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‫ُ ْ ْ َه َ ِﭬ‬

‫ُ رْسْ وْ ْ ْ َر ْ ْ ْ ُ ْ ْ ْ ْ ا ْآ ْ‬

‫آ ْ ُ َ رُوقْ ْ ْ ُ ْ ّ ْ ْ ْ ْ لْ ا ْ ا ْآ ِ‬ ‫‪ْ ْ !"# َ $َ %‬‬ ‫رَا ْ‬

‫& ْ ْ ْ َ‪$‬‬ ‫ْ‬


‫ِ ِْ ا‬

‫ْ( ُ بْ ‪:‬‬ ‫&ٌ َ‬ ‫‪ ,‬ا ِ‪َ َ *ِ +‬‬ ‫ ُ‬‫َ‬

‫ا َ ُْ ; َ‬

‫" ِ! َ‬ ‫" ِ! ٍ‪َ $‬و ُ ْ‬ ‫) ُ ْ‬ ‫ُآ "‬

‫‪ٍ ْ 1‬ء ِ ِ ْ( َ ِ‪.ْ.‬‬ ‫ع ِ ُ‪َ ْ 5‬ر‪َ ،.ِ4‬و َ‪َ 2‬ر آُ) َ‬ ‫ِ‪ ،.ِ +َ :‬ا ‪ِ9‬ي أ ْ َ َ‬

‫= ْ! َ<ْ‪.‬‬ ‫‪ ُ %‬ا ‪ ?َ5‬رْ > رَب َ‬ ‫‪َ ،ْA$َ َ َ ِ َ B‬و ُه َ ا َا ِ‬ ‫َ وَا‪َ ْ َ AC‬ر َ‪ ،ْA‬وَ> وَا ِ‬ ‫ل ا; َو ا ُ‪.ْ !ِ$ِ D‬‬ ‫‪ِ #‬‬ ‫‪ ،ًHْ+َ .ُ H‬وَا ِ‪ُ Fّ +‬ة ِ َ ُ‬ ‫وَا ُ‪َ ِ ِ ْDُ ُ ِ ْD‬آ ُ ْ‪ !َ $‬نْ َ‪ُ +ْ َ I ُ J‬‬ ‫َو ُ‪َ ْ)2‬ر " زدْ ِ‪:‬‬

‫‪. ْ !ِ %‬‬ ‫‪ *ُ %‬ا ا ِ‬ ‫‪ L‬أرْ َ‬ ‫ِ ً َو أ ْ‪َ :‬‬


‫لْ ))وْ(ِ'‬ ‫‪ ،Qَ %‬ﯕ‬ ‫‪ّ R‬دْ ْ ! َ? ا ّ ْ‬ ‫‪ ?َ ْ %‬و ْ‪ْ J‬‬ ‫ا; ْ‪ْ ْ J‬‬

‫‪!! ْ !ِ O‬‬


‫ا* ْ َا َ‬ ‫‪ ْ*#‬ا ا‪ 4َ QَJ‬عْ ا ْ ِْ‪ S‬بْ‪.‬‬ ‫‪ْ :ْ B‬ر"‪ ْVJ‬آِ! َ‪ U‬شْ ْ‪ْ ْ 4‬‬ ‫‪ ْ %‬ا ْ‪ ?َ $‬رْ ﯕ ْ‪ِ ْ ْL‬ي أ ِ‬ ‫وَا ْ‬ ‫‪R‬‬ ‫‪ِ ْ 4َ ?َ ْ ْ #‬‬ ‫‪ Qَ R‬أ ْ‪ ْ 2‬رْ ْ‬ ‫‪ ْ*#‬ا ّْ‪ْ $‬‬ ‫وْ‪ْ ْ $ْ 4َ ْLJِ ْ Y!ِ%‬‬

‫‪ ?َ ْ #‬؟‬ ‫= دِي ْ‪ْ ْ :‬‬ ‫‪ #‬آِ! َ‪ U‬شْ َ‬ ‫‪ّْ X‬لْ رَا ِ‬ ‫ْ ْ‪َ ،QَBْ +‬و َ‪ْ :ْ :‬‬

‫‪ B‬يْ ْ ْ ْ ْ‪.ْ +‬‬ ‫‪َ " 1‬‬ ‫‪َDX‬الْ ُه َ َه دْ ِ‬ ‫‪َ R‬ابْ َ‪ 4‬عْ َه ذْ ا ‪I‬‬ ‫وْا َ‬ ‫‪ْ #‬ه ‪،Q‬‬ ‫= دِي ‪ْ4‬ﯖ ُ َ‬ ‫‪َ َِ َ +‬‬ ‫‪ َ ,‬ا* ُ‬ ‫‪ َ ِ ُ #‬ا* ّْ ْ‬ ‫ِإَ ﯕ ْ‪ (ُ !ِ ْL‬مْ رْ ْ‬ ‫‪ (ُ !ِ ْ X‬مْ دَا َ ا ْ)ْ!!‬ ‫= دِي ْ‪ّْ Uْ :‬‬ ‫= دِي ْ‪ ْ^Uْ $ْ ْ ُ !ِ_4‬ا ُ ْ ِ()ْ‪َ ،‬‬ ‫‪َ ُ #‬ه َ‬ ‫َو ِ( ْ ‪ْ ْ 4ْ ْ !ِR4ْ Y!ِ%‬‬ ‫‪ْ ْ,ّ5ْ :ْ ْL!ِB Y!ِ%‬‬

‫‪ُ H‬و ِْ! ْ‪..‬‬ ‫& ِ‪ْ ْ J‬ه ْ‬ ‫‪َ %‬ا ْ‬ ‫‪ ُ %‬وْ َو ْ‬ ‫َه ذْ ُ ْ ِ()ْ‪ ْL!ِ5 ،‬أ ْ‪ْ !ِ0‬سْ وْ أ ُ ا* َ َ ءْ ا; ْ‪ْ ْ J‬‬

‫! رْ ْ ْ ْ ْ ِ ُ م ْ‬ ‫َو َ ْ ْ‬

‫‪ #ُ $َ %‬ا ‪.‬‬ ‫ا ِ ْ ِ َ دْ َ لْ أ ُ ا َ َ ءْ ا ُ زْ َ ِ َر ِ‬

‫' َ ْ ِ& َ ْ ّ ْ‪.‬‬ ‫) ِ(ْ دْ َ لْ ا ْ‬ ‫ط ْ ُ‪ْ $‬‬ ‫‪ #ُ $َ %‬ا َآ نْ ْ‪ْ ,ْ -‬زْ ْ‬ ‫أ ُ ا َ َ‪ 1‬ءْ َر ِ‬ ‫' ُ مْ ْ ُ ُ‬ ‫‪ّ :‬‬ ‫‪ $ُ 3‬ا ّ ْ َ ا ُ َ ِ َ ْ‬ ‫ل ْ َ‪ 4‬وْ ْ ْ ْ‬ ‫‪ ْ(ِ )ُ$‬دْ َ ُ مْ ُه َ أ‪ِ #ُ 6‬إ َ‬

‫َ رْ ِ‪َ ْ$ْ %ُ ْ8 1‬ه َ ﭬ َ! ُ رْسْ‪.‬‬

‫ت َ< عْ ْ‪َ ْ)%‬ر َ ْ(ْ ُ' ْ&ْ ْ‪6 $ْ 1‬ا ْآ‪.ْC‬‬ ‫> ْ ْ< ْ‪َ ُ ,‬‬ ‫)ْْ‬ ‫) ْ(ْ @? ْ‪ َ 1‬دْ ا ّْ‬ ‫‪ُ $ُ %‬ه َ َه ْذ ا ْ‬ ‫‪ َ ?@ ْ(B‬أ ُ ا َ َ‪ 1‬ءْ ا ْ ْ ْ‬ ‫ا ْ‬

‫‪َ ْ$َ %ُ B‬ه َ ِﭬ َ! ُ رْسْ‪.‬‬ ‫'َ‬ ‫' َ ْ ْ& ْ ُ‪ 1‬وْ ْ ْ ْ& ُ‪ $‬ا َ ْ' َ َ< عْ ِﭬ َ! ُ رْسْ ْ ُ‪ْ E‬‬ ‫‪ْ :‬‬ ‫‪ $ُ 3‬ا ّ ْ َ ‪ْ ،‬‬ ‫ل ْ ِ‪ْ ْ ْ َ 4‬‬ ‫ِإ َ‬ ‫? َه تْ ا ُ‪َ ْ ,ْ $‬ه َ ْ ِ* َ! ُ رْسْ ‪:‬‬ ‫‪ِ َ F‬ه َ‬ ‫' ِ? ْ ْ& َ‪ ُ ِ ْ ّْ Eْ ْ G‬مْ أ ْ‬ ‫‪ْ :‬‬ ‫ْ‬ ‫‪ J‬رْسْ َ< ْ ْ َاوْ َه ا ‪ <َ ْK -ِ L‬عْ ا‬ ‫َه دْ ا ِ& َ‪ <َ ,‬عْ ِﭬ َ ُ‬

‫‪. +َ '$َ, ْ(َ 3‬‬ ‫‪ J‬دِي ْ ْ‪َ ْ ّ E‬ه ْ‪ْ H‬‬ ‫إ ْ‪َG‬ادِي‪ ،‬أ َ ْه َ َ‬

‫‪ِ ، َ ْ ْ ْ َ :‬ه ْ ْ< ْ ْ‪ ْGْ ْ ْ8-ْ َ ْ E‬أ ُ ا َ َ‪ 1‬ء ا‬ ‫‪ ?ِ)-َ َ O‬ا ْ‬ ‫َه ذْ ا ّ‬

‫‪. $ُ %‬‬


‫ا )ا' ‪:‬‬ ‫َ< ْﯖ لْ إ ْ‪ْG ِQ‬سْ ْ‪ ُ َ 1‬ا‬

‫ب ا‪S‬ول‪ ،‬ا‪ QR‬اح ‪: 47‬‬ ‫‪" ْ8ْ َ :‬‬ ‫ن ُ‪ ْ-. $َ %‬ا َ َ‪َِ -ُ ْ$‬و ً ِ َ ْ ُ عْ ُ‪ ْ 0َ ّ $َ %‬ا ‪ ْ(ْ 0َ 123‬ا‪َ Z‬‬ ‫" ‪ ?ِ1‬ا ُ‪ X $‬ا َ ِ‪ ْ W‬ا ‪V6‬اِو َ َ ُ ُ‬

‫‪. ّ4‬‬ ‫‪ ّ%‬ا ُ‬ ‫‪ْ O‬‬ ‫وْ ْ َ‬ ‫' ا ْ ْ‪.ْ ِ E‬‬ ‫‪[ :‬‬ ‫‪ْ ْG%‬‬ ‫‪ B‬لْ ْ‪ ْ8-‬وَا ْ‬ ‫‪َF‬‬ ‫\ َ ْ ِ ‪َ ،ْ8‬و ِ‪ْ 8‬‬ ‫َآ نْ ْ ْ‪ َ ِ ْ8ْ $‬أّ َ ُ ﯕ ُ‪ْ E‬ه َ وْ ّ ُ‬ ‫‪. $ُ %‬‬ ‫‪ <َ َ O‬عْ أ ُ ا َ َ ا ْ ْ ْ‬ ‫? ِّ? ‪ َJ‬دِي ْ ْ @ر َ ِ ُ مْ‪َ ،‬و ِ‪ّ ْ 8‬‬ ‫‪ِ ّ 4‬ه َ‬ ‫^ا ُ‬ ‫َه ِد ّ‬ ‫‪: $ُ %‬‬ ‫َه َ شْ َ< ْ ْ‪َG,‬ا ا ْ‪ !َ 6‬بْ َ< عْ أ ُ ا َ َ‪ 1‬ا ْ ْ ْ‬

‫‪.ْ8 O‬‬ ‫‪ِ J‬‬ ‫‪ a‬جْ َ‬ ‫‪ُ ْ َa‬‬ ‫‪ ْ8 3‬وْ ا ‪ِ ْ Lْa‬‬ ‫ن ا ُ‪ِ Gِ ْ ْ $‬‬ ‫> وَا ْ َة‪ْ <َ ،‬ﯖ لْ أ ّ‬ ‫‪َ B‬‬ ‫‪ ْG%‬ا َ‬ ‫ْه َ َ< ْﯖ لْ أُ ا َ َ‪ 1‬ءْ وَا ْ‬ ‫ْ‪L‬شْ ؟‬ ‫! َ‪ $‬مْ وْلٌ ا ّ‪$َ3‬ي‪.‬‬ ‫‪ُ ْGْ ْ -َ َ a‬ه ْ‪ dَ -ْ ْC-‬ا ّ ْ‬ ‫‪ ، 0َ ْ 7‬وْ ا ‪ِ ْ Lْa‬‬ ‫لا ّ‬ ‫!‪ -َ ْG‬وْ ّ‬ ‫‪ُ ْGْ ْ -َ ْ8 3‬ه ْ‪ dَ -ْ ْC-‬ا ْ‬ ‫‪ #ُ ّS‬ا ُ‪ِ Gِ ْ ْ $‬‬ ‫‪ْ$:‬حْ ‪:‬‬ ‫‪ َ ?ِّ 7‬وْدْ َه وْ ْ‪َG‬ا ِ َ ا ّ‬ ‫ْ َ& وْدِْ ُ مْ دَا َ ا ِ‪ّ +‬‬

‫\‬ ‫َ< ْ َ& وْدْ ا ُ ا َ َ‪ 1‬ءْ ْ‪ َ 1‬دْ ا ْ َ بْ أّ ُ ْ ْ ْ ُ‬ ‫‪...‬آ َ< ْ ْ ْ ُو ْ‬

‫‪ َa‬و < ﯖ ل ‪:‬‬ ‫‪ 3‬وْا ‪ِ ْ Lْa‬‬ ‫> ِ َ‪ $‬عْ ِ ‪ َ ْ Eْ ْ8‬دْ َ لْ ا ْ ْ َ‪َ G‬‬ ‫‪ ْG%‬ا‪ْ R‬‬ ‫ِْ ْ‪َ #‬ا ْ‬

‫' وْ ُ ُ‪ْ ْ-ّ ْ$%‬آ ِ ‪ &َ ّْ $ُ <ْ <=< ْ8-ْ ْ$‬تْ ﯕ)ْ ﯕ)ْ ؟‬ ‫‪ J‬دِي ْ َ‬ ‫‪ِG 3‬ي ِآ َ‪ E‬شْ َ‬ ‫ا ُ‪ &َ ّْ $‬تْ‪ ،‬ﯕ ِ ^ْ أ ِ‬

