Sejarah Matematika : Sistem Numerasi Mesir Kuno, Mesopotamia (Babilonia), Yunani Kuno, China Kuno dan Hindu-Arab

@G@ EE ZFA@GOG\GK

Zrbsfs Zrbsfs pfrnfa pfrnfa`gk `gkmgk mgk agtfagt agtfagteng eng deaucg deaucgee sfhgn sfhgn gdgkyg gdgkyg pfrgdg pfrgdg`gk `gk agku agkuse seg. g.

Ngrf Ngrfkg kg

ogky ogkygg

agku agkuse segg

dfkm dfkmgk gk

nfag nfagap apug ugk k

nbau nbauke keng ngse se

dgk dgk

ektfcfmfksekyg ygkm agapu afkleptgngk pfrgdg`gk, heng de`gkdekmngk dfkmgk agnocu agnocun n ygkm ygkm cgek. cgek. \foekm \foekmmg mg agkuse agkusegg agapu agapu afklep afkleptgn tgngk gk `frgdg `frgdg`gk `gk ygkm ygkm dedgsgrngk gtgs nbktgn sbsegc ygkm `frnfa`gkm.  Deceogt dgre lgtgtgk sfhgrgo, aukluckyg pfrgdg`gk agkuseg `frgwgc dgre  pfrnfa`gkmgk `udgyg agkuseg ygkm sgkmgt detfktungk bcfo nbkdese mfbmrgies ygkm afkdunukm. Ger denfkgc agkuseg sf`gmge `fkdg ygkm `gkygn afa`frengk  pfkmgruo `gme nfoedupgkkyg. @fmetu pucg dfkmgk pusgt pfrgdg`gk pfrtgag agkuseg, ygkm rgtgrgtg `frgsgc dgre dgfrgo ygkm decgcue gcergk sukmge. Degktgrgkyg gdgcg gdgcgo o !fsb !fsbpb pbtga tgaeg, eg, !fse !fser, r,"k "kdeg deg dgk dgk #ekg #ekg.. Zfrg Zfrgdg dg`g `gk k nbtg nbtg !fsb !fsbpb pbtga tgaeg eg afapfkmgruoe pfrgdg`gk sukmge $ec de !fser, sukmge Nukekm de #ekg dgk %fa`go "kdus de "kdeg. Zfrg Zfrgdg dg`g `gk k de kfmg kfmgrg rgkf kfmg mgrg rg tfrsf tfrsf`u `utt afkh afkhgd gdee dgsg dgsgrr aukl aukluc ucky kygg  pfkleptggk ngryg agtfagteng. Zgdg &gagk pfrgdg`gk ofcfkesten, agtfagteng @g`ecbkeg `frpgdu dfkmgk agtfagteng !fser uktun afa`gkmnetngk agtfagteng 'ukgke kgke..

(gsec (gsec

ektf ektfrgn rgnse se

agsy agsygrg grgng ngtt

dfkm dfkmgk gk

pfrg pfrgdg dg`g `gk kpf pfrg rgdg dg`g `gk k

cgek cgek

afapfkmgru afapfkmgruoe oe pfrnfa`gkmg pfrnfa`gkmgk k agtfagteng agtfagteng sfcgkhutkyg. sfcgkhutkyg. $fmgrgkfmgr $fmgrgkfmgrgg tfrsf`ut tfrsf`ut tfcgo `gkygn afa`frengk sua`gkmgk tfrogdgp pfrnfa`gkmgk agtfagteng sggt eke. eke. @fr` @fr`gmg gmgee `unt `untee afku afkukh khun unng ngk k `gow `gowgg stru strunt ntur ur agtfa agtfagte gteng ng ygkm ygkm pgce pgcekm km sfdfrogkg`frupg `ecgkmgk tfcgo demukgngk dgre agsg nfagsg aucge dgre `gkmsg @g`ecbkeg, !fser, 'ukgke, #ekg, dgk "kdeg ygkm nfaudegk desfapurkgngk bcfo ecauwg ecauwgk k Zfrseg Zfrseg Gc Nogwgre Nogwgre&ae &ae.. (gc eke afkukh afkukhunn unngk gk `gowg `gowg pfrnfa pfrnfa`gk `gkmgk mgk agtfagteng agtfagteng dgre pfrgdg`gkp pfrgdg`gkpfrgdg` frgdg`gk gk tfrdgoucu tfrdgoucu afapfkmgru afapfkmgruoe oe pfrnfa`gkmgk pfrnfa`gkmgk agtfagteng pgdg pfrgdg`gkpfrgdg`gk deagsg `frenutkyg.

