81. Earliest Uses Of Symbols Of Operation And Grouping 2, page 78). The radical symbol first appeared in 1525 in Die Coss by ChristoffRudolff (14991545). He used (without the vinculum) for square roots. http://www.veling.nl/anne/templars/operation.html

Earliest Uses of Symbols of Operation and Grouping Last revision: Aug. 15, 1997 ADDITION AND SUBTRACTION SYMBOLS Plus (+) and minus (-). The plus symbol as an abbreviation for the Latin et (and), though appearing with the downward stroke not quite vertical, was found in a manuscript dated 1417 (Cajori). The + and - symbols first appeared in print in Mercantile Arithmetic or Behende und hubsche Rechenung auff allen Kauffmanschafft , by Johannes Widmann (born c. 1460), published in Leipzig in 1489. However, they referred not to addition or subtraction or to positive or negative numbers, but to surpluses and deficits in business problems (Cajori vol. 1, page 128). Cajori says, "There is clear evidence that, as a lecturer at the University of Leipzig, Widmann had studied manuscripts in the Dresden library in which + and - signify operations, some of these having been written as early as 1486." Johnson (page 144) says a series of notes from 1481, annotated by Widmann, contain the + and - symbols, and he asks whether Widman could have copied these symbols from some unknown professor at the University of Leipzig. Johnson also says that a student's notes from one of Widmann's 1486 lectures show the + and - signs. Giel Vander Hoecke used + and - as symbols of operation in Een sonderlinghe boeck in dye edel conste Arithmetica

82. Sciscape°Q½×°Ï :: Æ[¬Ý¤å³¹ - 0! The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.sciscape.org/phpBB2/viewtopic.php?p=25432&sid=bcedcfea814f129f9ca7a48

83. Sciscape°Q½×°Ï :: À˵ø¥DÃD - 0! The summary for this Chinese (Traditional) page contains characters that cannot be correctly displayed in this language/character set. http://www.sciscape.org/phpBB2/posting.php?mode=topicreview&t=14545&sid=5099b443

84. 2000 ”N‚Ì Column Translate this page The summary for this Japanese page contains characters that cannot be correctly displayed in this language/character set. http://www.nn.iij4u.or.jp/~hsat/column/col00.html