‫\ َ ْ ِ ‪.ْ8‬‬ ‫!‪َ ْ$ْ ُ ْ -ُ ْG‬ه َ ِﭬ َ! ُ رْسْ وْ ُ ُ‬ ‫‪ J‬دِي ْ ْ‬ ‫‪ْ 3‬ه َ‪ْ -‬ه ‪َ ،‬‬ ‫ِإ َو ا ْ* ْ‪ َ )ْ @ْ ْ @َ +‬ﯕ ُ وَا‪َ ْf‬‬ ‫‪ 1ْ :‬وَاُ ‪ ،‬هُ َ‪ْ $‬ﯖ ُ ِ ُ مْ َه دِي َ‪ْ -‬ه ْ َة َ‪ -‬وَاُ ‪.‬‬ ‫‪َ B‬ا ْ ِ‪ْ Bْ %َ َ E‬‬ ‫ِإ َو ا ْ= ْ' ِ َ وْ ا ْ‬ ‫' وْ ُ ِ ُ مْ ‪ْ - $%‬آ ِ ‪. ْ$‬‬ ‫‪ Cَ D‬رْ وْ ْ َ‬ ‫‪ J‬دِي ْ ْ@‪ 0َ ّ ْ$%ُ ُ ْ$‬تْ ْ‬ ‫‪ُ َ a‬ه َ ِآ َ‪ E‬شْ َ‬ ‫) ِ( ْ ّ ْ َ‪ِ ْ Lْaِ ,‬‬ ‫‪ #ُ 6S‬ا ُ‪ْ $‬‬


‫ل ُ‪ G‬زْلْ‪.‬‬ ‫‪ 3‬ﯕ ُ ِ ُ مْ‪ ،‬ا ﯕ ُ ِ َ ِآ َ‪ E‬شْ َ< ّ‪ُ G‬و َ دْ ا ّوّا َ‪ B‬وْ ّ‬ ‫ِإ َو ا ْ‪َ Gْ ْ <ْ َ ْ E‬‬ ‫‪: ْJ6ْ :‬‬ ‫> ْ‪ ُ &ْ $‬مْ ْ َ@ دْ ا ْ‬ ‫‪ ُ 3‬مْ وْ ْ‪ْ ْG&ْ ْ ْ8-‬‬ ‫‪ a‬تْ ْ‪ 0َ ْ ْ$%‬تْ وْ ْه ّ ْ‬ ‫‪َ a‬‬ ‫‪ :‬دْ <=< ْ< ِّ‬ ‫‪ ، a‬وْ َ‬ ‫‪ ْ8-ْ ْ)H‬ا ‪ِ ْ Lْa‬‬ ‫َ ضْ وَا ْ‬

‫ْ ْ ْ ُ‪ُ 0‬ه مْ َه ّآ ‪<--‬‬

‫) ْ(ْ ‪:‬‬ ‫‪ ُ &ْ $ْ a‬مْ ْ َ دْ ا ْ‬ ‫‪ ّ%‬أ َ ْ ْ‬ ‫) فْ وَاشْ ْ ْ‪ْG‬رْ ْ‬ ‫‪ ّ%‬أ َ وْ ْ ُ‬ ‫‪ّ a‬بْ ْ‬ ‫إ َو ﯕ ْ‪ dَ -ْ ْi‬رَا‪ ?ِ3‬أ َر ْ ْ‬

‫‪ B‬لْ ا ‪: ?ِaْ Lْa‬‬ ‫> ْ‪ ُ ْ &ْ $‬مْ ْ َ‬ ‫وْ ْ‪ْ ْG&ْ ْ ْ8-‬‬

‫‪ j‬وْ ْ‪ْ ْ-ّ ْ$%ُ ْi‬آ ِ‪.ْ ,‬‬ ‫‪ ?ِ ْ B‬وَاشْ ِ ‪َ ْi‬‬ ‫'َ‬ ‫‪ْ ّْ X %‬‬ ‫‪ِ ،?ِaْ Lْa <َ L‬‬ ‫‪ ْkEْ ْ 1ْ ْl O‬ا ‪ْ 1َC‬‬ ‫َو َ ْ ِ‬


‫‪L‬؟‬ ‫‪ُ َ F‬ه َ َه دْ ا ‪ْ 1َC‬‬ ‫\ْ ْ ِ ُْ أ ْ‬ ‫أشْ ْ‬

‫‪M‬‬ ‫‪ j‬وْبْ َ‪ِ %‬‬ ‫ّ‪َ ?ِ d‬‬

‫‪ $ُ %‬أّ ُ‪ َ -َ ?ِّ (ِ )ُ$ #‬قْ ِ ْ‪ُ ?ِaْ Lْ> #‬ه َ أّ ُ‪$ُ #‬‬ ‫< ﯖ ل أ ُ ا َ َ‪ 1‬ء ا ْ ْ ْ‬

‫‪.-ّ ْ$%‬‬ ‫ُ‬

‫وَا‪ِ ْO‬آ َ* شْ ؟؟‬ ‫‪ j‬وْ ْ َ َ‪.dّْ -ُ ?ِF -‬‬ ‫) ْ( أِّ? َ‬ ‫‪L‬شْ َه د ا ْ‬

‫ْ ْ‪َG,‬اوْ ْ ْ& َ‪َ $ُ ْ Eْ ْ G‬ه دْ ِ& َ‪ َ ،dّْ $ُ <ْ ,‬د ‪ّ E‬‬ ‫ْ ْ)َاوْ ْ‪ ْ(%‬ا ‪ْ 1‬ل ‪:‬‬

‫‪ َ B‬بْ‪.‬‬ ‫‪ُ B‬وفْ ِ? َ< ْ ْ ْ ُ ِ ُ ْ ْ‬ ‫‪ َ B‬بْ‪ُ ْ8 $ِ &ْ $ُ َ $ُ &ْ ْ <َ ،‬‬ ‫‪َG,ْ ْ <َ X %‬اوْ ْ ْ ْ& ُ‪ْ $‬‬ ‫ِ‬ ‫إ َو َ< ْ ْ& ُ‪ 1 َ $‬وْ ‪ 2‬وْ ‪ 3‬وْز ‪ G‬وز ‪....G‬‬ ‫وْ ْ‪ْ <َ Gْ&ْ ْ8-‬ﯖ‬ ‫‪ َ 1‬دْ ‪2‬‬

‫‪: ْ$ 6ِ $ Cِ D‬‬ ‫‪ُ Eُ ْ 3‬ه ْ‪ْ ْ8-‬‬ ‫َِ ْ‬

‫َ دْ ‪ َ 3‬دْ ‪4‬‬

‫َ< ْ ْ‪ُ ْ8‬آ نْ ﯕ‬

‫َ دْ ‪ َ 5‬دْ ‪6‬‬

‫وْز ‪ G‬وز ‪....G‬‬

‫‪!! ْ8ْ %‬‬ ‫ِ َ ْ‪ُ ْ$ Pِ 6 ْJ 1ِ+ ْ8-‬آ نْ ْ‪ْ َ $ْ ْ 1‬‬

‫‪ُ B‬وفْ ْ ْ@ ْ َ) َ ؟‬ ‫!‪ َ ْ -ُ ْG‬دْ ُ‬ ‫‪ J‬دِي ْ ْ‬ ‫ُ‪ ، ِ $‬دَا َ ِآ َ* شْ َ‬ ‫‪ 3‬ا ُ َاِرز ِ‪ ُ َ ْ 1ْ %‬ـ ا‬ ‫َ< ْﯖ لْ ‪َ -ُ ْ8ْ Gّ$Bُ-‬‬

‫ب ا ‪ ' !$‬ـ ‪:‬‬

‫‪ O‬لْ دْ َ‬ ‫‪ْ$,‬فْ‪ ،‬ا ّ‬ ‫' وْبْ ْ‪ْ ْ8-‬‬ ‫ل ْ ِ‪َ -ْ ْ-. ْ$%ُ ,ُ ْ ْ ْ َ 4‬‬ ‫> ُه َ أ‪ #ُ 6‬إ َ‬ ‫‪َ %‬‬ ‫أ ‪6‬ولْ َ‬

‫‪ ْ)H‬ا ُ‪.ْdّْ $‬‬ ‫? وَا ْ‬ ‫‪ِ ?ِّ ،ْG%‬ه َ‬ ‫‪ّ$ْ 1ْ ْG%‬اتْ وَا ْ‬ ‫ْ ْ& ِ? وَا ْ‬

‫‪ُ ْ -ِ ْ)H‬و‪َ f ,ُ ْ <َ ،‬ه ّآ ‪:‬‬ ‫وَا ْ‬

‫‪12‬‬

‫‪ َ B‬بْ َه ‪6‬آ ‪:‬‬ ‫وْ َ< ْ ْ ْ ُ ْ‬ ‫‪12 = 1× 1‬‬ ‫‪12 = 1‬‬


‫ْ ْ& ِ? أّ ُ‪: #‬‬

‫‪ْ(ْ F‬‬ ‫َه دْ ْ‬ ‫وْ َه دْ ْ ْ َ‪,‬‬

‫‪.‬‬

‫‪12‬‬

‫‪ 4‬لْ‪.‬‬ ‫‪ 4‬لْ ْ َ‬ ‫َْ‬

‫‪.ْ :‬‬ ‫‪ْ oْG%‬‬ ‫‪ ْG%‬ا ِ‪ $‬لْ وَا ْ‬ ‫‪ُG:‬و وَا ْ‬ ‫َ ْ‬ ‫‪ O‬لْ دْ َ‬ ‫‪ْ p‬فْ‪ ،‬ا ّ‬ ‫' وْبْ ْ‪ْ ْ8-‬‬ ‫ل ْ ِ‪َ -ْ ْd6ْ -ُ ,ُْ ْ ْ َ 4‬‬ ‫إَ‬

‫? رْ ْ َ‪ &َ ّْ $ُ < 0‬ت‪.‬‬ ‫> جْ‪ِ ?ِّ ،‬ه َ‬ ‫> جْ ْ‪ّ$ْ 1‬اتْ ُ‬ ‫ْ ْ& ِ? ُ‬

‫ُ جْ ِ‪ُ ْ -‬و‪َ f ,ُ ْ <َ ،‬ه ّآ ‪:‬‬

‫‪22‬‬

‫‪ َ B‬بْ َه ‪6‬آ ‪:‬‬ ‫وْ َ< ْ ْ ْ ُ ْ‬

‫ْ ْ& ِ? أّ ُ‪: #‬‬

‫‪.ْ :‬‬ ‫‪ْ oْG%‬‬ ‫‪ ْG%‬ا ِ‪ $‬لْ وَا ْ‬ ‫‪ُG:‬و وَا ْ‬ ‫َ ْ‬ ‫‪ O‬لْ دْ َ‬ ‫‪ْ p‬فْ‪ ،‬ا ّ‬ ‫' وْبْ ْ‪ْ ْ8-‬‬ ‫ل ْ ِ‪َ -ْ ْd6ْ -ُ ,ُْ ْ ْ َ 4‬‬ ‫إَ‬

‫‪ 0ُ S‬دْ < ُ‪ &َ ّْ $‬ت‪.‬‬ ‫?ْ ْ‬ ‫ْ ْ& ِ? ‪ّ$ْ 1ْ qَ Lq‬اتْ ‪ِ ?ِّ ، qLq‬ه َ‬

‫ُ جْ ِ‪ُ ْ -‬و‪َ f ,ُ ْ <َ ،‬ه ّآ ‪:‬‬

‫‪32‬‬


‫‪ َ B‬بْ َه ‪6‬آ ‪:‬‬ ‫وْ َ< ْ ْ ْ ُ ْ‬

‫ْ ْ& ِ? أّ ُ‪: #‬‬

‫ل ّ< ْ‪ْ َ ْ E‬‬ ‫إَ‬ ‫<ﯖ ل‪1‬‬

‫‪. $ُ %‬‬ ‫) ِ(ْ دْ َ لْ أ ُ ا َ َ‪ 1‬ء ا ْ ْ ْ ْ‬ ‫‪ J‬دِي ْ ْ‪ َ Vْ -ْ $ُ ْ E‬نْ ُ‪ْ $‬‬ ‫َه دْ ْ ْ َة‪َ ،‬‬ ‫ب‪:‬‬

‫‪ &َ ّْ $ُ < S‬ت‪.‬‬ ‫‪َ ْU‬‬ ‫‪ B‬لْ ِآ ‪ ْr‬دَارْ ْ ُ جْ ُ‪ &َ ّ -‬تْ وْ ْ‬ ‫‪ ْTS‬دُوكْ ا ُ‪ &َ ّْ $‬تْ ْ َ‬ ‫‪ ، $ُ %‬ا ‪ْ +ْ 'ْ 4َ ْ ?ِaْ Lْa‬‬ ‫ِآ ‪ r‬ﯕ ْل ا ُ ا َ‪ 1‬ء ا ْ ْ ْ‬ ‫‪ p‬حْ ْ‬ ‫ْ‪َG,‬اوْ ‪V‬وّل ‪َ (ِ )ُ-‬‬

‫‪: َa‬‬ ‫ا ‪ِ ْ Lْa‬‬

‫‪ B‬لْ َه ّآ ‪:‬‬ ‫‪َ ْ ْJ W‬‬ ‫‪ِ !َ S‬‬ ‫' وْ ُ ُ‪ْ %‬‬ ‫‪ J‬دِي ْ َ‬ ‫> ْ‪ُ َ &ْ $‬ه ْ‪َ ،‬‬ ‫‪ a‬تْ ْ‪ 0َ ْ ْ$%‬تْ‪ ،‬وْ ْ‬ ‫‪َ a‬‬ ‫‪ ُ َ Gِ :‬جْ ْ< ْ‬ ‫إِل ْ‬


‫‪$ُ <ْ H‬‬ ‫‪َ S‬‬ ‫‪َ ِ ْi,ْ ْ %‬‬ ‫َه ِآ َ‪ E‬شْ ْ‬

‫‪: ْ( O‬‬ ‫َْ ِ‬

‫)‪12 + 12 = (1× 1) + (1× 1‬‬ ‫‪12 + 12 = 1 + 1‬‬ ‫‪12 + 12 = 2‬‬ ‫‪.ْJ W‬‬ ‫‪ِ !َ S‬‬ ‫> جْ ُ‪ &َ ّْ -‬ت‪ْ %ُ ?ِ)-َ ،‬‬ ‫' و ُ ‪ُ ْ8-ْ -ّ $ُ%‬‬ ‫'َ ْ َ‬ ‫‪ْ :‬‬ ‫ا ‪ (ِ )ُ$‬دَا َ ُه َ أّ ُ‪ْ #‬‬ ‫‪: $ُ %‬‬ ‫َ< ْﯖ ل أ ُ ا َ َ‪ 1‬ء ا ْ ْ ْ‬ ‫( ُ‪ْdّْ -‬‬ ‫‪ ْ8ْ &َ ّْ -ُ ْ8-ْ -ّّ ْ$%ُ &ُ $ْ a‬ﯕ) ﯕ)‪ُ $ُ ْ Qْ ،‬آ ّ‬ ‫ل ْ ِ‪ْ <ْ ُ 4‬‬ ‫إَ‬

‫‪ J‬دِي ْ ّْ? ْ ْ‪ُ ْG‬آ رْ ْ َ‪ P1Pُ 1ْ 0‬ث‪.‬‬ ‫> ْ ا ُ‪َ ،$ْW+‬‬ ‫> جْ ْ‪ِ ْ8-‬‬ ‫ُ‬