G. \estf \estfa a Kuafrg Kuafrgse se Afser Afser Nukb Nukb

@gkmsg

!fser

nukb

tfcgo

afkmfkgc

tucesgk

dgk

sestfa

 `ecgkmgk.@egsgkyg tucesgk eke detfaungk pgdg sf`ugo `gtu eke dgk denfkgc dfkmgk dfkmgk sestfa oefrbmcei. \estfa oefrbmcei oefrbmcei afrupgngk afrupgngk sestfa `ecgkmgk `ecgkmgk ygkm sfrekm demukgngk demukgngk dgcga nfoedupgk nfoedupgk sfogreogre. )ucesgk oefrbmcei  oefrbmcei  `fr`fktun   `fr`fktun  mga`gr mga`gr nflec ygkm afkygtgngk afkygtgngk sf`ugo sf`ugo ngtg.\estfa ngtg.\estfa oefrbmcei  oefrbmcei  tfcgo demukgngk bcfo `gkmsg !fser nukb sfhgn sfnetgr tgouk *+- \!. \ea`bc \ea`bc `ecgkmgk `ecgkmgk gtgu kbtgse agtfagteng agtfagteng !fser Nukb `frseigt dfseagc `fr`gses /-: dgk dedgsgrngk pgdg sea`bcsea`bc oefrbmcei uktun tegp kecge  pfrpgkmngtgk /- /, /-, /--, /---, /----, /-----, /------: sgapge dfkmgk sfhutg. sfhutg. )egpt )egptegp egp sea`bc sea`bc eke dgpgt dgpgt detuce detucess sf`gky sf`gkygn gn gpgpuk gpgpuk sfsuge sfsuge dfkmgk dfkmgk  `ecgkmgk ygkm deekmekngk, sfoekmmg uktun afkucesngk `ecgkmgk dfcgpgk pucuo gtgu dfcgpgk rgtus, sea`bc sea`bc /- gtgu /-- detuces sf`gkygn dfcgpgk ngce.Dfkmgk ngce.Dfkmgk eke `frgrte `gowg afrfng afaecene sea`bc tfrpesgo uktun sgtugk, pucuogk, rgtusgk rgtusgk,, re`ugk re`ugk,, pucuo pucuo re`ugk re`ugk,, rgtus rgtus re`ugk re`ugk,, dgk hutggk. hutggk..@f .@fren renut ut eke tg`fc tg`fc  `fresengk sea`bcsea`bc ygkm demukgngk `gkmsg !fser nukb desfrtge dfkmgk tfrhfagogk cga`gkm ygkm sudgo netg mukgngk sfngrgkm. 7) \estfa \estfa Zfkucesgk Zfkucesgk Gkmng Gkmng Oefrbmce Oefrbmcei  i 

7ktun sgtugk gdgcgo sf`ugo mgres curus, cfkmnukmgk nf gtgs uktun   pucuogk, cfkmnukmgk sftfkmgo cekmngrgk afkygapekm sfpfrte b`gt kyga kygaun un::

uktu uktun n rgtu rgtusg sgk, k, dgk dgk uktu uktun n hutg hutggk gk decg decga a`gkm `gkmng ngk k dfkm dfkmgk gk

sea`bc sfbrgkm cgnecgne ygkm afkgenngk tgkmgk.Zfkucesgk oefrbmcei dgpgt deaucge deaucge dgre ngkgk nf nere, nere nf ngkgk, gtgu dgre gtgs nf `gwgo dgk dgre  `gwgo nf gtgs, tftgpe `egsgkyg deaucge dgre ngkgk nf nere sfpfrte dgcga  pfkucesgk Grg`, wgcgupuk dgcga pfkucesgk ibragc &gagk sfngrgkm eke afkmmukgngk nere nf ngkgk:.

!esgcky !esgckygg uktun uktun afa`ug afa`ugtt `ecgkm `ecgkmgk gk *0 nf> bcfo bcfo goc gocee agtf agtfagt agteng eng "kd "kdeg eg,, degd degdgp gptgs tgsee goce goce agtfagten  Zgrse GcNogwgre&ae dgcga dgcga `unu `unu tfktgk tfktgkm m pfkmer pfkmerggk ggk dfkmgk dfkmgk gkmng (ekdu ygkm detuces sfnetgr +*!: dgk goce agtfagten Grg` GcNekde afkfruse afkfruse `unukyg `unukyg tfktgkm pfkmmukgg pfkmmukggk k gkmng "kdeg nfcugrgk nfcugrgk +8-!:, +8-!:, dgk nfau nfaude degk gk tfrsf tfrsf`g `grr nf duke dukegg `grgt `grgt pgdg pgdg Hgagk Zfrtfkm Zfrtfkmgogk gogk.. \fhgrgwgk afcglgn gkmng abdfrk abdfrk de nf`gkygngk `gogsg dfkmgk gkmng gkmng @rgoae ygkm ygkm demukgngk sfnetgr pfrtfkmgogk g`gd nf8 \!. Gkmng @rgoae tfcgo detfaungk dgcga prgsgste de mugmug dgk de nbek de dgfrgo dfngt Zukf, !ua`ge, dgk 7ttgr Zrgdfso. "ke gkmng dfkmgk dfkmgk sfdenet =gregse: ygkm demukgngk demukgngk sfcgag wgntu ygkm lunup cgag oekmmg g`gd nf?. @frenut eke `f`frgpg pfr`fdggk gkmng (ekdu dfkmgk gkmnggkmng cgekkyg.

Zfretukmgk

Zgdg aucgkyg `gkmsg "kdeg afkhuacgongk `ecgkmgk dgre nere nf ngkgk, tftgpe nfaudegk `fru`go dgre ngkgk nf nere. aesgckyg pfkhuacgogk `ecgkmgk *0< dgk *