2000 ”N‚Ì column ‚ªŽ¦‚µ‚½•û–@‚ɂǂꂾ‚¯‚̐V‚µ‚¢‚à‚Ì‚ð•t‚¯‰Á‚¦‚邱‚Æ‚ªo—ˆ‚½‚Ì‚¾‚낤‚©, ‚ÆŠ´‚¶‚Ä‚¢‚é‚Ì‚ÍŽ„‚¾‚¯‚¾‚낤‚©B Îˆäˆê•½, Œc‰ž‹`m‘åŠw—HŠw•” ŽO‘Ì–â‘襐§ŒÀŽO‘Ì–â‘è “ÁW “V‘Ì‚Ì“®‚«‚ð’Ç‚Á‚½”ŠwŽÒ’B ”ŠwƒZƒ~ƒi[ (7), 1999. ¬à‰Æ‚ɂȂ邽‚߂ɐ”Šw‚ðŽ~‚ß‚½ˆ½‚éŠw¶‚ɂ‚¢‚Ä David Hilbert (18621943) ‚ªŒ¾‚Á‚½Œ¾—t —L–¼‚È de Moivre ‚ÌŒöŽ®‚Í de Moivre (16671754, UK) ‚Ì’˜ì u‹‰”‚Æ‹Ï‚ÉŠÖ‚·‚鐔ŠwŽG˜^v (London, 1730) ‚̈ê•Å–ڂɏo‚Ä‚¢‚é‚Æ‚¢‚¤B —L–¼‚È“ñ€’藝‚Ì”­Œ©‚Í Sir Isaac Newton (16421727) ‚Å, 1665 ”N ‚Ì‚±‚Æ‚Å‚ ‚é‚Æ‚¢‚¤B •¶Œ£“I‚É‚Í 1676 ”N 6 ŒŽ 13 “ú•t‚̎莆‚Ì’†‚ɏ‰‚ß‚ÄŒ©‚ç‚ê‚é‚Æ‚¢‚¤B ƒJƒWƒ‡ƒŠ u‰“™”ŠwŽjv (‹¤—§o”Å, p. 340 ŽQÆ) ‚£³m, ”ŠwŽÒ¥”ŠwŽj‰Æ dx ‚Æ dy ‚̉ðÍŠw -ƒIƒCƒ‰[‚ÉŠw‚Ô- II. ƒIƒCƒ‰[‚̐¢ŠE (‚»‚Ì2) ”ŠwƒZƒ~ƒi[ (8), 1999 Ž©‘R‘ΐ”‚Ì’ê e ‚Ì‚±‚Æ‚ð‘o‹Èü‘ΐ”‚ƌĂԂ±‚Æ‚ª‚ ‚é‚Ì‚¾‚»‚¤‚¾B ‚±‚ê‚Í’¼Šp (“™•Ó) ‘o‹Èü xy = 1 ‚Æ x Ž², “ñ’¼ü x = 1, x = t ‚ň͂܂ê‚é•”•ª‚Ì–ÊÏ S ‚ª S = ç x ƒJƒWƒ‡ƒŠ ¢‰“™”ŠwŽj£ (‹¤—§o”Å) p.235ŽQÆ‚Ì‚±‚ƁB ŽO•Ó‚Ì’·‚³‚ª‘S‚Đ®”‚Å‚ ‚éŽOŠpŒ`‚É‚¨‚¢‚Ä, ‚»‚ê‚çŽO•Ó‚̘a‚Æ‚»‚̖ʐςƂª“™‚µ‚­‚È‚é‚悤‚ÈŽOŠpŒ`‚Í, ‚»‚ÌŽO•Ó‚Ì’·‚³‚ª, (6, 8, 10), (5, 12, 13), (9, 10, 17), (7, 15, 20), (6, 25, 29) ‚Å‚ ‚é‚à‚Ì‚ÉŒÀ‚éB (‚±‚ê‚ç‚Í‘S‚Ä, ®”•Ó’·‚Ì’¼ŠpŽOŠpŒ` [ƒsƒ ƒ^ƒSƒ‰ƒXŽOŠpŒ`] ‚©‚çƒsƒ ƒ^ƒSƒ‰ƒXŽOŠpŒ`‚ð uˆø‚¢‚½v ‚à‚Ì‚É‚È‚Á‚Ä‚¢‚é) ‚»‚µ‚Ä (®”•Ó’·‚Å‚Í‚È‚­‚Æ‚à) ŽO•Ó‚̘a‚ƖʐςƂª“™‚µ‚¢ŽOŠpŒ`‚É‚¨‚¢‚Ä‚Í, ‚»‚Ì“àÚ‰~‚Ì”¼Œa‚Í2‚É‚È‚éB ‰~‚̃R[ƒc‚̐«Ž¿: x k=1 n (x2 - 2x cos((2k - 1)ƒÎ/(2n)) + 1).

85. Human Indexes Of My Books On Mathematics; Ru Re Ro In Japanese Translate this page The summary for this Japanese page contains characters that cannot be correctly displayed in this language/character set. http://www.com.mie-u.ac.jp/~kanie/tosm/humanind/jinmeir3.htm