‫‪ W‬رْ دْ َ لْ ُ‪ &َ ّْ $‬تْ ا ِْ ‪ُ ْ8‬ه َ‪ َ ّ $‬بْ ْ< ُ‪,ُ ْ ْ <َ ?ِ ْdّْ $‬‬ ‫) ْ(ْ ّ? ْ ّْ? ِ‪ #ْ 1‬ا‪َ Bْ Y‬‬ ‫‪ ْG%‬ا ْ‬ ‫‪ &ُ $ْ a‬ا ُ‪ $‬ث ْ َا ْ‬ ‫َ< ْ ْ‬

‫‪َ ْ$ْ %ُ B‬ه َ ِﭬ َ! ُ رْسْ ‪:‬‬ ‫'َ‬ ‫‪ J‬دِي ْ< َ‪ ,‬نْ ِ ُ ْ ا َ ْ' َ ْ ِﭭ َ! ُ رْسْ ْ ُ‪ْ E‬‬ ‫‪َ ،ْ(B‬‬ ‫ْ‪َ ْ8-‬ه دْ ا ْ‬

‫ِْ ْ‪: #‬‬


‫‪َ ْ$َ %ُ B‬ه َ ِﭬ ! ُ رْسْ ‪:‬‬ ‫'َ‬ ‫[ ُ دْ‪َ َ ْGْ ْ ،‬ه دْ ا &َ‪َ ْ $@ ْ ْ <َ ?ِّ Qَ L‬ه ْ ُ‪ْ E‬‬ ‫ْ ْ& ِ? ْ ‪ْ \1P‬‬

‫‪2‬‬

‫)‪( 2‬‬

‫= ‪1 +1‬‬ ‫‪2‬‬

‫‪2‬‬

‫‪ J‬دِي ْ ْ ْ ُ‪: ,‬‬ ‫‪ B‬لْ ﯕ ِ‪َ ، َ ,‬‬ ‫> َ ْ ْ ْ ُ‪َ ,‬ه دْ‪َ ْ ْ ْ ?ِF‬ة ْ َ‬ ‫ل ِ‬ ‫إَ‬ ‫‪2‬‬

‫)‪( 2‬‬

‫? ُ جْ < ُ‪$‬‬ ‫> جْ‪ِ ?ِّ ،‬ه َ‬ ‫‪ْ p‬فْ ا ُ‪ُ ْdّْ $‬‬ ‫> جْ ْ‪ّ$ْ 1‬اتْ ْ‬ ‫‪ْ$,‬فْ ا ُ‪ُ d6ْ $‬‬ ‫َ< ْ ْ& ِ? ْ‬

‫ْ ّ َ& ت‪.‬‬

‫> تْ آِ? ‪!! +ْ ِ ْ$ْ ْ ?ِF‬‬ ‫‪َ َ ِ B‬ه دْ ا ْ ْ َة َ‬ ‫ْ‪َ 1‬‬ ‫‪ W‬قْ ِ َ@ ‪.‬‬ ‫دَا ْآ)@? ْ‪L‬شْ َآ ُ ْ‪َ ْ $@ ْ ْ <َ ْ8 $ِ ْ $‬ه دْ ا [ عْ ْ< ‪َGْ S‬ادْ‪ ،‬ا‪َGْ S‬ادْ ا َ‪ُ ْ %َ ْ$ْ C‬‬ ‫‪!! ْuO‬‬ ‫‪ َ 7‬ءْ‪ ?ِ &ْ ْ ،‬ا ‪ُ '2‬و َ ‪ْ ْ ّْ -َ َ 1ِ -َ #ُ ّS .‬‬ ‫ْ ْ&‪ ْv‬ا ْ‪ّ $‬اتْ َ< ْ ْ @‪ُ ْ $‬ه ْ ا‪َGْ S‬ادْ ا ‪.‬‬ ‫ل ا ‪َ ?ِّ ْK -ِ L‬آ ْ ْ ْ& ْ ُ‪َ $‬ه دْ ا‪َGْ S‬ادْ‪.‬‬ ‫‪ َ ِ [ B‬ا ‪ 6‬سْ وْ ‪6‬‬ ‫' ُ& َ ِّ? َ< ْ ْ‬ ‫‪ّ ْ [B‬‬ ‫'َ ْ ْ‬ ‫‪ْ :‬‬ ‫ْه َ ْ‬ ‫\ ‪.ْ8‬‬ ‫‪َ p‬ه دْ ا‪َGْ S‬ادْ ْ‪6V,‬افْ َ< َ ِ‬ ‫) ُ‪ !ّ ْ 1‬ر'^‪ 4ْ -َ ،‬وشْ ْ ْ ْ ْ ُ‬ ‫> ُ ْ< ُ‬ ‫( ِ‬ ‫و َ‬ ‫> ُ& دَا َ ُ‪ $ُ ْ X $‬دْ ْ ْ& ِ? َ‪ ْ Wِ Q‬ا ‪6V‬او َ ‪:‬‬ ‫ْْْ‬ ‫[ ُ دْ ْ ْ‪: َ ْG‬‬ ‫> َ ْ ْ& ْ‪ $ُ $‬ا &َ‪< Qَ L‬ﯖ‪ْGْ ْ ، ,‬رُو ْﯖ ُ أّ ُ‪Vْ #‬يْ ‪ْ \1Pُ%‬‬ ‫ل ِ‬ ‫ِإ َ‬

‫‪2‬‬

‫ا ِ& َ‪,‬‬

‫‪a +b = c‬‬ ‫‪2‬‬

‫‪َ $ُ %‬ه دْ ا &َ‪Qَ L‬‬ ‫‪ J‬دِي ْ ْ‪ ّ E‬أ ُ ا َ َ ءْ ا ْ ْ ْ‬ ‫? ِآ َ‪ E‬شْ َ‬ ‫[‪َ$‬ة ِه َ‬ ‫َا ْ‬

‫‪2‬‬

‫ْ= ْ' ِ َ ‪.‬‬


‫) ُ‪ 1‬أ‪ +َ '$ّ, &ْ ْ ْ <َ #6‬ا ّ! ْ* ِ‪ ْ$ 6‬دْ َ' ُ@‪ َ ْT‬شْ ْ ْ&ّ ْ‪ ْ ُ $‬ا ِ* ْ‪َ$6‬ة دْ َ' ‪.‬‬ ‫‪ J‬دِي ْ< ُ‬ ‫وْ ْه َ َ‬ ‫‪ B‬ا ِ )َا ُ ِ َ ‪.‬‬ ‫'َ‬ ‫‪ Pِ% ْ(S‬لْ ْ ْ! ْ‪ْ Eُ ْ ،ْT 1ِ0‬‬ ‫‪َ H‬‬ ‫? ُه َ أ ْ‬ ‫وْهَ‪K‬ا ْ ّ ْ َ‪َ ِ ,‬‬ ‫‪َ$W‬ازْ ا ّ‪.ْ- ِ $‬‬ ‫‪ ْ(%ْ ْT1ْ0%ُ $ُ %‬ا ّ‬ ‫ن أ ُ ا َ َ‪ 1‬ء ا ْ ْ ْ‬ ‫وْه َ ْ ْ‪ْG‬رُو ْﯖ ُ أ ‪6‬‬ ‫‪ 0َ ّ ْ$ُ 1ْ S‬ت ‪:‬‬ ‫) ِ( ْ ْ ْ َ‬ ‫‪ْ $ُ 1ْ $ُ %‬‬ ‫) ُ‪ 1‬آِ? دَارْ أ ُ ا َ َ‪ 1‬ءْ ا ْ ْ ْ‬ ‫‪ J‬دِي ْ ُ‬ ‫دَا َ َ‬

‫‪ْ$W‬فْ ْ< ُ‪ ْ ,ِ ْ dّ $‬؟‬ ‫‪ O‬لْ َ< عْ ا ّ‬ ‫‪ B‬لْ ا ّ‬ ‫‪َF‬‬ ‫دَا َ ا ّ‪َw‬ال ُه َ ْ‬ ‫ْ‬

‫ل ُ‪َ ْ$ْ %‬ه َ ِﭬ َ! ُ رْسْ ‪:‬‬ ‫‪ َ %‬بْ ا َ ْ' َ ْ ِﭭ َ! ُ رْسْ وْ ‪6‬‬ ‫ْ‬

‫)‪22 + 12 = ( 2 × 2 ) + (1× 1‬‬ ‫‪22 + 12 = 4 + 1‬‬ ‫‪22 + 12 = 5‬‬ ‫‪2‬‬

‫==<‬

‫)‪( 5‬‬

‫= ‪22 + 12‬‬

‫‪ J‬دِي ْ ْ‪ $ُ ْ E‬أّ ُ‪ #‬ا ‪َ َ 0ِ 1‬آ ْ َ ْ ُ‪ \1P‬ا ْ‪ ُ 0‬دْ‪.‬‬ ‫‪ 1ُ ْ ْ -َ َ a‬شْ [َ= َ‪ِ B‬ﭬ َ! ُ رْسْ‪َ ،‬‬ ‫‪ِ ْ Lْ> :‬‬ ‫‪ J‬دِي ْ َ‪ ,‬نْ ِ ُ ْ أ‪ #ُ 6‬وَا ‪6‬‬ ‫وْ ْه َ َ‬


‫) ِ( دْ َ لْ <=< ْ‪ 0َ ّ ْ$ُ 1‬تْ‪.‬‬ ‫‪ُGْ ْX %‬وزُو ُ‪ْ $‬‬ ‫‪ J‬دِي ْ< َ‪ ,‬نْ ِ ُ ْ َه دْ ا ِ& َ‪ِ ,‬‬ ‫َ‬ ‫) ِ( دْ َ لْ <=< ْ‪ 0َ ّ ْ$ُ 1‬تْ‪.‬‬ ‫‪ْ $ُ 1ْ $ُ %‬‬ ‫) ُ‪ 1‬آِ? دَارْ أ ُ ا َ َ‪ 1‬ءْ ا ْ ْ ْ‬ ‫‪ J‬دِي ْ ُ‬ ‫دَا َ َ‬ ‫) ِ( ‪:‬‬ ‫‪ ْ(B‬ا ُ‪ْ $‬‬ ‫ْ‪ّ 1‬ل َ< ْ َ& وْدْ آِ? دَارْ ا ‪ َ ?ِaْ Lْa‬شْ ْ ْ‬

‫‪: ْJ6ْ :‬‬ ‫‪ @َ ْ $ُ ْ Qْ ْ8 :‬دْ ا ْ‬ ‫‪َG%‬ا ْ‬ ‫‪ َ a‬وْ ْ‬ ‫وْ>ْ‪ِ ْ L‬‬


‫) ِ(ْ ‪:‬‬ ‫‪ْ $ُ ْ(B‬‬ ‫‪ َ $ُ %‬شْ ْ ْ‬ ‫‪ J‬دِي ْ @ر ُ ْ ِآ ‪ ْr‬دَارْ أ ُ ا َ َءْ ا ْ ْ ْ‬ ‫دَا َ َ‬

‫ل !!‬ ‫ل َ‬ ‫‪ -َ ُ ْ 6%‬وْ ‪6‬‬ ‫‪ ،ْ ُ -ْ 1َ ْ8 %‬وْ ْ‬ ‫‪ َ ْ ، S‬وْ ِه ْ َ‬ ‫‪َ 1ُ F‬ه دْ ا ّ! ْ@‪َ 'َ$‬‬ ‫‪َ ْX %‬‬ ‫‪ِ َa‬‬ ‫َ< ْ ْ‪ ْ8‬أّ ُ‪ #‬ا ‪ِ ْ Lْa‬‬ ‫!‪ ِ Bَ =َ0ْ -ُ ْG‬ﭬ َ! ُ رْسْ‪.‬‬ ‫‪ْ O‬فْ ْ< ُ‪ْ ْ <َ ، ,ِ ْ d6ْ $‬‬ ‫‪ َ ، 3‬شْ ْ ْ& ْ ُ‪ 1‬ا ّ‬ ‫‪ ّ ,َ ْ ّ ْ ، َ ِ B‬سْ [‪َ Gَ ْ ْ ْ ْ8 Eِ $‬‬ ‫ْ‪َ 1‬‬ ‫وْ َه ِآ َ‪ E‬شْ َ< ْ ِ‪ُ G‬و ‪:‬‬


‫‪.ْ` ِ 'ْ =ْ َ 6%‬‬ ‫‪ْ ْ &ْ <ْ #ُ ّS ،ْ8 3‬‬ ‫‪ 1َ $ُ %‬تْ ا ُ‪ِ Gِ ْ ْ $‬‬ ‫َو ِ‪ ْ8‬أ ُ ا َ َ‪ 1‬ء ا ْ ْ ْ‬ ‫‪!! ْT 6ِ 4‬‬ ‫‪ ْ^ْ :‬ا َ‬ ‫‪ ُ ْ $ِ 3‬ا ‪.‬‬ ‫وْدَا ْآ)ِ? ْ‪L‬شْ َآ ْ‪ْ ْi‬‬ ‫) ُ‪ 1‬ا ّ ْ‬ ‫دَا َ أ َر ْ ُ‬ ‫وا ّ ْ‬

‫?اّْ‬ ‫> ْ‪ ْi‬ا َ& ‪ِ ?@ ،‬ه َ‬ ‫َ @? َ‬

‫‪ 0ُ S‬دْ ْ< ُ‪ &َ ّْ $‬تْ ‪:‬‬ ‫َ َ< ْ‪ْ ْ ْi‬‬

‫?اّْ‬ ‫‪ J‬رْسْ ْ ُ‪ \1P‬ا ْ‪ ُ 0‬دْ‪ِ ،‬ه َ‬ ‫َ ِّ? آ ْ ِ‪َ ْ ,ْ -ُ ْ8ّْ,‬ه َ ِﭬ َ ُ‬

‫‪ 0ُ S‬دْ ْ< ُ‪ &َ ّْ $‬تْ‪.‬‬ ‫َ َ< ْ‪ْ ْ ْi‬‬

‫‪: َa‬‬ ‫‪ِ ْ Lْa ُ H‬‬ ‫‪ َ $ْ ْ ?ِّ S‬أ ُ ا َ َ ءْ ا‪ْ ْ$'ْ a‬‬ ‫َه ِه َ ا ّ!@ْ‪َ '$‬‬ ‫‪ j‬وْ ْ ْ ُ ْ ْ َ‪.ْ( ِ 0‬‬ ‫‪ J‬دِي ُ ر ُ ْ‪َ ،‬‬ ‫) َ لْ ِ? َ‬ ‫ا ْ‬ ‫ﯕ ِ ُ ْ وَاشْ ْ ْ ُ‬

‫ْ‬

‫‪ 4‬لْ ا ْ‪.ْ8 @ِ x‬‬ ‫‪َ ْ ْ8 3‬‬ ‫‪ ، S‬إ َو ِز ‪ُG‬و ِْ َ رْ ْ َ‪ &َ ّْ $ُ <ْ 0‬تْ ْ‪ِ ْ ْ -‬‬ ‫‪َ ْU‬‬ ‫‪ َ S‬عْ ْ‬ ‫ا ّ!@ْ‪َ '$‬‬

‫‪ 7‬وْ ُ ِ ُ@‪ْT‬‬ ‫َ دِي ْ َ‬ ‫‪: ْ8 :‬‬ ‫‪ْ oَG%‬‬ ‫‪ J‬دِي ْ‪ُG V‬و ِْ ُ رْ ْ َ‪ &َ ّْ $ُ < 0‬ت وْ ْ‬ ‫َ دْ َ‬

