch v n\u00E1zorn\u00E9 geometrii, lze snadno obdr\u017Eet Descartovou metodou (viz odd\u00EDl Dixit Cartesius v knize Al-Chv\u00E1rizm\u00ED: Aritmetick\u00FD a algebraick\u00FD trakt\u00E1t, OPS, Nymburk 2008). Autorem koment\u00E1\u0159\u016F a text\u016F dopl\u0148uj\u00EDc\u00EDch Heibergovo (a tedy i \u010Desk\u00E9 Serv\u00EDtovo) vyd\u00E1n\u00ED Z\u00E1klad\u016F je Petr Vop\u011Bnka."@cs . . "[2DE2EC0EA409]" . . . . "978-80-87269-05-3" . . . "RIV/49777513:23330/09:00502398!RIV10-MSM-23330___" . "1"^^ . "Eukleides Z\u00E1klady. Knihy V-VI" . "130"^^ . "Eukleides; Elements; geometry; mathematics; antique philosophy F.Servit; P.Vopenka; planimetry; ratios"@en . "Eukleides Elements. Books V-VI"@en . "23330" . .