TOSMŽOd‚̃z[ƒ€ w‰ðÍ‹³’öx w”—‰ðÍ‚̃pƒCƒIƒjƒA‚½‚¿x w”Šw–¼ŠˆÄ“àx ... w“V‘‚̏ؖ¾x @l–¼õˆø@‚é‚ê‚ë l–¼õˆø‘–ÚŽŸ ƒ‹ƒ”ƒFƒN ƒ‹ƒ”ƒFƒŠƒG ƒ‹[ƒJƒX ... ƒgƒbƒv (Louis XIV, 1638-1715.) ƒ‰ƒCƒvƒjƒbƒc ‚̓GƒWƒvƒgª•ž‚ð‚»‚»‚Ì‚©‚µ‚ɃpƒŠ‚É”hŒ­‚·‚éD‰¤‚Ƃ̉‚ÍŽÀŒ»‚µ‚È‚©‚Á‚½‚ªCƒ‰ƒCƒvƒjƒbƒc‚Í ƒzƒCƒwƒ“ƒX ‚ƁC‚»‚µ‚Đ”Šw‚Æ’m‚荇‚¢C‘å—¤‚Ì”÷Ï•ªŠw‚ª¶‚Ü‚ê‚éD@ ƒgƒbƒv ƒ‹ƒ”ƒFƒN (William Judson LeVeque, 1923.8.9-) ƒgƒbƒv ƒ‹ƒ”ƒFƒŠƒG (Urbain Jean Joseph Le Verrier, 1811.3.11-1877.9.23.) @ƒtƒ‰ƒ“ƒXCƒTƒ“Eƒ[‚ɐ¶‚Ü‚êCƒpƒŠ‚ÉŽ€‚·D @1846”N J.C.ƒAƒ_ƒ€ƒY @“–Žžƒ‹ƒ”ƒFƒŠƒG‚Ì“¯—»‚Í u”ނ̓yƒ“‚̐æ‚Ő¯‚ðŒ©‚Â‚¯‚½DŒvŽZ‚̗͈ȊO‚Ì‚Ç‚ñ‚È“¹‹ï‚àŽg‚킸‚Ɂv ‚ÆŒ¾‚Á‚½‚Æ‚¢‚¤D @1855”N‚ɐ ¯‚Ì‹ß“ú“_‚̈ړ®‚ª ƒjƒ [ƒgƒ“ ‚Ì—˜_‚Å‚Ì—˜_’l‚æ‚è‘å‚«‚¢‚±‚Æ‚ð”­Œ©D‚±‚ê‚ðà–¾‚·‚邽‚߂ɐ ¯‚Ì“à‘¤‚ÉŒ©‚¦‚È‚¢¯Vulcan‚ðC‚Ü‚½Œã‚ɂ͏¬˜f¯‘Ñ‚ð‘z’肵C‚»‚ê‚ð’T‚µ‘±‚¯‚½D‚µ‚©‚µC”Þ‚ÌŽ€Œã1915”N‚É ƒAƒCƒ“ƒVƒ ƒ^ƒCƒ“ ‚̈ê”Ê‘Š‘ΐ«—˜_‚́C—]•ª‚È•¨‘Ì‚ð•K—v‚Æ‚µ‚È‚¢à–¾‚ð—^‚¦‚éD@@ ƒgƒbƒv ƒ‹[ƒJƒX (Francois Edouard Anatole Lucas, 1842.4.4-1891.10.3). @ƒtƒ‰ƒ“ƒXCƒAƒ~ƒAƒ“iƒpƒŠ‚Ì–k•û‚Ɉʒu‚·‚éH‹Æ“sŽsj‚ɐ¶‚Ü‚êCƒpƒŠ‚ÉŽ€‚·B ƒ‹ƒ”ƒFƒŠƒG ƒƒ‹ƒZƒ“ƒk ”M -1 ‚ª‘f”‚Å‚ ‚邱‚Æ‚ðŽ¦‚·DƒRƒ“ƒsƒ [ƒ^‚ðŽg‚킸‚ÉŽ¦‚³‚ꂽÅ‘å‚Ì‘f”‚Å‚ ‚éD‚à‚¿‚ë‚ñ M = 170141183460469231731687303715884105727 ‚ðŽÀÛ‚ÉŒvŽZ‚¹‚¸‚ÉŽ¦‚·‚Ì‚Å‚ ‚éD‚±‚Ì‘f”‚ɑ΂·‚郋[ƒJƒXEƒeƒXƒg‚Í1930”N‚É ‚³‚ꂽD (1882-94)‚Í‚±‚Ì•ª–ì‚ÌŒ“T‚É‚È‚Á‚Ä‚¢‚éD @@ ƒgƒbƒv ƒ‹ƒWƒƒƒ“ƒhƒ‹ (Adrian Marie Legendre, 1752.9.18-1833.1.10).

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