‫‪ 7‬وْ ُ ِ ُ@‪: ْT‬‬ ‫َ دِي ْ َ‬


‫> أ‪ َ ْ <َ #ُ 6‬وْ‪ ْf‬فْ ‪:‬‬ ‫‪ ْG%‬ا ‪6G‬ر َ‬ ‫‪َ B‬ا ْ ِ‪ ْ &َ <ْ َ E‬ا‪َ ،?ِ-Lْ3R‬ا ْ‬ ‫‪ َ a‬وْا ْ‬ ‫[ ْ‪ ْb‬ا ‪ِ ْ Lْa‬‬ ‫) ْ(ْ ْ‬ ‫َه دْ ا ْ‬

‫ا‬

‫'‬ ‫ْ‪ْ $‬‬

‫‪ @َ *َ D‬نْ ْ‪َ zِ1‬انْ‬ ‫‪ْ eِْ &َ $ُ a‬‬ ‫ْ< ُ‬

‫‪َ ْ َ 1ْ dِ1 َ 8‬وَانْ‬ ‫[ ْ‪ُ ْ َ +‬‬ ‫ْ‪ِ) ِ Gِaْ -‬ي ُ‬ ‫‪َ$3‬ة‪.‬‬ ‫‪ ْG%‬ا ْ@ ْ‬ ‫‪ َ ِ j‬وَا ْ‬ ‫‪َ$4‬ا ْ' ِ* َ ْ َ‪ 4‬وْ ْ ْ ْ‬ ‫) ْ(ْ ِّ? َ< ْ َ وْ‪ َ 1ْ ْf‬دْ ‪ ْ8ّ,ْ ْ <َ ْ{ْ Lْ,‬أّ ُ‪ #‬ا ْ‬ ‫‪َ َ ِ B‬ه دْ ا ْ‬ ‫ْ‪َ 1‬‬ ‫‪ْ ْ ,ْ ْ ّ%‬ه ُ َه ‪.‬‬ ‫‪ J‬رْسْ‪ ،‬وْ ْ ْ ُ‪ْ 1‬‬ ‫ُه َ أّ ُ ْ ْ ْ@ ُ ُ‪َ ,ْ -‬ه َ ِﭬ َ ُ‬ ‫\ َ تْ‪.‬‬ ‫) ْ(ْ ُه َ أّ ُ‪ ُ َ $ْ &ْ ْ <َ #‬جْ ْ< ِ& َ‪ ,‬تْ ُ‪6Vْ ْ8 $@ ِ -‬افْ ْ‪ِ َ ْ 1‬‬ ‫> ا َا ْ ة ﯕ عْ ْ‪ َ 1‬دْ ا ْ‬ ‫‪َ B‬‬ ‫وْا َ‬ ‫‪َG%‬ة‪.‬‬ ‫‪ +َ ِ W‬تْ ا َ@ ‪ Q6 ْG1ْ %.‬وْ ْ‬ ‫) ْ( َ< ْ ْ @ر َ ُ‪َ ْ$ْ %‬ه َ ِﭬ َ! ُ رْسْ وْ ا ُ َ! َ‬ ‫َه دْ ا ْ‬ ‫‪ +َ ِ W‬تْ ا َ@ ‪%.‬‬ ‫‪ِ َ F‬ه َ َه دْ ا ُ َ! َ‬ ‫أْ‬

‫َ ْ َ< ِ? ؟‬

‫) ُ‪: 1‬‬ ‫‪ J‬دِي ْ< ُ‬ ‫دْرُو َآ َ‬ ‫ي <&‪,‬ت‬ ‫‪َ F‬‬ ‫' ِ? ْ‪ِْ ْ ّ E‬‬ ‫‪ْ :‬‬ ‫ْ‬

‫‪ S‬بْ و ا @ ْ ِ َ تْ ْ َ ْ‪ ْ$‬وَا ُ‪. 1َ +‬‬ ‫‪َ 4‬‬ ‫ْ‬

‫‪ْc:‬‬ ‫‪ْ %َ )ِ ْ ْ y‬‬ ‫' ْ ا ْ& ْ‬ ‫ْ‪ْ Q‬‬


‫‪ 3‬ا ُ َاِرز ِ‪ ُ َ ْ 1ْ %‬ـ ا‬ ‫َ< ْﯖ لْ ‪َ -ُ ْ8ْ Gّ$Bُ-‬‬

‫ب ا ‪ ' !$‬ـ ‪:‬‬

‫‪ B‬لْ ِ‪ 1 6‬؟‬ ‫)َ‬ ‫! ّ ر‪ْ ْ ْ ْ ْ <َ ،‬‬ ‫) ْ‪ ْGْ ْ ْ8-‬ا ْ‬ ‫‪َ O‬‬ ‫) ي َ‪ِ -‬‬ ‫) ِ? ْ< ْ‬ ‫ل ْ‪ِ -‬‬ ‫ْ ْ& ِ? َ‪ِ L -‬إ َ‬ ‫َ< ْﯖ لْ ِ ^ْ ‪ 260‬رْ َ' لْ‪ْ <َ ،‬ﯖ لْ ِ ْ‪ #‬وَا‪!! َ َ ْf‬‬ ‫‪ ُ ْG%‬جْ ِآ ‪. 1‬‬ ‫‪ْ <َ َ J‬ﯖ لْ ِ ْ‪ِ #‬إ َو ِد ْ وَا ْ‬ ‫‪َ ْ^ a‬‬ ‫‪ِ ْ <َ :‬‬ ‫وَا ‪6‬‬ ‫‪ 4‬لْ ؟‬ ‫‪َM‬‬ ‫[ وْ َ ِ ْ‬ ‫> جْ ِآ ‪َ ْ ْ ْ <َ ،‬‬ ‫‪ُ ْ^ ِ ْ ,ْ &ْ ْ <َ X %‬‬ ‫ِ‬ ‫‪ #ُ 6S‬آ ْ ْ& ْفْ ‪َGْ S <ْ qLq‬ادْ ِّ? ُه َ‪ِ 1 $‬آ‬

‫وْ ‪ 260‬رْ َ لْ وْ ‪ِ 2‬آ ‪ ،‬وْ آ ْ ْ ّلْ ْ‬

‫ا ‪6‬ا ْ‪ُ ?@ ْd‬ه َ ا ْ ْ ُ@ لْ‪.‬‬

‫! ‪ 6‬رْ !!‬ ‫‪ p‬ا ْ‬ ‫‪ J‬دِي ْ َ وْ ا ْ ْ ُ@ لْ وْ َ‪ْ ,ْ ْ ْC Qِ َ -‬زْ ُ‬ ‫‪ِ $ُ %‬آ َ‪ E‬شْ َ‬ ‫وْ ْه َ َ ْ ْ& ْ‪ َ $‬ا ُ َارزْ ِ‪ %‬ا ْ ْ ْ‬

‫‪ J‬دِي ْ ْ‪َ ْ ّ E‬ه دْ ْ ْ َة ْ ّ‪: ْu Qِ ْG‬‬ ‫دَا َ َ‬ ‫ل ‪.le produit en croix‬‬ ‫‪َ ْ $@ ْ ْ <َ $ُ %‬ه ْ‪ 4ْ $ْ 1‬بْ ‪ la régle de trois‬وْ ‪6‬‬ ‫! َرَاز‪ ?ِ-‬ا ْ ْ ْ‬ ‫َه دْ ا ِ& َ‪َ ْ ّ Eْ ْ <َ ?ِّ ,‬ه ِ َ ا ُ‬ ‫‪@ُ S‬‬ ‫‪ ْ8-ْ ْi,ْ a‬ا ‪f‬‬ ‫‪ّ &ْ <ْ $ُ %‬‬ ‫! َرازْ‪ ?ِ-‬ا ْ ْ ْ‬ ‫أ َ ْآ ْ‪ ْi‬دَا ْ ً‪ ، َ 1ِ ْr ْ ْ <َ $‬وْ ْ‪ ْi Qْ ?@-‬ا ِ& َ‪ُ <ْ ,‬‬ ‫!‪ $ِ ْ -ُ ْG‬لْ َ< عْ ﯕ ِ‪,‬‬ ‫ْْ‬

‫‪: $ُ %‬‬ ‫! َارزْ‪ ?ِ-‬ا ْ ْ ْ‬ ‫‪ُ <ْ َ O‬‬ ‫َ شْ ْ ْ‪ ّ E‬ا ّ‬

‫> جْ ْ< ‪َGْ S‬ادْ ‪. Bَ =َ[g‬‬ ‫‪ u‬أ‪ #ُ 6‬دَا ْ ً‪ُ َ ْGْ ْ $‬‬ ‫‪ J‬دِي ْ< َ‬ ‫‪ُG1ْ ?ِ ْ ّ %‬وكْ ا‪َGْ S‬ادْ ا ‪َ qL‬‬ ‫ل ْ‬ ‫َ< ْﯖ لْ أّ َ‪ #‬إ َ‬ ‫‪. 1ِD ?ِF 6%‬‬ ‫> جْ ْ< ‪َGْ S‬ادْ َ‪ْ ُ <ْ َ ِ -‬‬ ‫&? ُ‬ ‫? ُ‪.(ِh َ %‬‬ ‫‪ِ ?@ B‬ه َ‬ ‫'َ‬ ‫‪ ْG%‬ا ْ َ‪ $‬زْو َ ‪ َ َ &َ 1‬ا ُ‪ْ E‬‬ ‫‪ (ْ$&ْ ْ 3‬وَا ْ‬ ‫‪ $ُ %‬ا ْ‬ ‫! َارز‪ ?ِ-‬ا ْ ْ ْ‬ ‫نا ُ‬ ‫‪6S‬‬

‫دْ َ َ ‪.‬‬


‫ن ا َ< َ&‬ ‫‪ ْj*ْ ْ ْ(%ْ :‬ا ِ ْ‪ ،ْj‬وَ< ْﯖ ُ ﯕ عْ ا ّ ‪ ْr‬أ ّ‬ ‫َ‪ُ ٌ(hِ َ َ &ْ -‬ه َ أّ ُ‪ِ %َ #‬‬

‫َ ‪.kِ+1َU ْ(%ِ (ِh‬‬

‫ل ِْ? ‪ Bَ =َ[g‬؟‬ ‫‪ُ َ ُ F‬ه َ‪ $‬ا‪َGْ S‬ادْ ْ ْ! َ ْ' ِ (ْ وْ ‪6‬‬ ‫? ْ‬ ‫! ْ َة‪ ،‬ﯕ ُ ِ َ‬ ‫> ُ& ُ‪ $‬لْ ْ‬ ‫> َ دَا َ ْ ْ ْ‬ ‫إل ِ‬ ‫‪ J‬دِي ْ< َ وْ ‪ 260‬رْ َ لْ وْ ‪ِ 2‬آ ُ ‪ 260 ْ8 ِ ?ِّ #ُ ّS ،‬رْ َ لْ وْ ‪ِ 1‬آ‬ ‫َ‬

‫)‪.‬‬ ‫‪َ O‬‬ ‫? َ‪ِ -‬‬ ‫ِه َ‬

‫‪ B‬لْ‪.‬‬ ‫‪B‬ل ْ َ‬ ‫) َْ‬ ‫‪َ p‬‬ ‫‪ J‬دِي ْﯖ لْ ِ ُ أ‪ 260 #ُ 6‬رْ َ لْ وْ ‪ِ 1‬آ ُ ْ< َ‪ِ $‬‬ ‫! ّ رْ َ‬ ‫‪ ُّ3‬ا ْ‬ ‫( ﯕ عْ ْ‬ ‫و َ‬ ‫‪6%‬‬ ‫( ْ‪ْ ?ّ1‬‬ ‫و َ‬

‫‪: ْ(B‬‬ ‫) ِ( ْ< ْ‬ ‫ْ ْ ِ? ْ ‪َGْ S‬ادْ ا ْ ْ! َ ْ' ِ (ْ‪ْ $ُ ،‬‬

‫‪ْ ْTS‬‬ ‫‪ْ$3‬بْ ا ْ ْ! َ ْ' ِ (ْ ْ ْ& ِ‪ ْ ُ <ْ 6‬وْ ْ ْ‪ْ +‬‬ ‫'^ْ ْ ْ‬ ‫‪ّ :‬‬ ‫‪ $ُ %‬أ‪ْ #ُ 6‬‬ ‫! َارزْ‪ ?ِ-‬ا ْ ْ ْ‬ ‫وْ ْه َ َ< ْﯖ لْ ِ َ ا ُ‬

‫ا ‪.\ P‬‬

‫‪260 × 2‬‬ ‫‪= 520‬‬ ‫‪1‬‬

‫‪ J‬دِي <ْﯖ ُ وَا‪َ ْf‬ه دْ‪ُ ?@F‬آ [‬ ‫َ‬

‫ْ‬

‫) ‪ ،‬رَا‪ ْ8-ْ َ ْ َ ْf‬ا ّْلْ !!‬ ‫‪َ O‬‬ ‫‪ B‬لْ ُ جْ ِآ ‪ِ $َ <ْ 1‬‬ ‫)َ‬ ‫‪ْ ْ ,ُ ْ B‬‬ ‫ْ‪ َ ْ(,ْ Q‬شْ ْ ْ‬

‫‪ َ $ُ %‬شْ ْ َ‪ ,‬نْ ِ ُ ْ ا ْ& ْ ُ نْ ‪:‬‬ ‫! ارز‪ ?-‬ا ْ ْ ْ‬ ‫‪ ْG%‬ا ِ‪ $‬لْ َ< عْ ا ُ‬ ‫‪ J‬دِي <ْ) ُ‪ 1‬وَا ْ‬ ‫دَا َ َ‬

‫‪ 6 ْi3‬مْ‪.‬‬ ‫‪ْG:‬مْ ِه ْ ْ‬ ‫ل ْ‬ ‫' ِإ َ‬ ‫! ُ‬ ‫‪ B‬لْ ْ< ْ‬ ‫‪َF‬‬ ‫) ْ ْ‪ْ ،‬‬ ‫) َة ْ<‪ْG‬رَا ْه ْ ْ‬ ‫! {ْ ْ ْ& ْ‬ ‫!‪ّG‬امْ َ< ْ ْ ْ‬ ‫‪ ْG%‬ا ْ‬ ‫‪ُ (ِ )ُ$‬ه َ وَا ْ‬ ‫ل ِْ? ‪ Bَ =َ[g‬؟‬ ‫‪ُ َ ُ F‬ه َ‪ $‬ا‪َGْ S‬ادْ ْ ْ! َ ْ' ِ (ْ وْ ‪6‬‬ ‫ْ‬ ‫!‪. -َ ْG‬‬ ‫? ْ‬ ‫‪ J‬دِي ْ< َ وْ ‪ 10‬دراه وْ ‪ َ 6‬مْ‪ 10 ْ8 ِ ?ِّ #ُ ّS ،‬دْرَا ْه وْ ‪ ُ 30‬مْ ِه َ‬ ‫َ‬ ‫‪ 4‬لْ‪.‬‬ ‫‪4‬ل ْ َ‬ ‫‪ 10 ْ^ ِ ,َ ْ ّ ْ #6S‬دْرَا ْه وْ ‪ ُ 30‬مْ ْ َ‬ ‫‪ْ ْTS‬‬ ‫‪ْ$3‬بْ ا ْ ْ! َ ْ' ِ (ْ ْ ْ& ِ‪ ْ ُ <ْ 6‬وْ ْ ْ‪ْ +‬‬ ‫'^ْ ْ ْ‬ ‫‪ّ :‬‬ ‫‪ $ُ %‬أ‪ْ #ُ 6‬‬ ‫! َارزْ‪ ?ِ-‬ا ْ ْ ْ‬ ‫وْ ْه َ َ< ْﯖ لْ ِ َ ا ُ‬

‫ا ‪.\ P‬‬

‫‪6 ×10‬‬ ‫‪=2‬‬ ‫‪30‬‬

‫'‬ ‫! ُ‬ ‫'^ْ ْ< ْ‬ ‫‪ّ :‬‬ ‫‪ْ ، $ُ %‬‬ ‫! َارز‪ ?ِ-‬ا ْ ْ ْ‬ ‫ْ ْ& ِ? آِ? ﯕ لْ ا ُ‬

‫! ْ !!‬ ‫‪ a‬ز ^ْ ِ ِ‬ ‫ُ جْ دْرَا ْه‪ ْT‬وْ <ْﯖ لْ ِ ْ‪ #‬ا ْ َ‬

‫ْ‪ُG‬وزُو دا @ ْ ِ َ تْ َ< عْ ا َ ْ‪ ْ$‬وْا ُ َ‪ُ َ َ -ُ ?ِ)-َ ، 1َ +‬آ َة ا َ َ‪G‬مْ !!‬ ‫' (ْ ْ ّ ُ‪ -‬زْ‪.‬‬ ‫‪ِ B‬‬ ‫‪ َ B‬بْ ‪ّ 1‬لْ ْ ‪َGْ S‬ادْ‪ َ ،‬دْ ْ‪ ?ِO&ْ ْ ْG&ْ ْ ْ8-‬ا َ‬ ‫‪ J‬دِي ْ ْ ْبْ ا ْ‬ ‫َ‬


‫‪: ْ$ :‬‬ ‫ْ ْ‪َG,‬اوْ ْ ْ ِ‬

‫‪َ)H‬اتْ‪.‬‬ ‫‪ ْ(%ْ ْ$U‬ا َا ْ‬ ‫‪ 4‬لْ ْ ‪ْ l‬‬ ‫‪َM‬‬ ‫[ َ)دْ ‪.$ْ 1‬اتْ ْ‬ ‫‪َ ْ^ O‬‬ ‫‪ِ &ْ ْ <َ ،ْ :‬‬ ‫‪ْ o ْG%‬‬ ‫\ ْ ْ ِ? ‪َ Gَ َ ?ِF‬د ْ‪َ 1‬ا ْ‬ ‫ل ْ‬ ‫ْ ْ& ِ? أ‪ِ #ُ 6‬إ َ‬ ‫> جْ ‪:‬‬ ‫? ُ‬ ‫‪.$ْ 1ْ ْ)H‬اتْ ُ جْ ِّ? ِه َ‬ ‫‪ ْ^ O‬وَا ْ‬ ‫‪ِ &ْ ْ <َ ،ْ)H‬‬ ‫\ ْ ْ ِ? ُ جْ ْ َا ْ‬ ‫' ّْرْ ْ‬ ‫دَا َ ْ< ْ‬ ‫‪2 ×1 = 2‬‬

‫‪: 63‬‬ ‫? ْ‬ ‫‪.$ْ 1ْ <=< ْ^ O‬اتْ ُ جْ ِّ? ِه َ‬ ‫\ ْ ْ ِ? ُ جْ ْ‪ِ &ْ ْ <َ ، <=P‬‬ ‫' ّْرْ َ وْ َ< ِ? ْ‬ ‫دَا َ ْ< ْ‬

‫‪2×3 = 2 + 2 + 2 = 6‬‬ ‫‪ َ 63‬وْ َ< ِ?‪.‬‬ ‫? ْ‬ ‫وْ ْ ْ‪ ,َ <ْ ْ8ْ $‬نْ ِ ُ ْ أ‪ ُ َ 6‬جْ ْ‪.$ْ 1‬اتْ <=< ِّ? ِه َ‬ ‫دَا َ ‪ J‬دي ) ‪ 1‬ا ْ ِ َ تْ َ< عْ ا ّْ ْبْ آُ‪ َ 1ْ ْT@ُ 1‬دْ ا ِ‪ $‬لْ ‪:‬‬

‫‪ ْ)H‬وْ < َ ِ‬ ‫? وَا ْ‬ ‫‪ 0ُ S‬دْ ِه َ‬ ‫‪ 0ُ S‬دْ ْ ْ! ْ‬ ‫>‪ْG‬وْلْ ا ّْ ْبْ‪ْ ْ ،‬‬ ‫‪ْ ْ8 y‬‬ ‫‪ِ 1ْ %‬‬ ‫ل ْآ ْ ُ َ‬ ‫‪ 0ُ S‬دْ‪ ،‬إ َو إ َ‬ ‫?ْ ْ‬ ‫‪ِ ْG%‬ه َ‬ ‫) َة ْ‪ ْ(Q‬وَا ْ‬ ‫ِ َ‪ $‬أ‪ْ ْ #ُ 6‬‬ ‫‪(10 − 1) × (10 − 1) = 9 × 9 = 81‬‬

‫(ْ ‪:‬‬


‫‪: ْ$ :‬‬ ‫) ُ‪ 1‬دَا َ ْ ْ ِ‬ ‫أ َر ْ ُ‬

‫‪ +َ ِ W‬تْ ا ‪. %َ @.‬‬ ‫> ُ& ‪ِ Bَ =َ0‬ﭬ ‪ ُ P‬رْسْ وْ ا ُ َ! َ‬ ‫‪ J‬دِي ْ ْ ْ‬ ‫إ َو دَا َ َ‬ ‫' َ ْ ْ ْ ُو ُه‪.ْT‬‬ ‫‪ْ :‬‬ ‫‪ S‬بْ‪ ،‬وْ ِد ^ْ ا ‪ْ َ 6‬‬ ‫‪َ 4‬‬ ‫‪L‬ا ْ‬ ‫‪َ B‬د ْ ً‪ْ ْ ُ ْ ُ ِْ $‬‬ ‫‪ُ O‬‬ ‫‪ +َ ِ W‬تْ ا َ@ ‪ُ %.‬ه َ‪ Qَ Lَ $‬تْ َ< ْ ِ‬ ‫َه دْ ا ُ َ! َ‬ ‫‪ B‬لْ ا ّ ْ َ تْ ْ‪.ْ( 1‬‬ ‫‪ َ B‬بْ ْ َ‬ ‫| ْ‬ ‫‪ْ 3‬‬ ‫' ُ ْ ْ َ‪ْ 1ُ َ ِ ُ ,‬‬ ‫‪ْ :‬‬ ‫‪ J‬دِي ْ ْ @‪ ْ ُ $‬ا ّ ْ َ تْ‪ْ ْ ُ ّS ،‬‬ ‫دَا ْآ)ِ? ْ‪L‬شْ َ‬ ‫‪ 0ُ S‬دْ ْ ُ‪ 0َ ّ ْ$‬تْ ‪:‬‬ ‫' وْبْ ْ‪ْ ْ ْ8-‬‬ ‫‪ +َ ِ W‬تْ ‪ 8-‬ا ُ‪َ -ْ ?@ ْ-ّ ْ$‬‬ ‫> ا ُ َ! َ‬ ‫!ُْ‬ ‫‪ J‬دِي ْ ْ‬ ‫‪ J‬دِي ُ @ر ُ ْ ِآ َ‪ E‬شْ َ‬ ‫دَا َ َ‬ ‫‪ َ B‬بْ ُه َ َه‪َG‬اكْ‪.‬‬ ‫) فْ وَاشْ ْ‬ ‫) ‪ْ ,ْ ْ Gَ &ْ ْ ْi‬تْ ْ ْ)ْ َر َ ْ(ْ ُ' ْ&ْ َ شْ ْ ُ‬ ‫ْ‪ِ -‬‬ ‫' رَة ‪:‬‬ ‫!‪ُG‬و ْ& َ‪ ,‬رْ ِّ? ْ‪ َ 1‬دْ ا [‬ ‫َْ‬

‫‪ْ O‬فْ < ُ‪ ْdّْ $‬ا ْ ِ‪.30 cm #ْ 1ِ ْ ,‬‬ ‫' ِ‪ 10 cm #ْ 1ِ ْ 4‬وْ ا ّ‬ ‫‪ْ O‬فْ < ُ‪ ْdّْ $‬ا ْ‬ ‫‪ َ O‬أ‪ #ُ 6‬ا ّ‬ ‫ْ& َ‪ ,‬رْ ْ َ‬


‫‪ j‬رَة ْ& َ‪ ,‬رْ ‪:‬‬ ‫? ُ‬ ‫وْ َه ِه َ‬

‫‪ O‬لْ دْ َ‬ ‫‪ْ$,‬فْ ا ّ‬ ‫' وْبْ ْ‪ْ ْ8-‬‬ ‫ل ْ ِ‪َ -ْ ْ-. ْ$%ُ ,ُ ْ ْ ْ َ 4‬‬ ‫(إَ‬ ‫ِآ ‪ r‬ﯕ ِ‪َ ,‬‬

‫‪َ f ,ُ ْ <َ ،10 cm‬ه ّآ ‪:‬‬

‫‪102‬‬ ‫‪ َ B‬بْ َه ‪6‬آ ‪:‬‬ ‫وْ َ< ْ ْ ْ ُ ْ‬ ‫‪2‬‬

‫‪10 = 10 × 10 = 100.cm‬‬

‫‪ O‬لْ دْ َ‬ ‫‪ْ$,‬فْ ا ّ‬ ‫' وْبْ ْ‪ْ ْ8-‬‬ ‫ل ْ ِ‪َ -ْ ْ-. ْ$%ُ ,ُ ْ ْ ْ َ 4‬‬ ‫(إَ‬ ‫ِآ ‪ r‬ﯕ ِ‪َ ,‬‬

‫‪2‬‬

‫‪َ f ,ُ ْ <َ ،30 cm‬ه ّآ ‪:‬‬

‫‪302‬‬ ‫‪ َ B‬بْ َه ‪6‬آ ‪:‬‬ ‫وْ َ< ْ ْ ْ ُ ْ‬ ‫‪2‬‬

‫‪10 = 30 × 30 = 900.cm‬‬ ‫‪2‬‬

‫‪ &َ 6ْ $ُ < S‬تْ ‪:‬‬ ‫‪َ ْU‬‬ ‫' وْبْ ْ‪ْ ْ8-‬‬ ‫ْ ْ‪َG,‬اوْ ْ ْ&‪َG‬ا ْ ُ‪ْ ْ-. ْ$‬آ ِ ‪َ -ْ ْ$‬‬

‫‪ &َ ّْ $ُ <ْ S‬تْ ﯕ‪G‬ﯕ‪: ?ِ &ْ ْ ،G‬‬ ‫‪َ ْU‬‬ ‫ْه َ ْ ْ‪ْ َ ْG‬‬ ‫‪5 × 102.cm 2 = 5 × 10.cm × 10.cm = 500.cm 2‬‬


: َْ O ِ &ْ ْ <َ ،ْ 4ِ j ْ ْ-. ْ$%ُ ْ‫ دْ و‬$ُ ْ ْ‫ ت‬$ُ <ْ 0َ ْ ْ‫ر‬

ْ ْ ‫ َ ُه‬$ْ ْ Qْ ‫ل‬ َ‫إ‬

 10.cm × 20.cm  2 2 2 2 4×  + 10 .cm = 400.cm + 100.cm 2   ............................................... = 500.cm 2

: ْ‫ ُ رْس‬P ‫ َه َ ِﭬ‬$ْ %ُ ْ‫ ّ َ< ع‬4 ُ ‫ ا‬6ّْ َ ‫ْه‬ 500.cm = 400.cm + 100.cm 2

(

)

2

2

2

500 cm2 = 20 2.cm 2 + 10 2.cm 2

.َy ْ Eْ B ْ ْ -َ Lْ ْ‫ رْس‬J ُ ‫ ْ َه َ ِﭬ‬$ُ ْ -ُ ْG! ْ ْ <َ َ Eِ ْ ‫ َا‬B ْ ‫ن‬ 6 ‫> ا َا ْ َة ُه َ أ‬ َ B َ ‫وْا‬ : ْ‫ َ& ت‬6ْ $ُ < ْ‫ د‬0ُ S ْ ْ ْ8-ْ ْ‫' وْب‬ َ -ْ ْ$ ِ ‫ْ ْآ‬-. ْ$ُ َ ‫ُوزُو دَا‬Gْ

: ْ‫ َ ب‬B ْ ُْ ْ ْ َ > ِ ‫ل‬ َ‫إ‬

: ْ‫ د‬$ُ ْ ‫ ث‬$ُ < 0َ ْ ْ‫ وْ ر‬202 L ْ ّ ْ !ْ %ْ ْd6ْ -ُ ْ‫ و‬102 ْ$ Cِ D ْ ْdّْ -ُ ْ8-ْ ْf َ ْ ْ‫ و‬j َ

(10.cm + 20.cm )

2

(a + b)

= 10 2.cm 2 + 2 ×10.cm × 20.cm + 202.cm2

2

: ْ$ : ِ ْ ْ ‫ْرُو ْ َ وْ َه‬Gْ ْ ?@ ، ْ ‫ ا‬-ّ َ ‫ ِ َ ا‬O َ َ $ُ ‫ ا‬6ّْ َ ‫ْه‬ = (a + b) × (a + b)

............ = a × a + a × b + b × a + b × b ............ = a 2 + 2 × a × b + b 2 .ْf $ُ &ْ ْ ْ -َ Lْ ْ ) ِ ْ ْ -ُ ْG! ْ ْ <َ َ Eِ ْ ‫ َا‬B ْ ‫ن‬ 6 ‫و< ? ُه َ أ‬

‫> ا َا ْ َة‬ َ B َ ‫وْا‬


.ْ-m ْ %ُ ْ$[ ْ ْ‫و‬Vْ ْ(ْ ) ْ ‫شْ َ< ْ َ وْ َه دْ ا‬Lْ ?@Fْ‫وْ َه د‬ .ْ‫ ش‬Eَ ‫ ِآ‬$ُ $ْ ! ْ <ْ ْ ُ ِ! ْ ْ ،(ْ ) ْ ‫ْ َه دْ ا‬8-ْ ْ8 ! ْ ْ‫ ِ َ ت‬O َ َ $ُ ‫> ا‬ ُْ! ْ ْ ‫ْرُو‬Gْ ْ ْ‫و‬ :L ْ 1َ ْ8 ِ xْ ‫ َ ا‬a ِ ْ Lْa <ْ ْ‫َ ت‬

ْ ّ ‫شْ ا‬Lْ ْ ُ ِ ‫ْرْ ْﯖ‬Gْ ْ َ ‫إ َو دَا‬

: ْJ6ْ : ْ ‫ ْ& ُ مْ ْ َ@ دْ ا‬$ْ > ْ ْG&ْ ْ ْ8-ْ ْ‫ ُ مْ و‬3 ْ ّ ‫ تْ وْ ْه‬0َ ْ ْ$%ْ ْ‫ ت‬a َ a ِّ <ْ <=< ْ‫ د‬: َ ?ِaْ Lْa ‫ ا‬#6‫ْآّ ﯕ َ أ‬

: َ‫ل‬ ّ ْ‫ْ و‬-ّ ْ$%ُ ‫ وَاشْ َه دَا‬1ُ ) ُ ْ ‫ْرُو‬Gْ ْ ،ْ‫ رْس‬J ُ ‫ ْ َه َ ِﭬ‬,ْ -ُ َ 1ْ ْ ْ ?@-ْ ‫دْرُو َآ‬ : ‫ج َد‬ ِ ‫ دْ هَـ‬$ُ &ْ ‫ل ا‬ 6 ْ‫اوْ َ و‬6V ‫ ْ ا‬Wِ َ ‫ ا‬X $ُ 1ْ ْ‫َاك‬G‫ َه‬6 ‫ َ بْ ُه‬B ْ ‫ وَاشْ ا‬1ُ ) ُ ْ ‫ دِي‬J َ

: ْ‫ َ ب‬B ْ ُ ْ ْ ْ َ ‫دَا‬ 2

2

2

   2  2  2   1 +  +  1 +  = 2 ×  1 +  2  2  2     : ْ‫ ِ َ ت‬O َ َ $ُ ‫ (ْ ا‬2 @ِ %ُ ْ‫ش‬Lْ 2 2    2  2   2   2 2 ×  1 +  = 2 × 1 +  2 × 1 ×  +    2 2 2          2

 2  2 ×  1 +  = 2 ×  1 + 2   

2+

1 2 1  = 2× + + 2 2 2

ُ &ِ <ْ ‫ دِي‬J َ َ ‫ْه‬

 2  : َO ِ &ْ ْ <َ ْ ! ْ 1

2

2

  2  2   1 +  +  1 +  = 3+ 2× 2  2   

(

2

)


‫‪ +َ ِ W‬ا َ@ ‪ َ %.‬شْ ْ ْ& ْ ْ‪ َ ْV-‬نْ ‪:‬‬ ‫‪ُ 6%‬ه َ ْ ُ َ! َ‬ ‫‪ َ B‬بْ ا ِ? ْ‬ ‫‪ J‬دِي ْ ِ‪ُ G‬و ْ‬ ‫َ‬ ‫‪2‬‬

‫‪2‬‬

‫‪1‬‬ ‫‪‬‬ ‫‪1 1‬‬ ‫‪2‬‬ ‫‪2 +  = 2 + 2× 2×  +  ‬‬ ‫‪2‬‬ ‫‪‬‬ ‫‪2 2‬‬ ‫‪1‬‬ ‫‪............. = 4 + 2 +‬‬ ‫‪4‬‬

‫‪: َO‬‬ ‫! ْ َ< ْ ْ& ِ‬ ‫‪ْ 1‬‬ ‫‪2‬‬

‫‪1‬‬ ‫‪25‬‬ ‫‪‬‬ ‫= ‪2+ ‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪‬‬ ‫‪ َ B‬بْ ْ‬ ‫> َ ْ ْ ُْ ْ‬ ‫إِل ِ‬

‫‪: َa‬‬ ‫ْ ‪ِ ْ <َ ،ْk‬‬

‫)‬

‫‪2 ≈ 5, 8 2 8 4 2 7 1 ......‬‬

‫‪2‬‬

‫‪‬‬ ‫‪2 ‬‬ ‫‪2 ×  1 +‬‬ ‫×‪ = 3+ 2‬‬ ‫‪2 ‬‬ ‫‪‬‬

‫(‬ ‫‪2‬‬

‫‪1‬‬ ‫‪25‬‬ ‫‪‬‬ ‫‪= 6, 2 5‬‬ ‫= ‪2+ ‬‬ ‫‪2‬‬ ‫‪4‬‬ ‫‪‬‬ ‫‪L‬؟‬ ‫> َه دْ ا ‪ْ 1َC‬‬ ‫‪ ،ً '$ْ+ْ ْ :‬وْ ْ‪َ ْ8 ِ -‬‬ ‫‪ْ o ْG%‬‬ ‫‪ ْG%‬ا َ& َ‪G‬دْ ‪ ْcْ g‬وْ وَا ْ‬ ‫إ َو دَا َ ِآ َ‪ E‬شْ وَا ْ‬ ‫‪ ُ H‬وْ َ< ْﯖ لْ ‪:‬‬ ‫وْ ْه َ َ< ْ ْ‪ َ ِ ْ ّ E‬أ ُ ا َ َ ءْ ا‪ْ ْ$'ْ a‬‬

‫‪ْ$,‬فْ ا ُ‪ ُ ْ-. ْ$‬جْ ِز ‪ُV‬ونْ وْ َ‪ْ)+ْ ْ %‬رُوشْ ْ ْ‪)َ 0َ ُ ْ$0‬دْ دْ َ'‬ ‫ل ْ‬ ‫ْ ْ& ِ? أ‪Kْ> #ُ 6‬رْ وْ ّ‬

‫‪.L‬‬ ‫‪ْ ْ3‬‬ ‫ْ ّ‬

‫‪: ُْ O‬‬ ‫‪ J‬دِي ْ ْ& ِ‬ ‫‪َ ْk ْ ِ َ ْ ُ ,ْ ْ %‬‬ ‫ل ْ‬ ‫إَ‬

‫‪2 ≈ 1, 4 1 4 2 1 3 5 6 .......‬‬ ‫‪ J‬دِي ْ َ‪ ,‬نْ ِ ُ ْ أ‪: #ُ 6‬‬ ‫وْ ْه َ َ‬

‫‪2 〈1 , 5‬‬ ‫| ا ‪ ?ِaْ Lْa‬؟‬ ‫‪ْ J‬‬ ‫| ْ‬ ‫‪ B‬لْ ْ ْ َ ْ< َ‪ْ 4‬‬ ‫‪َF‬‬ ‫دَا َ ْ‬ ‫> تْ ْ‪َ $ْ 1‬‬ ‫‪ 4‬لْ َ‬ ‫‪َM‬‬ ‫? ‪ْ ، َ $ْ 1ْ 100‬‬ ‫ل ﯕ َ ‪ِ 1.5‬ه َ‬ ‫إَ‬

‫‪2‬‬

‫؟‬


‫‪ْ ْTS‬‬ ‫'^ْ ْ< ْ ْبْ ا ْ ْ! َ ْ' ِ (ْ ْ ْ& ِ‪ ْ ُ <ْ 6‬وْ ْ ْ‪ْ +‬‬ ‫‪ّ :‬‬ ‫‪ $ُ %‬أ‪ْ #ُ 6‬‬ ‫! َارزْ‪ ?ِ-‬ا ْ ْ ْ‬ ‫ِإ َو آِ? ﯕ لْ ا ُ‬

‫ا ‪:X‬‬

‫‪2 × 100‬‬ ‫‪≈ 9 4, 2 8 0 9 ....%‬‬ ‫‪1, 5‬‬ ‫?‪:‬‬ ‫| ِه َ‬ ‫‪ َ S‬ا ِ َ‪ْ 4َ <ْ '. p‬‬ ‫ْ ْ& ِ? ا ‪ْ 2‬‬

‫‪1 0 0 % − 9 4, 2 8 0 9 % ≈ 5, 7 1 9 0 ....%‬‬ ‫‪!! ْ} a‬‬ ‫‪ J‬دِي ْ< ِ ‪ ,ً ْ <ْ ْd‬فْ ‪َ ْ$!ْ %ِ 6‬آِري دْ َ لْ ا ْ‬ ‫‪َ ْ$!ْ %ِ 100 ْ} a‬آِري‪َ ،‬‬ ‫ل ِ ِ? ْ< ْ‬ ‫ْ ْ& ِ? أ‪ِ #ُ 6‬إ َ‬ ‫‪ ُ F‬نْ ا ‪ ْ~,َ 6‬؟ ُ‪َ ْ$ْ %‬ه َ ِﭬ ‪ ُ P‬رْسْ !!‬ ‫وْ ْ‬ ‫‪. َa‬‬ ‫ط ا ‪ِ ْ Lْa‬‬ ‫‪ْ$ْ $ُ %‬زْ ْ‬ ‫َه ْ‪L‬شْ ﯕ عْ أ ُ ا َ َ‪ 1‬ءْ ا ْ ْ ْ‬ ‫‪ّْ ْ ْ 3‬‬ ‫‪ِ ْ ْ َ -ُ ْG:‬‬ ‫‪ ،ْl B‬وْ‪ 6‬وْ ِ‪ْ $6 ْ 1‬‬ ‫'ِ‬ ‫| وْ ْ< ْ& ُ‪ $‬ا ْ‬ ‫وْ ْ‪ $ُ ْ 1ْ ?@-‬ا َ‪ْ 4‬‬

‫‪. $ُ %‬‬ ‫َ <ْ‪ ُ H‬ا َ َ‪ 1‬ءْ ا ْ ْ ْ‬

‫) ْ(ْ‪.‬‬ ‫ل ا ُ& دْ َ ْ ُ@‪ُ ْT‬ه َ َه دْ ا ْ‬ ‫‪ ْ} a‬وْ ‪6‬‬ ‫وْ ْ‪ْG V‬كْ ﯕ عْ ْآ ْ ْ‪َ ْ8-‬ه دْ‪ُ ،?ِF‬ه َ أ‪ #ُ 6‬أ ْآ َ ْ< ّ‪V‬و‪6‬ا َ‪ Q‬تْ ِّ? ْ‪ّْ 1‬‬ ‫ي ْ< ‪: ِ -ْ S‬‬ ‫‪َ F‬‬ ‫ْﯖ لْ ِ ُ ْ ْ‬ ‫ق ْآ‪ %ُ ْ$‬سْ ْ‪: ْ( ِ 1ْS‬‬ ‫? وْرْا َ‬ ‫‪ ْG%‬ا ّ‪V‬و‪6‬ا َ‪َ ْ $@ ْ ْ <َ Q‬ه وْرَاقْ ا ‪ِ ?@ ْ( !2‬ه َ‬ ‫‪ َ a‬وَا ْ‬ ‫‪ j‬وْ ُ ا ‪ِ ْ Lْa‬‬ ‫) ُ‪ِ 1‬آ َ‪ E‬شْ َ‬ ‫‪ J‬دِي ْ ُ‬ ‫َ‬

‫‪.‬‬ ‫) ْ(ْ دْ َ َ ‪:‬‬ ‫َه ا ْ‬

‫‪.p‬‬ ‫‪َ$ْ 4‬اءْ ْ‪َ َ ْ 4ْ 1‬‬ ‫‪ ْ$7‬ا َ‬ ‫) ْ(ْ َ< ْ َ وْ‪ْ +ْ ْ ْf‬‬ ‫َه د ا ْ‬


‫> جْ ْ< ْ‪6 $‬اتْ ‪:‬‬ ‫‪ُ $ُ %‬‬ ‫) ْ(ْ َ< عْ أ ُ ا َ َ‪ 1‬ء ا ْ ْ ْ‬ ‫‪ $ُ 3‬ا ْ‬ ‫) ْ(ْ‪ْ ْ ْ <َ ،‬‬ ‫' وْ ُ َه دْ ا ْ‬ ‫ل ْ ِ‪َ ْ َ 4‬‬ ‫ِإ َ‬

‫‪: $ُ %‬‬ ‫) ْ(ْ <ْ‪ ُ H‬ا َ َ‪ 1‬ء ا ْ ْ ْ‬ ‫> رْ ْ َ‪ّ ْ 0‬و‪.‬ا َ‪ B‬تْ ْ‪ ْ8-‬ا ْ‬ ‫!ُْ‬ ‫ْ ْ& ِ? ْ ْ‪ْG‬رُو ْ ْ‬

‫‪َ$ْ 4‬اءْ‪ ،‬وْ ْ ْ‪ْG‬رُو ْ ْ‪ ُْG,‬ا َانْ ‪:‬‬ ‫‪ ْ$7‬ا َ‬ ‫( ‪6Vْ َ Qِ x‬افْ ْ‪ َ <َ ،ْ ُ ْ -‬وْ ا ّ‪ْV‬و‪6‬ا َ‪ْ +ْ ْ ?ِّ Q‬‬ ‫ِو َ‬

‫‪. ُH‬‬ ‫‪ ْJ6ْ M‬أ ُ ا َ َءْ ا‪ْ ْ$'ْ a‬‬ ‫' وْ ِ ‪ْ ْ8-ْ ْ8‬‬ ‫ل ا ُ& دْ ْ‪َ -‬‬ ‫‪ ْ} a‬وْ ‪6‬‬ ‫وْ َآ ْ ِ ‪ ْ8‬زْو‪6‬ا َ‪ Q‬تْ ْ‪6V‬افْ ْ‪ْ 1‬‬


‫[‪ !ُ +ِ ْ( ِ !ُ ْ ْ$‬؟‬ ‫‪ْ ، $ُ %‬‬ ‫) ْ(ْ <ْ‪ ُ H‬ا َ َ‪ 1‬ءْ ا ْ ْ ْ‬ ‫‪ْ ْ -ُ ْG:‬‬ ‫) ‪َ ْ)ْ ْ ْ8 1ِ ْ~ ْ ْ <َ ْi‬ر ْ ْ(ْ ُ' ْ&ْ ْ‬ ‫‪ِ -ْ ْX %‬‬ ‫وْ ِ‬ ‫‪S <ْ ْ} a‬رْضْ‪ ْfْ $@ ْ ْ <َ ،‬ا ّ‪ ْ 1‬ا ْ‪ِ)1‬ي ‪:‬‬ ‫>ِ َ ‪ّ 1ْ ?ِ &ْ ْ ،‬‬ ‫‪ْ ْiB‬ر ْ‬ ‫ْ< ْ‬

‫> ُ&‬ ‫أ>ِ? دَا َ ْ ْ ْ‬

‫> بْ ِ َ َه دْ ا ْ ْ ُآ[ ‪.‬‬ ‫[‪َw‬الْ ا ْ‪ ?ِ x‬ﯕ عْ‪ ،‬أ@? َ‬

‫ل ْ ْ ُ ْآ ْ‪ ْi‬ﯕ ‪: ْi‬‬ ‫إَ‬ ‫‪R‬‬ ‫‪ِ ْ 4َ ?َ ْ ْ #‬‬ ‫‪ Qَ R‬أ ْ‪ ْ 2‬رْ ْ‬ ‫‪ ْ*#‬ا ّْ‪ْ $‬‬ ‫‪ْ ْ $ْ 4َ L‬‬ ‫وْ‪ْ Jِ ْ Y!ِ%‬‬

‫‪ ?َ ْ #‬؟‬ ‫= دِي ْ‪ْ ْ :‬‬ ‫‪ #‬آِ! َ‪ U‬شْ َ‬ ‫‪ّْ X‬لْ رَا ِ‬ ‫‪َ ، 1‬و َ‪ْ :ْ :‬‬ ‫ْ ْ‪َ ْ 2‬‬

‫‪. $َ a‬‬ ‫‪ ْ3‬ا ّ ْ‬ ‫‪ َ $ُ %‬شْ ْ ْ ْ‬ ‫‪ J‬دِي ُ @ر ُ ْ آِ? دَارْ أ ُ ا َ َ ءْ ا‪ْ ْ ْ a‬‬ ‫دْرُو َآ َ‬ ‫‪: $َ a‬‬ ‫) ْ(ْ دْ َ لْ ا ّْ ْ‬ ‫َه ا ْ‬ ‫‪ O‬لْ دْ َ‬ ‫‪ْ O‬فْ"أ ب"‪ ،‬ا ّ‬ ‫‪ ْG%‬ا ّ‬ ‫‪ $ُ 3‬وَا ْ‬ ‫‪ J‬دِي ْ< ْ ْ‬ ‫ْ‪ّ 1‬لْ َ‬

‫ِآ ْ‪. ُ ِ $ّ E‬‬

‫? ْ‪ْ Q‬‬ ‫‪ O‬فْ "أ ب"‪ ،‬وْ ا ّ ْ‪" O‬ج" ِه َ‬ ‫[ ُ دْ وْ ﯕ)‪f‬و ﯕ)ْ ا ّ‬ ‫‪ْ ْ:‬‬ ‫‪ْ p‬فْ وَا‪ْ oGْ%‬‬ ‫‪ْ $ُ 3‬‬ ‫‪ J‬دِي ْ< ْ ْ‬ ‫وْ ْ‪َ ،ْG&ْ ْ ْ8-‬‬

‫‪:‬‬


‫‪ْ O‬فْ "د ج" َه ّآ ‪:‬‬ ‫‪ $ُ 3‬ا ّ‬ ‫‪ O‬فْ "أ ب"‪ ،‬وْ ْ< ْ ْ‬ ‫> تْ ْ ّ‪ّ <ْ ْs‬‬ ‫‪ $ُ 3‬ا ّ ْ‪" O‬د" ّ? َ‬ ‫‪ J‬دِي ْ< ْ ْ‬ ‫وْ ْ‪َ ،ْG&ْ ْ ْ8-‬‬

‫? ْ‪ْ$%‬آ ْ َه ‪:‬‬ ‫‪ O‬فْ "د ج"‪ ،‬وْ "د" ِه َ‬ ‫‪ َ ُ &َ F‬ا ّ‬ ‫‪ُ B‬‬ ‫'َ‬ ‫[ َ@ ْ ُ‪ْ E‬‬ ‫‪ َ ,ِ ْ $ُ 3‬رْ ا ْ َ "ج هـ" ذرَا ْ‬ ‫‪ J‬دِي ْ< ْ ْ‬ ‫وْ ْ‪َ ،ْG&ْ ْ ْ8-‬‬

‫‪ W‬لْ َ< ْ ْ ‪.‬‬ ‫‪ ْG%‬ا ‪" ، 1ْ4‬أ هـ" ُه َ ا ّ‬ ‫‪ J‬دِي <ْ‪ B‬ا ِ‪ َ ,‬رْ وَا ْ‬ ‫وْ ْ‪َ ،ْG&ْ ْ ْ8-‬‬ ‫‪ َ ,ِ ْ $ُ 3‬رْ > ج < ْ َ ت‬ ‫وْ ْ‪ْ ْ <ْ ،ْG&ْ ْ ْ8-‬‬

‫? ْ‪ْ -‬آ‪َ ْV‬ه ‪.‬‬ ‫‪G‬ه ‪ kE‬ا ‪K‬رَاعْ "أ هـ"‪ ،‬و‪G%‬ة ْ‪ْ -‬آ‪َ ْV‬ه " أ " وا‪ :S‬ى " ب " ِه َ‬

‫‪: َ ْ ْ $ِ 3‬‬ ‫‪" O‬ر" ْ‬ ‫‪ J‬دِي ْ'!ْ= َ‪ B‬وْ ْ‪َ ْ ّ 1‬‬ ‫َه دُوكْ ا ْ ْ َ تْ َ‬

‫‪ O‬لْ َ< ْ ْ ‪.‬‬ ‫‪ ْG%‬ا ‪" ، 1ْ4‬أ ب" ُه َ ا ّ‬ ‫‪ J‬دِي <ْ‪ B‬ا ِ‪ َ ,‬رْ وَا ْ‬ ‫وْ ْ‪َ ،ْG&ْ ْ ْ8-‬‬ ‫‪ َ ,ِ ْ $ُ 3‬رْ رْ ْ َ& < ْ َ ت ْ ْ‪ُ ْG‬ه ْ ْ ْ‪ ْkE‬ا ‪K‬رَاعْ "أ ب"‪ " ،‬أ " وْ" ب " وْ" ر " ُه َ‪ $‬ا َ‪َ$‬ا ِآ ْ‪.‬‬ ‫وْ ْ‪ْ ْ <ْ ،ْG&ْ ْ ْ8-‬‬ ‫‪: َ ْ ْ $ِ 3‬‬ ‫‪" O‬ط" ْ‬ ‫‪ " O‬ح " وْ ا ّ ْ َ‬ ‫َه دُوكْ ا ْ ْ َ تْ ْ!ْ= َ‪ B‬وْ ْ‪َ ْ ّ 1‬‬

‫‪. $ُ %‬‬ ‫) ْ(ْ ِ? ْ‪ َ ْ 1‬بْ أ ُ ا َ َ ء ا ْ ْ ْ‬ ‫َه دَا ُه َ ا ْ‬


‫) ْ(ْ ا ُ َ ِ ‪:‬‬ ‫‪َ ?ِ $ْ 3‬ه دْ ا ْ‬ ‫إ َو دَا َ إل رْ ْ‬

‫‪u‬ا ّ َْ ‪:‬‬ ‫| وْ < َ‬ ‫‪ J‬دِي ِه ْ ْ= ِ‪ B‬ا ّ َ ْ‬ ‫َ‬

‫‪: $َ a‬‬ ‫‪ S‬سْ َ شْ ْ ِ َ ا ّ ْ‬ ‫‪. ْ ُْ B‬‬ ‫أ>ِ? دَا َ ْ ْ‬ ‫‪ W‬لْ َ< ُ ؟‬ ‫‪ B‬لْ ْ ُ نْ ا ‪f‬‬ ‫‪َF‬‬ ‫‪ O‬فْ "د ج" ُه َ ا ‪ 6‬سْ‪ ،‬إ َو ْ‬ ‫ن ا ّ‬ ‫‪ J‬دِي ْ َ‪ ,‬نْ ِ ُ ْ أ ‪6‬‬ ‫َ‬ ‫ْ‬

‫‪ J‬رْسْ ‪:‬‬ ‫ل ُ‪َ ْ ,ْ -‬ه َ ِﭬ َ ُ‬ ‫‪ J‬رْسْ وْ ‪6‬‬ ‫‪ َ %‬بْ ا َ‪ِ <ْ َ ْ ,‬ﭭ َ ُ‬ ‫ْ‬

‫> ُ‪. $ّ ِ -‬‬ ‫‪َ %‬‬ ‫‪َ ْ:‬‬ ‫دَا َ ‪ِ o‬‬ ‫‪ O‬فْ "د هـ" وْ ْ‪ْ #ْ ِ $ْ ْ Q‬‬ ‫‪ ?ِ O‬ا ّ‬ ‫ل ْ‪ْ ,ْ Q‬‬ ‫إَ‬

‫[ ِ ‪: ْb‬‬ ‫‪َ 1ْ B‬ا‪ Gْ%‬ا َ‪)َ 0‬دْ َ‬ ‫‪ُ O‬‬ ‫‪ J‬دِي ْ< ِ‬ ‫‪ O‬فْ ا ّلْ ? ُه َ "أ ب"‪َ ،‬‬ ‫ا ّ‬

‫‪$ْ4S‬ي‪ َ ْ <َ #ُ 6S ،‬وْ‪6V,ْ 1ْ ْf‬افْ < ‪. َ ْ Gّ 1ْ ْ{ْ Lْ,‬‬ ‫ل ا َ‪)َ 0‬دْ ا ‪2‬‬ ‫َ< ْ ْ ّ‪ fْ $‬ا‪S‬ورُو‚ ‪ ،8‬ا َ‪)َ 0‬دْ ا ّ‪ْ u‬ه ِ وْ ‪6‬‬


‫‪ D‬ﯕ‪.ْ`ْ < ?ِ &ْ ْ ،$‬‬ ‫ن َه دْ ا َ& َ‪G‬دْ َ< ْ ْ‪َ َ ,‬‬ ‫) ُ‪ 1‬أ ّ‬ ‫‪ J‬دِي ْ< ُ‬ ‫‪ J‬دِي ُ ّر ُ ْ ا‪ ، ِ -ْ S‬وْ َ‬ ‫وْ َه ْ ُ َ‪َ -‬‬

‫[ دا‪j :‬‬

‫‪34‬‬ ‫‪= 1, 6 1 . ...‬‬ ‫‪21‬‬

‫ا ْ‪ ْc'$ْW‬وْ ا ّ ْ‪1‬‬

‫‪ 7‬رْ وْ ‪.‬ل ا ْ‪َ َ 0‬‬ ‫[ َ‬ ‫ا‪ْ v‬‬

‫ا‪Y‬دن ‪ADN‬‬

‫ذرَاعْ‬

‫' (ْ ‪:‬‬ ‫‪ِ B‬‬ ‫ا َ‬ ‫‪ْGْ ْ ْ$ Cِ D‬رُو ْ ْ‪ّVْ #ْ ِ $ُ ْ E‬افْ ْ< ِ& َ‪ ,‬تْ‪.‬‬ ‫‪ْ ْJ6ِ :‬‬ ‫‪ J‬دِي ْ ُ نْ َ نْ ِ ُ ْ أ‪ْ ُ ْ #ُ 6‬‬ ‫َ‬ ‫‪L‬نْ‪.‬‬ ‫‪ّB‬‬ ‫' َ ْ ْ ْ& ُ‪ْ +َ '$َ, $‬‬ ‫‪ْ :‬‬ ‫‪َ B‬ه ْ‬ ‫‪ َ F‬ءْ ْ‪ ، 1ْ ْ %‬وْ َ شْ ْ ْ‬ ‫‪ [ B‬أّ ُ‪ #‬ﯕ عْ ا‪ْ S‬‬ ‫\ّ َ شْ ْ< ْ‬ ‫وَا َ ْ< ْ& ّ‪ْG$‬تْ َه دْ ا َ ْ‬ ‫\ َ تْ‪.‬‬ ‫‪ِ B‬ر َ ِ‬ ‫'َ‬ ‫‪ َ %‬بْ‪ْ Eُ ْ ،‬‬ ‫> ُ& ‪ْ ْf‬‬ ‫) ِ(ْ وْ ْ ْ ْ‬ ‫> ُ‪ْ -ُ ?ِF $‬‬ ‫? ِآ َ* شْ ‪َJ‬دِي ْ ْ ْ ْ‬ ‫‪L‬نْ ِه َ‬ ‫‪ّB‬‬ ‫وْ َه دْ ‪ْ +َ '$َ,‬‬ ‫‪ْGْ ْ ْJ6ْ M‬رُو ْﯖ‬ ‫ي ْ‬ ‫' َ ْ ْ ْ& ُ‪ُ $‬ه َ أ‪ #6‬أ @‬ ‫‪ْ :‬‬ ‫ْ ْ& ِ? أّ ُ‪ْ ?@ #‬‬ ‫‪&َ ,ِ O‬‬ ‫ل ْ‪ّ 1‬‬ ‫‪ 3‬وْ ّ‬ ‫‪َ Gَ ْ ْ 1ْ ْJ6ْ M‬‬ ‫ي ْ‬ ‫‪ #ُ ّS‬أ @‬

‫‪ S‬بْ‪.‬‬ ‫‪َ 4‬‬ ‫‪ْ ْf‬‬

‫‪ S‬بْ‪ ،‬وْ َه دَاك ﯖِ‪ُ ْ('$‬ه َ ِّ? َ< ْ ْ ُ‪,‬‬ ‫‪َ 4‬‬ ‫ْ ْ‪ُG‬و ﯕِ‪ْ ْ ُ '$‬‬

‫ِْ ْ‪ِ #‬د ً‪. $‬‬

‫‪ َ B‬بْ‪.‬‬ ‫‪ُ ?ِّ ْG%‬ه َ ِآ َ‪ E‬شْ ْ َ وْ ا ﯖ‪ َ ْ('$‬شْ ْ ْ ْ ُ ْ‬ ‫) ِ( وَا ْ‬ ‫‪ْ $ُ 1ْ B‬‬ ‫‪ُ O‬‬ ‫‪ J‬دِي ْ ِ‬ ‫وْا ّ سْ ِ? ْ َ‪ 4‬وْ ْ ْ ْ& ُ‪ $‬ا ُ& مْ‪َ ،‬‬ ‫‪: 1ِP%ْ Y ْ َ F‬‬ ‫) ُ‪ْ 1‬‬ ‫ُْ‬


‫) ِآ(ْ ِه ْ ْ ْ@ ْ َ) َ ‪.‬‬ ‫‪ B‬ا َ‪َ $‬‬ ‫‪ّ 1‬لْ َآ ُ ا ‪ 6‬سْ َ< ْ ْ‬ ‫‪ُ B‬ه مْ‪.‬‬ ‫ل َ‪ Qَ L‬تْ‪ 1ُ ْ &ْ ْ <َ -َ ،‬شْ ْ ْ‬ ‫‪ 0َ ُ ْ B‬دَ‪g‬تْ وْ ّ‬ ‫‪ُ O‬‬ ‫‪ S‬بْ وْ َ< ْ ِ‬ ‫‪َ 4‬‬ ‫وْ‪ْ ُ ْ ْ ْ <َ ْX %‬‬ ‫‪ B‬لْ َآ نْ ْ ْ‪ْG‬كْ ْ< ْ‪ E‬سْ ؟‬ ‫‪َF‬‬ ‫‪ْG<ْ َ $ْ :‬رَا ْه ‪ْ ،‬‬ ‫> جْ دْرَا ْه ْ وْ ْ َ ِ ^ْ ْ‬ ‫' ِ? ْ‪ 1ْ ?ِF ْ8-‬سْ ُ‬ ‫ل ْْ ْ‬ ‫) ( دْ َ لْ‪ِ ،‬إ َ‬ ‫‪ B‬لْ ُ‪ْ $‬‬ ‫َْ‬ ‫ْ‪َG‬اوْ َ< ْ ْ ُ‪,‬‬

‫ْ‬

‫‪َ B‬ه ْ ْ@ ْ َ) َ @? َ< ْ ْ ُ َه ‪.‬‬ ‫ل ا &َ‪ َ Qَ L‬شْ ْ ْ‬ ‫ﯖ‪َ &َ $ُ <ْ ْ('$‬د وْ ّ‬

‫وْ ْ‪ ْ8-‬ا ّ سْ @? ْ ْ ُ ْ‪Lْ 1‬بْ ْ‬

‫[ ‪ xَS‬ا @َ‬ ‫‪ِ ْ(ْ ْ)ّ 4‬‬ ‫[ َ‪ ْ$‬ا ْ ّ مْ وْ ُ‪ْ %‬‬ ‫ﯖْ‪َ 0َ ُ ْ ْ('$‬د ‪ُ َ ْGْ ْ ،‬‬

‫‪ ُ $ْ %‬مْ‪.‬‬ ‫ا ْْْ‬

‫ل ْ‪ ْ(%‬ا ‪َ ).‬ر َ ا ‪x3 − 20 x 2 + 200 x − 2000 = 0 P P‬‬ ‫' وْبْ ْ‪ ْ8-‬ا ُ َ‪ 0‬دَ‪g‬تْ ا ُ ْ‪ َ 0. 6‬وْ ‪6‬‬ ‫) ْ( ْ‪َ -‬‬ ‫َه د ا ْ‬ ‫‪. $ُ %‬‬ ‫[ َ‪ ْ$‬ا َ ّ مْ ا ْ ْ ْ‬ ‫‪ َ %‬بْ ُ‬ ‫ْ ْ‬


‫‪B‬‬ ‫وْ ْ‪ $ُ &ْ <ْ ?ّ-ْ ْGْ&ْ ْ8-‬ا ‪ 6‬سْ ْ ْ‬

‫ُ‪ &َ $‬دَ‪x‬تْ ِه ْ ْ َ ْ‪َGْ ،ْ$‬اوْ َ< ْ ْ ُ‪,‬‬

‫وْ ْ‪ ْ8-‬ا ّ سْ @? ْ ْ ُ ْ‪Lْ 1‬بْ ْ‬

‫ْ‬

‫‪ S‬بْ !!‬ ‫‪َ 4‬‬ ‫‪ْ ْf B‬‬ ‫ﯖ‪ َ ( ) <ْ ْ('$‬شْ ْ ْ‬

‫‪ َ ْGْ ْ ،ْJ6ْ :‬دِ' َ‪ 6‬رْتْ وْ ْﭬ \ْ‪.‬‬ ‫ﯖْ‪ْ ْ ْ('$‬‬

‫‪ -ِ ْ َ F‬لْ ُه َ ْ‪ yُ yَ VْS%‬سْ ‪: le problème de Pappus,‬‬ ‫أْ‬

‫‪َ,‬‬ ‫‪ [%‬دِ' َ‪ 6‬رْتْ ْ ُ‪ &َ $‬دَ‪x‬تْ ا ُ ْ‪ُ$‬و ِ‬ ‫) ِ(ْ ْ ْ@ ْ َ) َ ْ‬ ‫َه دْ ا ُ‪ْ $‬‬ ‫)‪y × (ax + by + c) = (dx + ey ) × ( fx + gy + h‬‬ ‫‪!! P'ِ)4‬‬ ‫‪ 1ُ0 ْ ْ ُ ِ ,َ %‬مْ ا َ‬ ‫)‪ 6‬تْ‪ ،‬إ َو ْ‪ْ ْ -‬‬ ‫> جْ ْ< ِ‬ ‫و ( ْ< ْ ْ ُ َه دْ ُ‬ ‫!‪ -َ ْG‬دْ َ لْ ا ‪ 6‬سْ @? َ< ْ ْ ْ [‪ &ُ ْ $‬مْ‪.‬‬ ‫‪ ْ ُ ِ ْ(j‬ا ‪ّ$‬وحْ < ْ‬ ‫‪ %‬وْ ‪ -َ ْi‬أ ْ‪ّْ ُ ْ8َ -‬‬ ‫ُ‪ ْ ِ $‬رَا ِ? َ‬ ‫\ ْ ْ ِ ‪.ْ#‬‬ ‫ن ا‪ َ ْ R‬نْ ْ ُ نْ َد ْ' ً َ ْ'‪َGْ ْc‬ا ْآ)@? @? َ‬ ‫وْ َ‪ َ ْ <ْ -‬وْشْ أ‪ َ 1ْ ْ ِ $ُ #ُ 6‬دْ‪ُ ?@F‬ه َ أ ‪6‬‬ ‫? ‪ J6M‬أ‬ ‫> ? ِه َ‬ ‫‪َ %‬‬ ‫‪ } a‬وا ‪V‬وَاق َو َ< َ و أ َه َ‬ ‫ل د‪ :‬ا ّ‪ 6‬ح ‪G$‬رَ‪ ،r3 ُ 8 3‬آ &‪ّ 1 ,a‬‬ ‫َ‪ L -‬إ َ‬ ‫وْ‪6%‬‬

‫ِﯖ ‪ْ <َ ْG‬‬

‫ا‬

‫ء‪.‬‬

‫‪.ْ} a‬‬ ‫‪ S‬سْ َ< ع ا ‪ّ < 1َ َ :ّV‬‬ ‫ِو َ& ود < ر'^ ‪G-‬رَ‪ُ r3 ُ 8 3‬آّ ‪ ،‬وْ َ< ْ َ ا ‪.‬‬

‫‪ ْc+ّ 4‬و ' ْ ّ‪ َ ْV-ْ #ْ 1ِ ْT‬نْ !!‬ ‫\ ْ ْ ِ ‪ ،#‬و ْ' ْ‬ ‫‪ :‬صْ ا‪ َ ْ R‬نْ ْ‪ َ ْV-ْ ?ِ B‬ن دَاآ)@? @? َ‬ ‫ُ‪َ ِ $‬‬ ‫‪َ $ْ B‬اءْ‪.‬‬ ‫'ْا َ‬ ‫‪ B‬لْ ا ّ‪V‬و‪6‬ا َ‪ Q‬تْ < ْ ْ‬ ‫‪َ ْ &َ ,6O 1ْ َ ْX %‬‬ ‫‪ِ ِ :‬‬ ‫> ِ‪َVW‬ة ُ ْ(ْ ْ ‪2‬‬ ‫‪ َ !ْ :‬نْ رْ ْ‪َ ْl‬‬ ‫‪ْ M‬‬ ‫‪ ،ْ :‬دَانْ ِ‬ ‫وْ ْ‪ َ 1‬دْ ا ‪َ 6‬ا ِ‬ ‫‪َ h َ ْ ْ ِ B‬ة ُ ْ‪: ْJ‬‬ ‫‪ َa‬ا ّ ْ‬ ‫وْﯕ ‪ْ ْi‬‬ ‫‪ 4‬لْ ا ‪ .‬جْ‪.‬‬ ‫‪ُ َ $@ 3‬ه ْ ْ َ‬ ‫> تْ @? ﯕ‪ ْG‬ا ‪6Gَ 6‬ة ْ< ‪K‬ر‪6‬ات َ‪ 0َ !ْ ْ َ %‬وْدُوشْ ْ‬ ‫‪َ B‬‬ ‫ن ْ ْ&‪ ْv‬ا َ‬ ‫َِ أ‪6‬‬ ‫‪ ) S‬درب إ‪ %‬م ‪ َ Eَ jH1‬ن‪.‬‬ ‫ل ْ‪ْ %‬‬ ‫‪ p‬وْ ‪6‬‬ ‫‪َ$ْ 4‬اءْ ْ‪َ َ ْ 4ْ 1‬‬ ‫‪ ْ$7‬ا َ‬ ‫‪ 4‬لْ ا ‪ .‬جْ < ْ َ وْ ُه مْ ْ‪Vّ 1‬و‪6‬ا َ‪ Q‬تْ ْ‪ْ +‬‬ ‫> تْ @? ْ َ‬ ‫‪َ B‬‬ ‫َه دْ ا َ‬ ‫ل ْ‬ ‫‪ B‬لْ ا ْ َ‪ ِ +‬وْ ‪6‬‬ ‫‪َ ْ ْ8 Gِ ْ a‬‬ ‫[(ْ ْ‪ْ -‬‬ ‫‪ a‬جْ ‪ْ %.‬‬ ‫‪ B‬لْ ا ‪6‬‬ ‫' وْ ُ ْ ْ‪َ ,‬‬ ‫‪ َ ِG 3‬أ‪ْGْ ْ َ 6‬رُو ْ َ‬ ‫) َآ ْ‬ ‫‪ ْG%‬ا ّ‬ ‫وْ ت وَا ْ‬ ‫‪ُ p‬و َ‪ ُ ُ 1ْ 1‬رْ ْ َ زُوطْ‪.‬‬


The Nobel Prize in Chemistry 2011 A remarkable mosaic of atoms In quasicrystals, we find the fascinating mosaics of the Arabic world reproduced at the level of atoms: regular patterns that never repeat themselves. However, the configuration found in quasicrystals was considered impossible, and Dan Shechtman had to fight a fierce battle against established science. The Nobel Prize in Chemistry 2011 has fundamentally altered how chemists conceive of solid matter. Aperiodic mosaics, such as those found in the medieval Islamic mosaics of the Alhambra Palace in Spain and the Darb-i Imam Shrine in Iran, have helped scientists understand what quasicrystals look like at the atomic level. In those mosaics, as in quasicrystals, the patterns are regular – they follow mathematical rules – but they never repeat themselves. Naturally occurring quasicrystals have since been discovered in mineral samples from a Russian river. A Swedish company has also found them acting as a reinforcement in a certain form of steel. Scientists, who have since also reproduced quasicrystals in the laboratory, are currently experimenting with using them in products including frying pans and diesel engines. Andrew Goodwin, of the Department of Chemistry at Oxford university, who praised the discovery as “fantastic”, said: “Shechtman’s quasi-crystals are now widely used to improve the mechanical properties of engineering materials and are the basis of an entirely new branch of structural science. If there is one particular lesson we are taking from his research it is not to underestimate the imagination of nature herself.”

ْ‫ ْء‬3 . ‫ فْ ا‬W َ 0ِ ْ ‫ ٱ‬B َ' ْ Eُ ْ xَ0: ْ ْ ْ‫ َاج‬0ْ !ّ ‫ا‬ ْ‫ ج‬. ‫ لْ ا‬4 َ ْ ْ ْ‫ْ َ< ْ ْ ْب‬X % ِ

‫َاء‬$ْ 4 َ ‫ْ ا‬$7 ْ +ْ ْ Qَ ‫ا‬6‫و‬Vّ , َ َ ْ$Cْ ْ

: ْ‫ َ< ْﯖ ل‬،ْ‫اف‬6Vْ ?ِ ,ْ a ْ &ْ ْ <َ ْ ِ % َ ?ِ َ َ ْ( $َ ‫ْ ا‬G% ْ ‫(ْ َه دْ ا ْ ْ َة ْ َا‬$ّ ْ ‫ دِي‬J َ

O |+'‫ ا‬.... W , ‫ & ف‬# ‫ & ف ا‬x‫ و‬, ‫ي & ف‬K ‫ذ ^ ا‬ O 1[ ....(Ep , ‫ & ف‬x # ‫ و & ف ا‬, ‫ & ف‬x ‫ي‬K ‫وذ ^ ا‬ O‫ * دو‬....u$%‫ ا‬, ‫ & ف‬x # ‫ & ف ا‬x‫ و‬, ‫ & ف‬x ‫ي‬K ‫وذ ^ ا‬ O 0 ‫ ا‬..... % (>‫ ر‬, ‫ & ف‬# ‫ و & ف ا‬, ‫ي & ف‬K ‫وذ ^ ا‬

. y ِ &َ ‫ا‬

‫قا‬ َ Gَ j َ "= ً 1ِBَ g. ‫ ِإ‬Tِ 1ْ 0ِ ْ ‫(ْ ا‬%ِ ْT!ُ ِ ‫ أُو‬%َ ‫ " َو‬:

&< ‫ ل ا‬Q ‫و‬


‫وأ ‪V‬ل ا‪ a‬أن ' *‪ k -‬ا ‪W‬‬

‫( و '* ) ا ‪$‬ا‬ ‫وا ‪ a ) 4‬رب ا ‪0‬‬

‫( و ' ‪71 % k10‬‬ ‫(‬

‫@‪ k‬ا ‪T'$6‬‬


‫ ت‬- &$ ‫ا‬ : ‫ت‬g +َ ْ‫ ُ! َ و‬6ْ .?> ‫ ز‬, ‫ ا‬G$B- 8 G$B- ‫ ء‬1 ‫ أ ? ا‬، َ )َ ْ @َ ‫[ َ لْ ا‬ ْ ‫(ْ أ‬%ِ ْ- 7 . ‫ ا‬kِ ْ ‫ج إ‬ ُ !َ 4ْ 'َ َ ِ ‫آِ! ب‬ Grid Method Classification of Islamic Geometric Patterns, Ahmad M. Aljamali and Ebad Banissi Visualisation and Graphics Research Unit Department of Computing, Information Systems & Mathematics South Bank University. Ornamental brickwork theoretical and applied symmetrology and classification of patterns E. MAKOVICKY, University of Copenhagen, Institute of Mineralogy. Mathematics and Arts: Connections between Theory and Practice in the Medieval Islamic World Alpay¨Ozdural, Faculty of Architecture, Eastern Mediterranean University. Pythagoras, his theorem and some gadgets James Clifton Eaves. Mosaîques, cristaux et quasi-cristaux Jean-René Chazottes. Art inspired by some classical geometry problems and by modularity SARHANGI Reza. Play with Infinite Jean-Marc Castera, Artist mathematician. TheWhirlingKites of Isfahan : Geometric Variations on a Theme PETERR. CROMWELL AND ELISABETTABELTRAM.


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http://www.cut-the-knot.org/pythagoras/index.shtml http://fr.wikipedia.org/wiki/Pavage_de_Penrose http://debart.pagesperso-orange.fr/college/carre_college.html http://www.cut-the-knot.org/manifesto/ArtisansAndMathematicians.shtml http://www.antiochgate.com/index.htm http://www.qucub.com/home_en http://www.planete-revelations.com/t9883-les-quasi-cristaux-geometrie-hyper-dimensionnelle http://therese.eveilleau.pagesperso-orange.fr/pages/jeux_mat/textes/pavage_17_types.htm http://dar.bibalex.org/webpages/mainpage.jsf?BibID=273407 http://www.inclassablesmathematiques.fr/tag/abu%27l%20wafa http://www.rtbot.net/zellige http://www.celtech.ma/zellijbeldi/Arabe/chabakat02.html http://younesdesign.com/category/publications/ http://www.zellige.ma/Fontaines-en-zellige-marocain-4.html http://islamic-arts.org/2012/tiles-of-infinity/ http://www.qinomics.com/2011/10/ridiculed-scientist-is-vindicated-with-nobel-prize/ http://www.nobelprize.org/nobel_prizes/chemistry/laureates/2011/press.html http://images.math.cnrs.fr/Prix-Nobel-de-chimie-quasi.html http://i369.photobucket.com/albums/oo131/a_arabbeigi/Emamzadeha/DarbeEmam/25.jpg http://www.ft.com/cms/s/0/ed418b02-ef53-11e0-8c49-00144feab49a.html#axzz26TMvdc34 http://www.planete-revelations.com/t9883-les-quasi-cristaux-geometrie-hyper-dimensionnelle http://www.fondamentaldesign.com/wp-content/uploads/175.jpg


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