Το βιβλίο του δασκάλου στ τάξη του δημοτικού

™Ùã T¿ÍË BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ ™ËÌ›ˆÛË: ™Ù· Ï·›ÛÈÔ Ù˘ ‡·Ú͢ ÂÍ·ÈÚ¤ÛÂˆÓ Û οı ηÓfiÓ· ı· ‹Ù·Ó ›Ûˆ˜ ¯Ú‹ÛÈÌÔ Ó· ·ÚÔ˘- ÛÈ¿ÛÔ˘Ì ÛÙÔ˘˜ Ì·ıËÙ¤˜ Û¯‹Ì·Ù· Ù· ÔÔ›· ‰ÂÓ ¤¯Ô˘Ó Î·Ó¤Ó·Ó ¿ÍÔÓ· Û˘ÌÌÂÙÚ›·˜ (.¯. ÙÔ Ï¿ÁÈÔ ·Ú·ÏÏËÏfiÁÚ·ÌÌÔ). ∂Ê·ÚÌÔÁ¤˜ 1Ë & 2Ë ™ÙȘ ÂÚÈÛÛfiÙÂÚ˜ Û˘ÌÌÂÙÚÈΤ˜ ηٷÛÙ¿ÛÂȘ ÔÈ ¿ÍÔÓ˜ ¤¯Ô˘Ó Ï¿ÁÈ· ‰È‡ı˘ÓÛË ˆ˜ ÚÔ˜ ÙÔ ÂÚ›- ÁÚ·ÌÌ· ÙÔ˘ ‚È‚Ï›Ô˘ Î·È fi¯È ÔÚÈ˙fiÓÙÈ· ‹ ηٷÎfiÚ˘ÊË. ™Ùfi¯Ô˜ Â›Ó·È Ó· ·ÔÊ¢¯ı› Ô ÂÁÎψ‚ÈÛÌfi˜ ÙÔ˘ Ì·ıËÙ‹ ÛÙȘ ÚÔÓÔÌȷΤ˜ ηÙ¢ı‡ÓÛÂȘ ÙÔ˘ ÂÚÈ‚¿ÏÏÔÓÙÔ˜ Î·È Ó· ÌÂȈı› Ë Èı·ÓfiÙËÙ· Ó· ÎÈÓÂ›Ù·È ·Ú¿ÏÏËÏ· ÚÔ˜ ÙÔ ÂÚ›ÁÚ·ÌÌ· ÙÔ˘ ‚È‚Ï›Ô˘, ÁÂÁÔÓfi˜ Ô˘ Ô‰ËÁ› Û ϿıË fiˆ˜ Ê·›ÓÂÙ·È ÛÙÔ ‰ÈÏ·Ófi Û¯‹Ì· : ∏ ÚÒÙË Û˘ÛÙËÌ·ÙÈ΋ ηٷÛ΢‹ Û˘ÌÌÂÙÚÈÎÔ‡ Û¯‹Ì·ÙÔ˜ (ÂÊ·ÚÌÔÁ‹ 2Ë) Á›ÓÂÙ·È Û ÙÂÙÚ·ÁˆÓÈ- Ṳ̂ÓÔ ¯·ÚÙ› ÙÔ ÔÔ›Ô ‰È¢ÎÔχÓÂÈ ÙË Ì¤ÙÚËÛË ·ÏÏ¿ Î·È ÙËÓ Î›ÓËÛË fiÙ·Ó Ô ¿ÍÔÓ·˜ Â›Ó·È ÔÚÈ˙fiÓÙÈÔ˜ ‹ ηٷÎfiÚ˘ÊÔ˜. ™ËÌ›ˆÛË: ÙÔ ÙÂÙÚ·ÁˆÓÈṲ̂ÓÔ ¯·ÚÙ› ÂÌÔ‰›˙ÂÈ ÙË Ì¤ÙÚËÛË Î·È ÙËÓ Î›ÓËÛË fiÙ·Ó Ô ¿ÍÔÓ·˜ Â›Ó·È Ï¿ÁÈÔ˜. ŒÙÛÈ, ‰›ÓÂÙ·È Ë Â˘Î·ÈÚ›· Ó· ·Ó·‰Âȯı› Èı·Ó‹ ηٿÛÙ·ÛË ·ÔÙ˘¯›·˜ ÛÙÔÓ Ï¿- ÁÈÔ ¿ÍÔÓ· Î·È Ó· ·ÓÙÈÌÂÙˆÈÛÙ› ¿ÌÂÛ·. ∏ ÂÈÙ˘¯‹˜ ·ÓÙÈÌÂÙÒ- ÈÛË ÙÔ˘ Ê·ÈÓÔ̤ÓÔ˘ ı· ÂÈÙÚ¤„ÂÈ ÛÙÔ˘˜ Ì·ıËÙ¤˜ Ó· ·ÓÙÈÌÂÙˆ- ›ÛÔ˘Ó ¯ˆÚ›˜ ‰˘ÛÎÔÏ›· Û˘ÓËıÈṲ̂Ó˜ ηٷÛÙ¿ÛÂȘ ηٷÛ΢‹˜ Û˘ÌÌÂÙÚÈÎÔ‡ ۠ϢÎfi ¯·ÚÙ›, Ô˘ ı¤ÙÂÈ ÏÈÁfiÙÂÚ· ÂÌfi‰È· ÛÙËÓ ÂÚ›ÙˆÛË ÙÔ˘ Ï¿ÁÈÔ˘ ¿ÍÔÓ·. TETPA¢IO EP°A™IøN √È ·Û΋ÛÂȘ ÛÙÔ ∆ÂÙÚ¿‰ÈÔ ∂ÚÁ·ÛÈÒÓ ÍÂÎÈÓÔ‡Ó ·fi ÙËÓ ·Ó·ÁÓÒÚÈÛË Î·È Ô‰ËÁÔ‡Ó ÛÙËÓ Î·Ù·Û΢‹ Û˘ÌÌÂÙÚÈÎÒÓ Û¯ËÌ¿ÙˆÓ. ∏ ÔÚ›· Ô˘ ·ÎÔÏÔ˘ıÂ›Ù·È Â›Ó·È ·fi ÙÔ ÁÂÓÈÎfi ÛÙÔ ÂȉÈÎfi: ·fi ÙÔ ÌË Áˆ- ÌÂÙÚÈÎfi Û¯‹Ì· ÛÙÔ ÁˆÌÂÙÚÈÎfi Û¯‹Ì· ÒÛÙÂ Ë Ù˘È΋ ηٷÛ΢‹ Û˘ÌÌÂÙÚÈÎÔ‡ Û¯‹Ì·ÙÔ˜ ˆ˜ ÚÔ˜ ¿ÍÔÓ· Î·È Ë ‰È·Ù‡ˆÛ‹ Ù˘ Ó· ·Ó·‰ÂȯıÔ‡Ó Ì¤Û· ·fi ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ÙˆÓ Ì·ıËÙÒÓ. ÕÛÎËÛË 1Ë ¶Ú¤ÂÈ Ó· ¯·Ú¿ÍÔ˘Ó fiÛÔ˘˜ ¿ÍÔÓ˜ Û˘ÌÌÂÙÚ›·˜ ¤¯ÂÈ Î¿ı ۯ‹Ì·. ÕÛÎËÛË 2Ë ™˘ÌÌÂÙÚ›· (ˆ˜ ÚÔ˜ ÙÔÓ ¿ÍÔÓ· Ô˘ Â›Ó·È ¯·Ú·Á̤ÓÔ˜) ˘¿Ú¯ÂÈ ÌfiÓÔ ÛÙÔ Û¯‹Ì· Á. ÕÛÎËÛË 3Ë ∆Ô ÙÂÙÚ·ÁˆÓÈṲ̂ÓÔ ¯·ÚÙ› ı· ‚ÔËı‹ÛÂÈ Ôχ ÙÔ˘˜ Ì·ıËÙ¤˜ ÛÙË Û¯Â‰›·ÛË ÙˆÓ Û˘ÌÌÂÙÚÈÎÒÓ. ¶Úfi‚ÏËÌ· 1Ô ∞·ÓÙ‹ÛÂȘ ∆· ÁÚ¿ÌÌ·Ù· ∞, µ, ¢, ∂, ∫, §, ª, ¶, ™, ∆, À, æ Î·È ø ¤¯Ô˘Ó ¤Ó·Ó ¿ÍÔÓ· Û˘ÌÌÂÙÚ›·˜ Ù· ∏, £, π, •, √, º Î·È Ã ¤¯Ô˘Ó ‰˘Ô ¿ÍÔÓ˜ Û˘ÌÌÂÙÚ›·˜. ∆Ô ÁÚ¿ÌÌ· «√» ·Ó Â›Ó·È ÔÏÔÛÙÚfiÁÁ˘ÏÔ, Û·Ó Î‡ÎÏÔ˜ (Î·È fi¯È Ì·ÎÚfiÛÙÂÓÔ), ¤¯ÂÈ ¿ÂÈÚÔ˘˜ ¿ÍÔÓ˜ Û˘ÌÌÂÙÚ›·˜. ¢Ú·ÛÙËÚÈfiÙËÙ· Ì ÚÔÂÎÙ¿ÛÂȘ: «∏ Û˘ÌÌÂÙÚ›· ÛÙË Ê‡ÛË» ∏ Û˘ÁÎÂÎÚÈ̤ÓË ‰Ú·ÛÙËÚÈfiÙËÙ· ‰›ÓÂÈ ÛÙÔ˘˜ Ì·ıËÙ¤˜ ÙËÓ Â˘Î·ÈÚ›· ÁÈ· Â¤ÎÙ·ÛË ÙÔ˘ ı¤Ì·ÙÔ˜ «Û˘ÌÌÂÙÚ›·» ÛÙË Ê‡ÛË Î·È ÙË ˙ˆ‹. ∏ ‚Ô‹ıÂÈ· Î·È ÔÈ Ô‰ËÁ›Â˜ ÙÔ˘ ‰·ÛοÏÔ˘ Â›Ó·È ÔχÙÈ̘ ÒÛÙ ٷ ·È‰È¿ Ó· ¿ÚÔ˘Ó ÙȘ ‚·ÛÈΤ˜ ηÙ¢ı‡ÓÛÂȘ ÛÙÔÓ ÙÚfiÔ Ì ÙÔÓ ÔÔ›Ô ı· ÂÚÁ·ÛÙÔ‡Ó Î·È ı· ÚÔÛÂÁÁ›- ÛÔ˘Ó ÙÔ ı¤Ì·. ∆Ô ‰Â‡ÙÂÚÔ ı¤Ì· ÁÈ· ‰ÈÂÚ‡ÓËÛË Î·È Û˘˙‹ÙËÛË ·ÚÔ˘ÛÈ¿˙ÂÈ Ôχ ÌÂÁ¿ÏÔ ÂӉȷʤÚÔÓ ÁÈ· Ù· ·È- ‰È¿ ηıÒ˜, ·Ó ÂÍÂÙ¿ÛÔ˘Ó ÙÔ Â›‰ˆÏÔ ÙÔ˘ ÌÈÛÔ‡ ÚÔÛÒÔ˘ ÌÈ·˜ ʈÙÔÁÚ·Ê›·˜ ÙÔ˘˜ Ì ηıÚ¤ÊÙË, ı· ‰È·ÈÛÙÒÛÔ˘Ó fiÙÈ ÙÔ ÚfiÛˆÔ «‰ÂÓ Â›Ó·È ÙÔ ‰ÈÎfi ÙÔ˘˜» ·ÊÔ‡ ÛÙË Ê‡ÛË Û¿ÓÈ· ˘¿Ú¯ÂÈ Ù¤ÏÂÈ· Û˘Ì- ÌÂÙÚ›·.150

BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ ™Ùã T¿ÍËKÂÊ¿Ï·ÈÔ 61Ô ªÂÙÚÒ ÂÈÊ¿ÓÂȘ Καλύπτω, βάφω, σκεπάζω√È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ηٷÓÔ› ÙË Ì¤ÙÚËÛË Ù˘ ÂÈÊ¿ÓÂÈ·˜ Î·È Ó· ˘ÔÏÔÁ›˙ÂÈ ÙÔ ÂÌ‚·‰fi ÔÚıÔÁˆÓ›Ô˘. ✒ ¡· ÁÚ¿ÊÂÈ Î·È Ó· ‰È·‚¿˙ÂÈ ÌÂÙÚ‹ÛÂȘ ÂÈÊ·ÓÂÈÒÓ Ì ‰Âη‰ÈÎÔ‡˜, Û˘ÌÌÈÁ›˜ Î·È ÎÏ·ÛÌ·ÙÈÎÔ‡˜ ·ÚÈıÌÔ‡˜. ✒ ¡· χÓÂÈ ÚÔ‚Ï‹Ì·Ù· Û¯ÂÙÈο Ì ÌÂÙÚ‹ÛÂȘ ÂÈÊ·ÓÂÈÒÓ.√ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ˘ÔÏÔÁ›˙ÂÈ ÙÔ ÂÌ‚·‰fi ÔÚıÔÁÒÓÈÔ˘ Û¯‹Ì·ÙÔ˜ Î·È Ó· ÙÔ ÂÎÊÚ¿˙ÂÈ Ì ‰Âη‰ÈÎÔ‡˜, Û˘ÌÌÈÁ›˜ Î·È ÎÏ·ÛÌ·ÙÈÎÔ‡˜ ·ÚÈıÌÔ‡˜.¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ¶·Ú·ÙËÚ‹ıËÎ·Ó ‰˘ÛÎÔϛ˜ ÛÙË ‰È·‰Èηۛ· ÂÎÙ›ÌËÛ˘ ÙÔ˘ ÂÌ‚·‰Ô‡ ÌÈ·˜ ÂÈÊ¿ÓÂÈ·˜. ∆· ·È‰È¿,ÂÓÒ ÂÎÙÈÌÔ‡Ó Û¯ÂÙÈο ‡ÎÔÏ· ÙÔ Ì‹ÎÔ˜ ‹ ÙÔ Ï¿ÙÔ˜ ÌÈ·˜ ÂÈÊ¿ÓÂÈ·˜, ‰˘ÛÎÔχÔÓÙ·È Ó· ˘ÔÏÔÁ›-ÛÔ˘Ó ÙÔ ÂÌ‚·‰fi Ù˘ (Û˘Ó‰˘¿˙ÔÓÙ·˜ ÙȘ ‰˘Ô ÂÎÙÈÌ‹ÛÂȘ Ô˘ ¤Î·Ó·Ó) Î·È ·˘ı·›ÚÂÙ· ·Ó·Ê¤ÚÔ˘Ó ˆ˜ÂÌ‚·‰fi, ÙÔ Ì‹ÎÔ˜ Ù˘ ÌÂÁ·Ï‡ÙÂÚ˘ ÏÂ˘Ú¿˜ Û ÙÂÙÚ·ÁˆÓÈο ÂηÙÔÛÙ¿ ·Ó Ë ÂÈÊ¿ÓÂÈ· Â›Ó·È ÌÈÎÚ‹ ‹ÙÂÙÚ·ÁˆÓÈο ̤ÙÚ· ·Ó Ë ÂÈÊ¿ÓÂÈ· Â›Ó·È ÌÂÁ¿ÏË. √ ÚÔÛ‰ÈÔÚÈÛÌfi˜ (Î·È Ë Î·Ù·Û΢‹) ÙÔ˘ ÙÂÙÚ·ÁˆÓÈ-ÎÔ‡ ÂηÙÔÛÙÔ‡ Î·È ÙÔ˘ ÙÂÙÚ·ÁˆÓÈÎÔ‡ ‰ÂηÙfiÌÂÙÚÔ˘ ˆ˜ ÂÚÁ·Ï›ˆÓ ̤ÙÚËÛ˘ ÂÌ‚·‰Ô‡ Ô˘ ›ӷȿÌÂÛ· ¯ÂÈÚ›ÛÈÌ· ·fi ÙÔ˘˜ Ì·ıËÙ¤˜ (‰Ú·ÛÙËÚÈfiÙËÙ· 1Ë) ‚ÔËı¿ÂÈ ÛÙËÓ Î·Ù·ÓfiËÛË Î·È ÂÈÙ˘¯‹ ·ÓÙÈÌÂ-ÙÒÈÛË Ù¤ÙÔÈˆÓ ‰˘ÛÎÔÏÈÒÓ. ∫¿ÔȘ ¤ÓÓÔȘ ÛÙÔ ‚È‚Ï›Ô ÙÔ˘ Ì·ıËÙ‹ (fiˆ˜ ÛÙËÓ ÂÚ›ÙˆÛË ·˘Ù‹ ÙÔ ÙÂÙÚ·ÁˆÓÈÎfi ̤ÙÚÔ Î·È ÔÈ˘ԉȷÈÚ¤ÛÂȘ ÙÔ˘) ÂÈÛ¿ÁÔÓÙ·È ¿ÌÂÛ· ¯ˆÚ›˜ Ó· ÚÔËÁËıÔ‡Ó ‰Ú·ÛÙËÚÈfiÙËÙ˜. ∏ ÂÈÏÔÁ‹ ·˘Ù‹ ¤ÁÈÓÂÛÎfiÈÌ·, ηıÒ˜ ÔÈ ·Ó·Áη›Â˜ ÁÈ· ÙËÓ ÚÔÛ¤ÁÁÈÛË ÙˆÓ ÂÓÓÔÈÒÓ ·˘ÙÒÓ ‰Ú·ÛÙËÚÈfiÙËÙ˜ ı· ‹Ù·Ó ÈÔÂÚ›ÏÔΘ ·fi ÙËÓ ¿ÌÂÛË ·ÚÔ˘Û›·ÛË ÌÈ·˜ ÌÂÚÈÎÒ˜ ÁÓˆÛÙ‹˜ ¤ÓÓÔÈ·˜. ¢Ú·ÛÙËÚÈfiÙËÙ· 1Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ Ú¤ÂÈ Ó· ηٷÛ΢¿ÛÔ˘Ó ÙË ÌÔÓ¿‰· ̤ÙÚËÛ˘ ÙÔ˘ ÂÌ‚·‰Ô‡:ÙÔ ÙÂÙÚ·ÁˆÓÈÎfi ÂηÙÔÛÙfi Î·È ÙÔ ÙÂÙÚ·ÁˆÓÈÎfi ‰ÂηÙfiÌÂÙÚÔ. √È Ì·ıËÙ¤˜ ı· ‰È·ÈÛÙÒÛÔ˘Ó, ÚÔÛ·ıÒÓÙ·˜ Ó· ÌÂÙÚ‹ÛÔ˘Ó ÂÌ‚·‰¿ Ì ÙȘ ÌÔÓ¿‰Â˜ Ô˘ ηٷÛ·-·Û·Ó, ˆ˜ ÌÔÏÔÓfiÙÈ ¤¯Ô˘Ó ÙȘ ÌÔÓ¿‰Â˜ ̤ÙÚËÛ˘ ‰ÂÓ Â›Ó·È Â‡ÎÔÏÔ Ó· ÌÂÙÚ‹ÛÔ˘Ó ÙȘ ÂÈÊ¿ÓÂȘ ηÈÓ· ÊÙ¿ÛÔ˘Ó Û ·ÎÚÈ‚¤˜ ·ÔÙ¤ÏÂÛÌ·. ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ ÚÔ¯ˆÚÔ‡Ó (ÌÂÙ¿ ÙË ‰È·›ÛÙˆÛË ÙˆÓ ‰˘ÛÎÔÏÈÒÓ Ô˘ ·Ó·Î‡-ÙÔ˘Ó Î·Ù¿ ÙÔÓ ˘ÔÏÔÁÈÛÌfi ÙÔ˘ ÂÌ‚·‰Ô‡ ÌÈ·˜ ÂÈÊ¿ÓÂÈ·˜ Ì ÙÔ ÙÂÙÚ·ÁˆÓÈÎfi ÂηÙÔÛÙfi ‹ ÙÔ ÙÂÙÚ·-ÁˆÓÈÎfi ‰ÂηÙfiÌÂÙÚÔ) ÛÙËÓ ÂÊ·ÚÌÔÁ‹ ÙÔ˘ «Ì·ıËÌ·ÙÈÎÔ‡ ÙÚfiÔ˘» ÁÈ· ÙÔÓ ˘ÔÏÔÁÈÛÌfi ÙÔ˘ ÂÌ‚·‰Ô‡.∂ÈϤÔÓ ÂȯÂÈÚÂ›Ù·È Ô ¤ÏÂÁ¯Ô˜ Ù˘ ÂÎÙ›ÌËÛ˘ ÙÔ˘ ÂÌ‚·‰Ô‡ Ô˘ οÓÂÈ Ô Ì·ıËÙ‹˜ Ì ÙÔ ÓÔ˘ Ì ÙÔÚ·ÁÌ·ÙÈÎfi ÂÌ‚·‰fi, fiˆ˜ ˘ÔÏÔÁ›ÛÙËΠÌÂÙ¿ ·fi ̤ÙÚËÛË ÙˆÓ ‰È·ÛÙ¿ÛÂˆÓ Î·È ˘ÔÏÔÁÈÛÌÔ‡˜.∂Ó·ÏÏ·ÎÙÈÎÔ› ÙÚfiÔÈ Ì¤ÙÚËÛ˘ (‚‹Ì·Ù·, ¿ÓÔÈÁÌ· ·Ï¿Ì˘, ‰¿¯Ù˘Ï· Î.Ï.) ı· ‚ÔËı‹ÛÔ˘Ó ÙÔ˘˜ Ì·ıË-Ù¤˜ Ó· ÂÎÙÈÌÔ‡Ó Ì ÙÔ ÓÔ˘ ÈÔ Â‡ÎÔÏ· Î·È Ì ÌÂÁ·Ï‡ÙÂÚË ·ÎÚ›‚ÂÈ· Ù· ÂÌ‚·‰¿ ‰È¿ÊÔÚˆÓ ÂÈÊ·ÓÂÈÒÓ.∂›Û˘ Ì ÙËÓ ·ÚÔ˘Û›·ÛË ÙˆÓ ÌÔÓÙ¤ÏˆÓ «ÙÂÙÚ·ÁˆÓÈÎfi ̤ÙÚÔ» Î·È «ÌÈÛfi ÙÂÙÚ·ÁˆÓÈÎfi» ̤ÙÚÔ ı·ÔÙÈÎÔÔÈ‹ÛÔ˘Ó ÙȘ ¤ÓÓÔȘ Î·È ı· ‚ÔËıËıÔ‡Ó Î·Ù¿ ÙË ‰È·‰Èηۛ· ÂÎÙ›ÌËÛ˘. TETPA¢IO EP°A™IøN ∆Ô ‰Â‡ÙÂÚÔ Úfi‚ÏËÌ· Ú¤ÂÈ Ó· Ï˘ı› ÛÙÔ Û›ÙÈ, ηıÒ˜ οı ·È‰› ¯ÚÂÈ¿˙ÂÙ·È Ó· ÌÂÙÚ‹ÛÂÈ ÙȘ ‰È·-ÛÙ¿ÛÂȘ ÙÔ˘ ‰ˆÌ·Ù›Ô˘ ÙÔ˘. 151

™Ùã T¿ÍË BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ KÂÊ¿Ï·ÈÔ 62Ô µÚ›ÛΈ ÙÔ ÂÌ‚·‰fi ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘ Πλαγιάζω αλλά δεν αλλάζω! √È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ‰È·ÈÛÙÒÛÂÈ fiÙÈ ‰È·ÊÔÚÂÙÈο Û¯‹Ì·Ù· ÌÔÚ› Ó· ¤¯Ô˘Ó ÙÔ ›‰ÈÔ ÂÌ‚·‰fi. ✒ ¡· ˘ÔÏÔÁ›˙ÂÈ ÙÔ ÂÌ‚·‰fi ÔÔÈÔ˘‰‹ÔÙ ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘ Ì ÙË ‚Ô‹ıÂÈ· Ù‡Ô˘. ✒ ¡· χÓÂÈ ÚÔ‚Ï‹Ì·Ù· ˘ÔÏÔÁÈÛÌÔ‡ ÂÌ‚·‰Ô‡ ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘. √ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ˘ÔÏÔÁ›˙ÂÈ ÙÔ ÂÌ‚·‰fi ÔÔÈÔ˘‰‹ÔÙ ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘ Î·È Ó· ÙÔ Û˘ÁÎÚ›ÓÂÈ Ì ¿ÏÏ· ÂÌ‚·‰¿. ¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ∆· ‡„Ë ÙˆÓ ·Ú·ÏÏËÏÔÁÚ¿ÌÌˆÓ ÂÌÊ·Ó›˙Ô˘Ó ‰˘ÛÎÔϛ˜ ÂȉÈο ÛÙȘ ÂÚÈÙÒÛÂȘ ηٿ ÙȘ Ôԛ˜ ·ÊÔÚÔ‡Ó ¿ÏϘ, ÂÎÙfi˜ ·fi ÙËÓ Î·Ù·ÎfiÚ˘ÊË, ‰È¢ı‡ÓÛÂȘ. ∏ ÛˆÛÙ‹ ¯Ú‹ÛË ÙÔ˘ ÁÓÒÌÔÓ· ‚ÔËı¿ ÙfiÛÔ ÛÙÔ ÍÂ¤Ú·ÛÌ· ÙˆÓ ‰˘ÛÎÔÏÈÒÓ fiÛÔ Î·È ÛÙÔÓ ÂÌÏÔ˘ÙÈÛÌfi Ù˘ ÂÌÂÈÚ›·˜ ÙˆÓ Ì·ıËÙÒÓ ÁÈ· ηıÂÙfiÙË- Ù˜ ¤Íˆ ·fi ÙȘ ΢ڛ·Ú¯Â˜ ‰È¢ı‡ÓÛÂȘ (ÔÚÈ˙fiÓÙÈ· Î·È Î¿ıÂÙ·). ¢Ú·ÛÙËÚÈfiÙËÙ· 1Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ Ú¤ÂÈ Ó· «ÌÂÙ·ÊÚ¿ÛÔ˘Ó» ÙËÓ ÂÈÎfiÓ· Ì ÙÔ ·Ú·ÏÏËÏfiÁÚ·ÌÌÔ. ªÂ ¿ÏÏ· ÏfiÁÈ· Ú¤ÂÈ Ó· ÂÂÍÂÚÁ·ÛÙÔ‡Ó ÙȘ ÏËÚÔÊÔڛ˜ Ô˘ ·Ú¤¯ÂÈ ÁÈ· Ó· ··ÓÙ‹ÛÔ˘Ó ·Ó Ë πÊÈÁ¤- ÓÂÈ· ¤¯ÂÈ ‰›ÎÈÔ. ∂ȉÈÎfiÙÂÚ· Ú¤ÂÈ Ó· ·Ú·ÙËÚ‹ÛÔ˘Ó Ù· ‰‡Ô ÌÈÛ¿ ÙÚ›ÁˆÓ·, Ù· ÔÔ›· ÌÔÚÔ‡Ó Ó· ıˆ- ÚËıÔ‡Ó ˆ˜ ¤Ó·, Î·È Ó· ˘ÔÛÙËÚȯÙ› Ë ¿Ô„Ë fiÙÈ ÙÔ ÂÌ‚·‰fi Â›Ó·È 3 ÙÂÙÚ·ÁˆÓÈο ÂηÙÔÛÙ¿. ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ ÌÂÏÂÙÔ‡Ó ÙȘ ȉÈfiÙËÙ˜ ÙÔ˘ ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘ ÙȘ Ôԛ˜ ¤¯Ô˘Ó Û˘Ó·ÓÙ‹ÛÂÈ Û ÚÔËÁÔ‡ÌÂÓ˜ Ù¿ÍÂȘ (‚¿ÛÂȘ Î·È ‡„Ô˜). ªÔÚÔ‡Ó Ó· ¯·Ú¿ÍÔ˘Ó fiÔÈÔ ·fi Ù· ‡„Ë ı¤ÏÔ˘Ó Û ÔÔÈÔ‰‹ÔÙ ˙‡ÁÔ˜ ·Ú¿ÏÏËÏˆÓ Ï¢ÚÒÓ. ÀÔÁÚ·ÌÌ›˙Ô˘Ì fiÙÈ ÔÈ Ï¢ڤ˜ ÙȘ Ôԛ˜ Ù¤ÌÓÂÈ ÙÔ ‡„Ô˜ ÔÓÔÌ¿˙ÔÓÙ·È ‚¿ÛÂȘ ÙÔ˘ ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘. ™ÙË Û˘Ó¤¯ÂÈ· ÔÈ Ì·ıËÙ¤˜ ÚÔ¯ˆÚÔ‡Ó Û ÌÂÙ·Û¯ËÌ·ÙÈÛÌfi ÙÔ˘ ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘ Û ÔÚıÔÁÒÓÈÔ Ì ‰È·‰Èηۛ˜ ÎÔ‹˜ Î·È ·Ú¿ıÂÛ˘ ÙˆÓ ‰‡Ô ÎÔÌÌ·ÙÈÒÓ ÙÔ˘. ŒÙÛÈ ·Ó·Î·Ï‡ÙÔ˘Ó fiÙÈ ÔÈ ‚¿ÛÂȘ ÙÔ˘ ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘ Â›Ó·È ›Û˜ Ì ÙÔ Ï¿ÙÔ˜ ÙÔ˘ ÔÚıÔÁˆÓ›Ô˘ Î·È ÙÔ ‡„Ô˜ ÙÔ˘ Â›Ó·È ›ÛÔ Ì ÙÔ Ì‹ÎÔ˜ ÙÔ˘ ÔÚıÔÁˆÓ›Ô˘ ·ÓÙ›ÛÙÔȯ·. ™˘ÌÂÚ·›ÓÔ˘Ó fiÙÈ ÙÔ ÂÌ‚·‰fi ÙÔ˘˜ Â›Ó·È ÙÔ ›‰ÈÔ (Ë ·Ú¯È΋ ÂÈÊ¿ÓÂÈ· ·Ú·Ì¤ÓÂÈ Ë ›‰È·, ·Ú¿ ÙÔ˘˜ ÌÂÙ·Û¯ËÌ·ÙÈÛÌÔ‡˜, fiˆ˜ Î·È ÛÙÔ Ù¿ÓÁÎÚ·Ì ÛÙËÓ ÂÊ·ÚÌÔÁ‹ 1) Î·È ÙÂÏÈο ηٷϋÁÔ˘Ó ÛÙÔÓ Î·ÓfiÓ· Ô˘ ÔÚ›˙ÂÈ fiÙÈ «ÙÔ ÂÌ‚·‰fi ÙÔ˘ ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘ ÈÛÔ‡Ù·È Ì ÙÔ ÁÈÓfiÌÂÓÔ ÌÈ·˜ ‚¿Û˘ Â› ÙÔ ·ÓÙ›ÛÙÔÈ¯Ô ‡„Ô˜». TETPA¢IO EP°A™IøN ÕÛÎËÛË 2Ë ∏ Â͛ۈÛË Â›Ó·È 4,5 . ‚ = 38,25. ÕÛÎËÛË 3Ë ™ÙÔ ‰) ÌÔÚÔ‡Ó Ó· Û˘ÌÏËÚÒÛÔ˘Ó ÔÔÈÔ˘Û‰‹ÔÙ ·Ú¿ÁÔÓÙ˜ ‰›ÓÔ˘Ó ÁÈÓfiÌÂÓÔ ›ÛÔ Ì 225. ¶Úfi‚ÏËÌ· 1Ô ∆Ô Î·ı¤Ó· Â›Ó·È 16 . 12 = 192 Ù.Ì., Û˘ÓÔÏÈο 192 . 24 = 4.608 Ù.Ì. ¶Úfi‚ÏËÌ· 2Ô ∆Ô ÂÌ‚·‰fi ÙÔ˘ ˘Ê¿ÛÌ·ÙÔ˜ Â›Ó·È 25.368 Ù.ÂÎ. £· ¯ÚÂÈ·ÛÙԇ̠18% ÂÚÈÛÛfiÙÂÚÔ, ‰ËÏ·‰‹ 25.368 . 18% = 4.566,24. ™˘ÓÔÏÈο ı· ¯ÚÂÈ·ÛÙԇ̠29.934,24 ‹ 3 ÙÂÙÚ·ÁˆÓÈο ̤ÙÚ· ÂÚ›Ô˘ Ô˘ ı· ÎÔÛÙ›- ÛÔ˘Ó 45 ú.152

BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ ™Ùã T¿ÍËKÂÊ¿Ï·ÈÔ 63Ô µÚ›ÛΈ ÙÔ ÂÌ‚·‰fi ÙÚÈÁÒÓÔ˘ Αδυνάτισα! Μισός έµεινα!√È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ηٷÓÔ‹ÛÂÈ ÙË ‰È·‰Èηۛ· ‡ÚÂÛ˘ ÙÔ˘ ÂÌ‚·‰Ô‡ ÙÔ˘ ÙÚÈÁÒÓÔ˘. ✒ ¡· ˘ÔÏÔÁ›˙ÂÈ ÙÔ ÂÌ‚·‰fi ÙÚÈÁÒÓÔ˘ Ì ÙË ‚Ô‹ıÂÈ· Ù‡Ô˘. ✒ ¡· χÓÂÈ ÚÔ‚Ï‹Ì·Ù· ÂÌ‚·‰ÒÓ ÙÚÈÁÒÓÔ˘.√ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ˘ÔÏÔÁ›˙ÂÈ ÙÔ ÂÌ‚·‰fi ÙÚÈÁÒÓÔ˘.¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ¶·Ú·ÙËÚ‹ıËÎ·Ó ‰˘ÛÎÔϛ˜ ÛÙË ‰È·‰Èηۛ· ¯¿Ú·Í˘ ÙÔ˘ ‡„Ô˘˜ ÙÚÈÁÒÓÔ˘, ÂȉÈο ÛÙȘ ÂÚÈÙÒÛÂȘÔ˘ ·ÊÔÚÔ‡Ó ¿ÏϘ, ÂÎÙfi˜ ·fi ÙËÓ Î·Ù·ÎfiÚ˘ÊË, ‰È¢ı‡ÓÛÂȘ, ‹ ‚Ú›ÛÎÔÓÙ·È ¤Íˆ ·fi ÙÔ Û¯‹Ì·. ∏ 2ˉڷÛÙËÚÈfiÙËÙ· ‚ÔËı¿ ÚÔ˜ ·˘Ù‹ ÙËÓ Î·Ù‡ı˘ÓÛË Î·ıÒ˜ ÔÈ Ì·ıËÙ¤˜ ηÏÔ‡ÓÙ·È Ó· ·ÓÙÈÌÂÙˆ›ÛÔ˘ÓÌfiÓÔÈ ÙÔ˘˜ ·˘Ù¤˜ ÙȘ ȉȷ›ÙÂÚ˜ ηٷÛÙ¿ÛÂȘ. ∏ ÛˆÛÙ‹ ¯Ú‹ÛË ÙÔ˘ ÁÓÒÌÔÓ· ‚ÔËı¿ÂÈ ÛÙËÓ ·ÓÙÈÌÂÙÒ-ÈÛË ·˘ÙÒÓ ÙˆÓ ‰˘ÛÎÔÏÈÒÓ. ¢Ú·ÛÙËÚÈfiÙËÙ· 1Ë ¢È·ÈÛÙÒÓÔ˘Ó fiÙÈ «ÙÔ ÂÌ‚·‰fi ÙÔ˘ ÙÚÈÁÒÓÔ˘ Â›Ó·È ›ÛÔ Ì ÙÔ ÌÈÛfi ÙÔ˘ ÂÌ‚·‰Ô‡ ÙÔ˘ ÙÂÙÚ·ÁÒÓÔ˘». ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ ÌÂÏÂÙÔ‡Ó Ù· ̤ÚË ÙÔ˘ ÙÚÈÁÒÓÔ˘ Î·È ÍÂÎÈÓÒÓÙ·˜ ·fi ÙË̤ÙÚËÛË ÙÔ˘ ÙÚÈÁÒÓÔ˘ ÚÔ¯ˆÚÔ‡Ó ÛÙË Û‡ÁÎÚÈÛË ÙÚÈÁÒÓÔ˘ Î·È ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘ Ì Ú·ÎÙÈÎfiÙÚfiÔ (Û‡ÓıÂÛË ‰‡Ô ·ÓÔÌÔÈfiÙ˘ˆÓ ÙÚÈÁÒÓˆÓ, ‰ËÌÈÔ˘ÚÁ›· ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘) Î·È Î·Ù·Ï‹ÁÔ˘ÓÛÙË ‰È·›ÛÙˆÛË fiÙÈ «ÙÔ ÂÌ‚·‰fi ÙÔ˘ ÙÚÈÁÒÓÔ˘ Â›Ó·È ›ÛÔ Ì ÙÔ ÌÈÛfi ÙÔ˘ ÂÌ‚·‰Ô‡ ÙÔ˘ ·Ú·ÏÏËÏÔÁÚ¿Ì-ÌÔ˘ Ô˘ ¤¯ÂÈ ÙËÓ ›‰È· ‚¿ÛË Î·È ÙÔ ›‰ÈÔ ‡„Ô˜». ªÔÚÔ‡Ó ÛÙË Û˘Ó¤¯ÂÈ· Ó· Â·ÏËı‡ÛÔ˘Ó ÙÔÓ Î·ÓfiÓ· οÓÔÓÙ·˜ ÙȘ Ú¿ÍÂȘ. ∂Âȉ‹ Ë ÁÂӛ΢ÛË ·˘Ù‹ Â›Ó·È ‰‡ÛÎÔÏË ÁÈ· ÙÔ˘˜ Ì·ıËÙ¤˜, ηÏfi ı· ‹Ù·Ó Ó· ÂÈÚ·Ì·ÙÈÛÙÔ‡Ó Û‰ȿÊÔÚ· ›‰Ë ÙÚÈÁÒÓˆÓ, ‰Ô˘Ï‡ÔÓÙ·˜ ·ÙÔÌÈο ‹ Û ÔÌ¿‰Â˜.∂Ê·ÚÌÔÁ‹ 1Ë ∆Ô Ù¿ÓÁÎÚ·Ì Î·Ïfi ı· Â›Ó·È Ó· ηٷÛ΢·ÛÙ› ·fi ¯·ÚÙfiÓÈ Ì ‰È·ÛÙ¿ÛÂȘ 10 x 10 ÂηÙÔÛÙ¿. ∏ÂÊ·ÚÌÔÁ‹ Â·ÏËı‡ÂÈ (Ú·ÎÙÈο) ÙÔÓ Î·ÓfiÓ· Ì ÙÚÂȘ ÙÚfiÔ˘˜: ✒ ÂÓÒÓÔ˘Ì ٷ ÙÚ›ÁˆÓ· Î·È Û¯ËÌ·Ù›˙Ô˘Ì ¤Ó· ·Ú·ÏÏËÏfiÁÚ·ÌÌÔ. ∫·ÙfiÈÓ ˘ÔÏÔÁ›˙Ô˘Ì ÙÔ ÂÌ‚·‰fi ÙÔ˘ Î·È ÙÔ Û˘ÁÎÚ›ÓÔ˘Ì Ì ÙÔ ÂÌ‚·‰fi ÙÔ˘ ÙÂÙÚ·ÁÒÓÔ˘ (Â›Ó·È ›Û·). ✒ ÂÓÒÓÔ˘Ì ٷ ÙÚ›ÁˆÓ· Î·È Û¯ËÌ·Ù›˙Ô˘Ì ¤Ó· ÙÂÙÚ¿ÁˆÓÔ. ™˘ÁÎÚ›ÓÔ˘Ì ٷ ‰‡Ô ÙÂÙÚ¿ÁˆÓ· (Â›Ó·È ›Û·). ✒ ÙÔÔıÂÙԇ̠ٷ ÙÚ›ÁˆÓ· Â¿Óˆ ÛÙÔ ÙÂÙÚ¿ÁˆÓÔ Ì ÙÚfiÔ ÒÛÙ ӷ Û¯ËÌ·Ù›ÛÔ˘Ó ¤Ó· ÙÂÙÚ¿- ÁˆÓÔ. ∆· ‰‡Ô ÙÂÙÚ¿ÁˆÓ· (ÙÔ Â¿Óˆ Î·È ÙÔ Î¿Ùˆ) Û˘Ì›ÙÔ˘Ó. TETPA¢IO EP°A™IøN¶Úfi‚ÏËÌ· 1Ô ∆Ô ÂÌ‚·‰fi Â›Ó·È 32 . 16 : 2 = 256 Ù.Ì. 256 – 64 = 192 (¯ˆÚ›˜ ÙÔ Û›ÙÈ) 192 . 8 = 1.536 ú 153

™Ùã T¿ÍË BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ KÂÊ¿Ï·ÈÔ 64Ô µÚ›ÛΈ ÙÔ ÂÌ‚·‰fi ÙÚ·Â˙›Ô˘ Το εµβαδό του τραπεζίου;; √È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ·Ó·ÁÓˆÚ›˙ÂÈ ÙÔ ÙÚ·¤˙ÈÔ Î·È Ó· ηٷÓÔ› ÙË ‰È·‰Èηۛ· ‡ÚÂÛ˘ ÙÔ˘ ÂÌ‚·‰Ô‡ ÙÔ˘. ✒ ¡· ‚Ú›ÛÎÂÈ ÙÔ ÂÌ‚·‰fi ÙÔ˘ ÙÚ·Â˙›Ô˘ Ì ÙË ‚Ô‹ıÂÈ· Ù‡Ô˘. ✒ ¡· χÓÂÈ ÚÔ‚Ï‹Ì·Ù· ÂÌ‚·‰ÒÓ ÙÚ·Â˙›Ô˘ Î·È ¿ÏÏˆÓ ÔÏ˘ÁÒÓˆÓ. √ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ·Ó·ÁÓˆÚ›˙ÂÈ Ù· ÙÂÙÚ¿Ï¢ڷ, Ó· Ù· ÔÌ·‰ÔÔÈ› ·Ó¿ÏÔÁ· Ì ÙȘ ȉÈfiÙËÙ¤˜ ÙÔ˘˜ ✒ ¡· ‚Ú›ÛÎÂÈ ÙÔ ÂÌ‚·‰fi ÙÚ·Â˙›Ô˘ Î·È Ó· χÓÂÈ ÚÔ‚Ï‹Ì·Ù· Ì ÂÌ‚·‰¿ ÙÂÙÚ·χڈÓ. ¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ∆· ·Ú·ÏÏËÏfiÁÚ·ÌÌ· Â›Ó·È ÁÓˆÛÙ¿ ÛÙÔ˘˜ Ì·ıËÙ¤˜. øÛÙfiÛÔ ÂӉȷʤÚÔÓ ·ÚÔ˘ÛÈ¿˙ÂÈ Ë Î·Ù·- ÓfiËÛË ÙˆÓ ÎÔÈÓÒÓ Î·È ‰È·ÊÔÚÂÙÈÎÒÓ È‰ÈÔًوÓ, fiˆ˜ Î·È Ë ‰È·‰Ô¯È΋ ÔÚÁ¿ÓˆÛ‹ ÙÔ˘˜. ∏ ÚÒÙË ‰Ú·- ÛÙËÚÈfiÙËÙ· Â›Ó·È ‚ÔËıËÙÈ΋ ÚÔ˜ ·˘Ù‹ ÙËÓ Î·Ù‡ı˘ÓÛË. ∆· Û¯‹Ì·Ù· Ô˘ ·ÚÔ˘ÛÈ¿˙ÔÓÙ·È Â›Ó·È ‰È·- ÊÔÚÂÙÈÎÒÓ ÌÂÁÂıÒÓ Î·È ÚÔÛ·Ó·ÙÔÏÈÛÌÒÓ ÚÔÎÂÈ̤ÓÔ˘ Ó· ·ÔʇÁÂÙ·È Ë ÛÙÂÚÂfiÙ˘Ë ÂÎÌ¿ıËÛ‹ ÙÔ˘˜, fiˆ˜ ›ӷÈ, ÁÈ· ·Ú¿‰ÂÈÁÌ·, Ó· ÌËÓ ·Ó·ÁÓˆÚ›˙ÂÙ·È ¤Ó·˜ ÚfiÌ‚Ô˜ fiÙ·Ó ÙÔÔıÂÙÂ›Ù·È Ï¿ÁÈ· ‹ ¤Ó· ÙÂÙÚ¿ÁˆÓÔ fiÙ·Ó ÙÔÔıÂÙÂ›Ù·È fiˆ˜ Û˘ÓËı›˙ÂÙ·È ÁÈ· ÙÔ ÚfiÌ‚Ô. ™ÙËÓ ÂÓfiÙËÙ· ·˘Ù‹ Ú¤ÂÈ Ó· ‰Ôı› ȉȷ›ÙÂÚË ¤ÌÊ·ÛË Î·È ¯ÚfiÓÔ˜ ÛÙËÓ ÂÎÌ¿ıËÛË ÙˆÓ ÂȉÈÎÒÓ ¯·Ú·ÎÙËÚÈÛÙÈÎÒÓ Î¿ı ÙÂÙÚ¿Ï¢ÚÔ˘. ∆· ‡„Ë ÙˆÓ ·Ú·ÏÏËÏÔÁÚ¿ÌÌˆÓ ÂÌÊ·Ó›˙Ô˘Ó ÙȘ ›‰È˜ ‰˘ÛÎÔϛ˜ Ì ٷ ‡„Ë ÙˆÓ ÙÚÈÁÒÓˆÓ. ∏ ÛˆÛÙ‹ ¯Ú‹ÛË ÙÔ˘ ÁÓÒÌÔÓ· ‚ÔËı¿ ÙfiÛÔ ÛÙËÓ ¿ÚÛË ÙˆÓ ‰˘ÛÎÔÏÈÒÓ fiÛÔ Î·È ÛÙÔÓ ÂÌÏÔ˘ÙÈÛÌfi Ù˘ ÂÌÂÈÚ›·˜ ÙˆÓ Ì·ıËÙÒÓ ÁÈ· ηıÂÙfiÙËÙ˜ ¤Íˆ ·fi ÙȘ ΢ڛ·Ú¯Â˜ ‰È¢ı‡ÓÛÂȘ. ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ ÌÂÏÂÙÔ‡Ó ÙÔ ÙÚ·¤˙ÈÔ Ì Ú·ÎÙÈÎfi ÙÚfiÔ. ŒÙÛÈ ¯ÚËÛÈÌÔÔÈÒ- ÓÙ·˜ ÙÔ ÌÈÏÈÌÂÙÚ¤ ¯·ÚÙ› ۯ‰ȿ˙Ô˘Ó ¤Ó· ÙÚ·¤˙ÈÔ, ÌÂÙÚÔ‡Ó Ù· ÙÂÙÚ¿ÁˆÓ¿ ÙÔ˘ Î·È ÂÎÙÈÌÔ‡Ó Ì ÙÔ ÓÔ˘ ÙÔ ÂÌ‚·‰fi. ™ÙË Û˘Ó¤¯ÂÈ· Îfi‚Ô˘Ó ‰‡Ô ·ÓÔÌÔÈfiÙ˘· (Ì ÙÔ Û¯¤‰Èfi ÙÔ˘˜) ÙÚ·¤˙È· Î·È Û˘Ó‰˘¿˙ÔÓÙ¿˜ Ù· Û¯ËÌ·Ù›˙Ô˘Ó ¤Ó· ·Ú·ÏÏËÏfiÁÚ·ÌÌÔ. ªÔÚÔ‡Ó Â‡ÎÔÏ· Ó· ˘ÔÏÔÁ›ÛÔ˘Ó ÙÔ ÂÌ‚·‰fi ÙÔ˘ ·Ú·ÏÏË- ÏÔÁÚ¿ÌÌÔ˘ ·ÏÏ¿ ··ÈÙÂ›Ù·È Ë ÂÓÂÚÁÔÔ›ËÛË Ù˘ ·Ú·ÙËÚËÙÈÎfiÙËÙ·˜ Î·È ‚ÔËıËÙÈÎÒÓ ÂÚˆÙ‹ÛÂˆÓ ÁÈ· Ó· ‚ÚÔ˘Ó ÙË Û¯¤ÛË ·Ó¿ÌÂÛ· ÛÙȘ ‚¿ÛÂȘ ÙÔ˘ ÙÚ·Â˙›Ô˘ Î·È ÙȘ ‚¿ÛÂȘ ÙÔ˘ ·Ú·ÏÏËÏÔÁÚ¿ÌÌÔ˘. ™ËÌ›ˆÛË: √ ˘ÔÏÔÁÈÛÌfi˜ ÙÔ˘ ÂÌ‚·‰Ô‡ ÙÔ˘ ÙÚ·Â˙›Ô˘ Ì ÙÔÓ ÙÚfiÔ Ô˘ ÚÔÙ›ÓÂÙ·È ‰ÂÓ Â›Ó·È Ô ÌÔÓ·‰ÈÎfi˜ ·ÏÏ¿ ¤Ó·˜ ·fi ÌÈ· ÏËıÒÚ· ÙÚfiˆÓ Ô˘ ÌÔÚ› Ó· ÛÎÂÊÙÔ‡Ó ÔÈ Ì·ıËÙ¤˜. TETPA¢IO EP°A™IøN ¶Úfi‚ÏËÌ· 1o ∆Ô ÂÌ‚·‰fi οı ÙÚ·Â˙›Ô˘ Â›Ó·È (17 + 11) . 3 : 2 = 42 Ù.Ì. ∆Ô ÂÌ‚·‰fi οı ÙÚÈÁÒÓÔ˘ Â›Ó·È 6 . 3 : 2 = 9 Ù.Ì. Î·È ÙÔ Û˘ÓÔÏÈÎfi ÂÌ‚·‰fi 102 Ù.Ì. (ÌÔÚ› Ó· ‚ÚÂı› Î·È ˆ˜ 6 . 17 = 102). ¢Ú·ÛÙËÚÈfiÙËÙ· Ì ÚÔÂÎÙ¿ÛÂȘ: «ÈÛÔÚÚÔË̤ÓË ‰È·ÙÚÔÊ‹» ∆· ÎfiÎÎÈÓ· ΢ÎÏ¿ÎÈ· Â›Ó·È Ù· ÏÈ·Ú¿ Î·È Ù· ÌÏ ÙÚÈÁˆÓ¿ÎÈ· ÔÈ ˘‰·Ù¿ÓıڷΘ.154

BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ ™Ùã T¿ÍËKÂÊ¿Ï·ÈÔ 65Ô µÚ›ÛΈ ÙÔ ÂÌ‚·‰fi ΢ÎÏÈÎÔ‡ ‰›ÛÎÔ˘ Κόβω κύκλους!√È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ηٷÓÔ› ÙË ‰È·‰Èηۛ· ‡ÚÂÛ˘ ÙÔ˘ ÂÌ‚·‰Ô‡ ÙÔ˘ ΢ÎÏÈÎÔ‡ ‰›ÛÎÔ˘. ✒ ¡· ‚Ú›ÛÎÂÈ ÙÔ ÂÌ‚·‰fi ÙÔ˘ ΢ÎÏÈÎÔ‡ ‰›ÛÎÔ˘ Ì ÙË ‚Ô‹ıÂÈ· Ù‡Ô˘. ✒ ¡· χÓÂÈ ÚÔ‚Ï‹Ì·Ù· Ì ÂÌ‚·‰¿ ΢ÎÏÈÎÒÓ ‰›ÛΈÓ.√ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ·Ó·ÁÓˆÚ›˙ÂÈ ÙȘ ȉÈfiÙËÙ˜ ÙÔ˘ ·ÎÏÔ˘, Ó· ‚Ú›ÛÎÂÈ ÙÔ ÂÌ‚·‰fi ΢ÎÏÈÎÔ‡ ‰›ÛÎÔ˘ Î·È Ó· χÓÂÈ Û¯ÂÙÈο ÚÔ‚Ï‹Ì·Ù·.¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ∆Ô ÎÂÊ¿Ï·ÈÔ ·˘Ùfi ÛÙԯ‡ÂÈ ÛÙËÓ ˘ÂÓı‡ÌÈÛË ÙÔ˘ ·ÎÏÔ˘, ÙˆÓ ¯·Ú·ÎÙËÚÈÛÙÈÎÒÓ ÛÙÔȯ›ˆÓ ÙÔ˘ ηÈÛÙËÓ Â‡ÚÂÛË ÙÔ˘ ÂÌ‚·‰Ô‡ ÙÔ˘. √ ·ÎÏÔ˜ ˆ˜ Û¯‹Ì· ÂÌÊ·Ó›˙ÂÈ È‰È·ÈÙÂÚfiÙËÙ˜ Û ۯ¤ÛË Ì ٷ ¿ÏÏ· Û¯‹Ì·Ù·. ∞ÔÙÂÏ› ¤Ó·Û‡ÓÔÏÔ ÛËÌ›ˆÓ Ô˘ ÈÛ·¤¯Ô˘Ó ·fi ÙÔ Î¤ÓÙÚÔ, ‰ËÏ·‰‹ ¤Ó·Ó ÁˆÌÂÙÚÈÎfi ÙfiÔ Ô˘ ‰‡ÛÎÔÏ· Á›ÓÂÙ·È·ÓÙÈÏËÙfi˜ ·fi ÙÔ˘˜ Ì·ıËÙ¤˜ ÔÈ ÔÔ›ÔÈ ÙÔÓ ·ÓÙÈÌÂÙˆ›˙Ô˘Ó ˆ˜ ¤Ó· fiÏÔ (ÌÈ· Û˘Ó¯‹ ηÌ‡ÏËÁÚ·ÌÌ‹). ∏ ¯Ú‹ÛË ÙÔ˘ ‰È·‚‹ÙË Î·È Ù· ÚÔ‚Ï‹Ì·Ù· ·ÔÛÙ¿ÛÂˆÓ ‚ÔËıÔ‡Ó ÙÔ˘˜ Ì·ıËÙ¤˜ ÛÙËÓ Î·Ï‡-ÙÂÚË Î·Ù·ÓfiËÛË Ù˘ ¤ÓÓÔÈ·˜ ÙÔ˘ ·ÎÏÔ˘. ™˘ÓËıÈṲ̂ÓË Â›Ó·È Â›Û˘ Ë Û‡Á¯˘ÛË Î‡ÎÏÔ˘ Î·È Î˘ÎÏÈÎÔ‡ ‰›ÛÎÔ˘ Ô˘ Ú¤ÂÈ Ó· ·ÓÙÈÌÂÙˆÈÛÙ› ÌÂȉȷ›ÙÂÚË Û˘˙‹ÙËÛË (Úfi‚ÏËÌ· 1Ô). ¢Ú·ÛÙËÚÈfiÙËÙ· 1Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ Ú¤ÂÈ Ó· ͯˆÚ›ÛÔ˘Ó Î˘ÎÏÈο Û¯‹Ì·Ù· ·fi ÙËÓ Î·ıËÌÂÚÈÓ‹˙ˆ‹, Ó· ·Ó·ÁÓˆÚ›ÛÔ˘Ó ÙȘ ȉÈfiÙËÙ˜ (ÂȉÈο ¯·Ú·ÎÙËÚÈÛÙÈο) ÙÔ˘ ·ÎÏÔ˘ Î·È Ó· ÂÈÎÂÓÙÚÒÛÔ˘Ó ÙËÓÚÔÛÔ¯‹ ÙÔ˘˜ ÛÙ· ¯·Ú·ÎÙËÚÈÛÙÈο Ù· ÔÔ›· ¯ÚËÛÈÌÂ‡Ô˘Ó ÁÈ· ÙËÓ ÂÚÈÁÚ·Ê‹ ÙÔ˘ ÌÂÁ¤ıÔ˘˜ ÙÔ˘. ¢È·-ÈÛÙÒÓÔ˘Ó fiÙÈ ÌÔÚԇ̠‡ÎÔÏ· Ó· ÌÂÙÚ‹ÛÔ˘Ì ÙËÓ ·ÎÙ›Ó· Î·È ÙË ‰È¿ÌÂÙÚÔ ÙÔ˘ ·ÎÏÔ˘ ÂÓÒ ÁÈ·ÔÔÈ·‰‹ÔÙ ¿ÏÏË Ì¤ÙÚËÛË ¯ÚÂÈ·˙fiÌ·ÛÙ ÙÔ . ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë ª¤Û· ·fi ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜, ÚÔÛ·ıÒÓÙ·˜ Ó· ÂÎÙÈÌ‹ÛÔ˘Ó ÙÔ ÂÌ‚·‰fi ÙÔ˘ ÌÂÁ¿-ÏÔ˘ (Ì·‡ÚÔ˘) ΢ÎÏÈÎÔ‡ ‰›ÛÎÔ˘ Ô‰ËÁÔ‡ÓÙ·È ÛÙȘ ·ÎfiÏÔ˘ı˜ ‰È·ÈÛÙÒÛÂȘ: ✒ ∏ ·ÎÙ›Ó· ÙÔ˘ ·ÎÏÔ˘ Â›Ó·È ÛËÌ·ÓÙÈÎfi˜ ·Ú¿ÁÔÓÙ·˜. ✒ ∆Ô ÙÂÙÚ¿ÁˆÓÔ Ô˘ ÔÚ›˙ÂÙ·È Ì ÏÂ˘Ú¿ ÙËÓ ·ÎÙ›Ó· ÙÔ˘ ·ÎÏÔ˘ ¤¯ÂÈ ÂÌ‚·‰fi ÌÂÁ·Ï‡ÙÂÚÔ ·fi ÙÔ _ ÙÔ˘ ·ÎÏÔ˘. ✒ ¢ÂÓ Â›Ó·È Â‡ÎÔÏÔ Ó· ˘ÔÏÔÁ›ÛÔ˘Ì ÙÔ ÂÌ‚·‰fi ÙÔ˘ ·ÎÏÔ˘ ÔÚ›˙ÔÓÙ·˜ ˆ˜ ÌÔÓ¿‰· ̤ÙÚËÛ˘ ÙÔ ÙÂÙÚ¿ÁˆÓÔ Ù˘ ·ÎÙ›Ó·˜, ηıÒ˜ ÁÈ· Ó· ηχ„Ô˘Ì ÙËÓ ÂÈÊ¿ÓÂÈ· ÙÔ˘ ·ÎÏÔ˘ ¯ÚÂÈ·˙fiÌ·ÛÙ 3 Ì 4 ÙÂÙÚ¿ÁˆÓ· (Ù· ·È‰È¿ ı· ··ÓÙ‹ÛÔ˘Ó «ÂÚ›Ô˘ 3 ‹ ÂÚ›Ô˘ 4, ‹ ÏÈÁfiÙÂÚ· ·fi 4 ‹ Ï›ÁÔ ÂÚÈÛÛfiÙÂÚ· ·fi 3») ✒ ∂·Ó·Ï·Ì‚¿ÓÔÓÙ·˜ ÙË Ì¤ÙÚËÛË Ì ¿ÏÏÔ˘˜ ·ÎÏÔ˘˜ Ë ‰È·›ÛÙˆÛË Â›Ó·È Ë ›‰È·. ÀÂÓı˘Ì›˙Ô˘Ì ÛÙÔ ÛËÌÂ›Ô ·˘Ùfi ÙÔ Úfi‚ÏËÌ· Ù˘ ‡ÚÂÛ˘ Ù˘ ÙÔ˘ Ì‹ÎÔ˘˜ ÙÔ˘ ·ÎÏÔ˘ (·Ó·Ê¤Ú-ıËΠÛÙË ‰Ú·ÛÙËÚÈfiÙËÙ· 1). ∆Ô Ì‹ÎÔ˜ ÙÔ˘ ·ÎÏÔ˘ Â›Ó·È «Ï›ÁÔ ÂÚÈÛÛfiÙÂÚÔ ·fi 3 ÊÔÚ¤˜ Ë ‰È¿ÌÂÙÚÔ˜ÙÔ˘ ·ÎÏÔ˘» (3,14 ÊÔÚ¤˜ ‹ ). ¢ÔÎÈÌ¿˙Ô˘Ì ÙÔ  Î·È Ì ÙÔ ÙÂÙÚ¿ÁˆÓÔ Ù˘ ·ÎÙ›Ó·˜ Î·È Ì ̤ÙÚËÛË (ÎψÛÙ‹, ÎÔ‹ ÂÓfi˜ ›‰ÈԢ·ÎÏÔ˘ Î·È Î‡ÏÈÛË ÛÙÔ ¯¿Ú·Î·) Â·ÏËı‡ԢÌ ÙÔ ·ÔÙ¤ÏÂÛÌ·. 155

™Ùã T¿ÍË BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ KÂÊ¿Ï·ÈÔ 66Ô ∫‡‚Ô˜ Î·È ÔÚıÔÁÒÓÈÔ ·Ú·ÏÏËÏÂ›‰Ô: ¤‰Ú˜ Î·È ·Ó·Ù‡ÁÌ·Ù· Να το κάνω πακέτο; √È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ۯ‰ȿ˙ÂÈ ·Ó·Ù‡ÁÌ·Ù· Î·È Ó· ηٷÛ΢¿˙ÂÈ Î‡‚Ô˘˜ Î·È ÔÚıÔÁÒÓÈ· ·Ú·ÏÏËÏÂ›‰·. ✒ ¡· ·Ú·ÙËÚ› Î·È Ó· ·Ó·ÁÓˆÚ›˙ÂÈ ÔÌÔÈfiÙËÙ˜ Î·È ‰È·ÊÔÚ¤˜ ÛÙËÓ ÂÈÊ¿ÓÂÈ· ÙÔ˘ ·‚Ô˘ Î·È ÙÔ˘ ÔÚıÔÁÒÓÈÔ˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘. ✒ ¡· ηٷÓÔ› ÙË ‰È·‰Èηۛ· ‡ÚÂÛ˘ ÙÔ˘ ÂÌ‚·‰Ô‡ ÙˆÓ ‚¿ÛˆÓ, Ù˘ ·Ú¿Ï¢Ú˘ Î·È Ù˘ ÔÏÈ- ΋˜ ÂÈÊ¿ÓÂÈ·˜ ÙÔ˘ ·‚Ô˘ Î·È ÙÔ˘ ÔÚıÔÁÒÓÈÔ˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘. √ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ·Ó·ÁÓˆÚ›˙ÂÈ ÙÔÓ Î‡‚Ô Î·È ÙÔ ÔÚıÔÁÒÓÈÔ ·Ú·ÏÏËÏÂ›‰Ô, Ó· ˘ÔÏÔÁ›˙ÂÈ ÙËÓ ·Ú¿Ï¢ÚË Î·È ÙËÓ ÔÏÈ΋ ÂÈÊ¿ÓÂÈ¿ ÙÔ˘˜ Î·È Ó· ·Ó·ÁÓˆÚ›˙ÂÈ ÙË Û¯¤ÛË ·Ó¿ÌÂÛ· ÛÙËÓ ÙÚÈۉȿÛÙ·ÙË ÌÔÚÊ‹ ÂÓfi˜ ÛÙÂÚÂÔ‡ Î·È ÛÙË ‰ÈۉȿÛÙ·ÙË ·Ó··Ú¿ÛÙ·Û‹ ÙÔ˘ (·Ó¿Ù˘ÁÌ·). ¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ∆Ô ¤Ú·ÛÌ· ·fi ÙȘ ‰‡Ô ‰È·ÛÙ¿ÛÂȘ Ù˘ ÂÈ‰ÔÌÂÙÚ›·˜ ÛÙȘ ÙÚÂȘ ‰È·ÛÙ¿ÛÂȘ Ù˘ ÛÙÂÚÂÔÌÂÙÚ›·˜ ··ÈÙ› ÙËÓ ‡·ÚÍË ˘„ËÏÔ‡ ÂÈ¤‰Ô˘ ¯ˆÚÔÙ·ÍÈÎÒÓ ÈηÓÔÙ‹ÙˆÓ ·fi ÙËÓ ÏÂ˘Ú¿ ÙÔ˘ Ì·ıËÙ‹ Î·È ÙË Û˘ÛÙËÌ·ÙÈ΋ ÔÚÁ¿ÓˆÛË Î·È ÙË ‰È·¯Â›ÚÈÛË ÔÙÈÎÒÓ ÏËÚÔÊÔÚÈÒÓ ÁÈ· ÙËÓ Â›Ï˘ÛË ÙˆÓ Û¯ÂÙÈÎÒÓ ÚÔ- ‚ÏËÌ¿ÙˆÓ. ™Ù· ·Ú¯Èο ÛÙ¿‰È· Ù˘ ÙÚÈۉȿÛÙ·Ù˘ ·ÂÈÎfiÓÈÛ˘ Â›Ó·È Ôχ ÛËÌ·ÓÙÈÎfi Ó· ·Ó··Ú›ÛÙ·Ù·È ÙÔ Úfi- ‚ÏËÌ· Ì ÙÚfiÔ ÔÙÈÎfi Î·È ¿ÌÂÛ· ¯ÂÈÚ›ÛÈÌÔ ·fi ÙÔ˘˜ Ì·ıËÙ¤˜, ÒÛÙ ÔÈ Î·Ù·Û΢¤˜ ÛÙÂÚÂÒÓ Ó· ÏÂÈ- ÙÔ˘ÚÁ‹ÛÔ˘Ó ˆ˜ ÌÔÓÙ¤ÏÔ Ù˘ ÚÔ‚ÏËÌ·ÙÈ΋˜ ηٿÛÙ·Û˘. ∆Ô ÂÔÙÈÎfi ˘ÏÈÎfi ı· ‚ÔËı‹ÛÂÈ ÙÔ Ì·ıËÙ‹ Ó· ηٷÛ΢¿ÛÂÈ ÌfiÓÔ˜ ÙȘ ‰ÈΤ˜ ÙÔ˘ ÂÈÎfiÓ˜ Î·È ıˆڛ˜, ÔÈ Ôԛ˜ ‰ÂÓ Û˘Ì›ÙÔ˘Ó Î·Ù’ ·Ó¿ÁÎË Ì ÙȘ ıˆڛ˜ ÙÔ˘ ‰·ÛοÏÔ˘ ÙÔ˘ ‹ ÙÔ˘ Û˘ÁÁڷʤ· ÙÔ˘ ‚È‚Ï›Ô˘. ¢Ú·ÛÙËÚÈfiÙËÙ· 1Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ Ú¤ÂÈ Ó· ·Ó·ÁÓˆÚ›˙Ô˘Ó ÙÔÓ Î‡‚Ô Û ·ÓÙÈΛÌÂÓ· ηıËÌÂÚÈ- Ó‹˜ ¯Ú‹Û˘. ∞ÎfiÌ· ¤Ú¯ÔÓÙ·È Û ÚÒÙË Â·Ê‹ Ì ٷ ¯·Ú·ÎÙËÚÈÛÙÈο ÙÔ˘. ™ÙË Û˘Ó¤¯ÂÈ· ·ÓÙÈÌÂÙˆ›- ˙Ô˘Ó Ú·ÎÙÈο ÙÔ ·Ó¿Ù˘ÁÌ· ÙÔ˘ ·‚Ô˘ Û·Ó Î·Ù·Û΢‹ ˙·ÚÈÔ‡ ·fi ‰ÔṲ̂ÓÔ ·Ó¿Ù˘ÁÌ·. ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ Ì ÙËÓ ›‰È· ‰È·‰Èηۛ· ÌÂÏÂÙÔ‡Ó ÙÔ ÔÚıÔÁÒÓÈÔ ·Ú·ÏÏËÏÂ›- Â‰Ô Ì¤Û· ·fi ¤Ó· ηıËÌÂÚÈÓfi ·ÓÙÈΛÌÂÓÔ (ÎÔ˘Ù› ‰ËÌËÙÚÈ·ÎÒÓ, ÌÈÛÎfiÙˆÓ, Î.Ï.). ∂ÈÛËÌ·›ÓÔ˘Ó ÙȘ ‰È·ÊÔÚ¤˜ ÛÙ· ‰‡Ô ·Ó·Ù‡ÁÌ·Ù· Î·È ÙË ‰˘Ó·ÙfiÙËÙ· ÙÔ˘ ·‚Ô˘ Ó· ¤¯ÂÈ ÂÚÈÛÛfiÙÂÚ· ·Ó·Ù‡ÁÌ·Ù· (11 Û˘ÓÔÏÈο) ·fi fi,ÙÈ ÙÔ ·Ú·ÏÏËÏÂ›‰Ô. TETPA¢IO EP°A™IøN ÕÛÎËÛË 1Ë (™˘ÓÈÛÙ¿Ù·È Ë ¯Ú‹ÛË ¯¿ÚÙÈÓˆÓ ÌÔÓÙ¤ÏˆÓ fiÔ˘ ¯ÚÂÈ¿˙ÂÙ·È) §‡ÛË: ∆Ô ÚÒÙÔ Ù˘ Â¿Óˆ ÛÂÈÚ¿˜ Î·È ÙÔ ÙÂÏÂ˘Ù·›Ô Ù˘ οو. ÕÛÎËÛË 2Ë ∏ χÛË ·ÂÈÎÔÓ›˙ÂÙ·È ÛÙÔ Û¯‹Ì· Â¿Óˆ ‰ÂÍÈ¿. ¶Úfi‚ÏËÌ· 3Ô ∏ χÛË ·ÂÈÎÔÓ›˙ÂÙ·È ÛÙÔ ‰ÈÏ·Ófi Û¯‹Ì·.156

BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ ™Ùã T¿ÍËKÂÊ¿Ï·ÈÔ 67Ô ∫‡‚Ô˜ Î·È ÔÚıÔÁÒÓÈÔ ·Ú·ÏÏËÏÂ›‰Ô: ·Î̤˜ Î·È ÎÔÚ˘Ê¤˜ Συναρµολογώντας κοµµάτια√È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ·Ó·ÁÓˆÚ›˙ÂÈ ÙȘ ·Î̤˜ Î·È ÙȘ ÎÔÚ˘Ê¤˜ ÙˆÓ ÛÙÂÚÂÒÓ ÛˆÌ¿ÙˆÓ. ✒ ¡· ηٷÛ΢¿˙ÂÈ Î·È Ó· ·Ú·ÙËÚ› ÌÔÓ٤Ϸ ·‚ˆÓ Î·È ÔÚıÔÁÒÓÈˆÓ ·Ú·ÏÏËÏÂÈ¤‰ˆÓ. ✒ ¡· ۯ‰ȿ˙ÂÈ Î‡‚Ô Î·È ÔÚıÔÁÒÓÈÔ ·Ú·ÏÏËÏÂ›Â‰Ô Û ¯·ÚÙ›.√ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ·Ó·ÁÓˆÚ›˙ÂÈ ·Î̤˜ Î·È ÎÔÚ˘Ê¤˜ Î·È Ó· ηٷÛ΢¿˙ÂÈ ÌÔÓ٤Ϸ ·‚Ô˘ Î·È ÔÚıÔÁÒÓÈÔ˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘. ✒ ¡· ·ÔÙ˘ÒÓÂÈ ÙÚÈۉȿÛٷٷ ·ÓÙÈΛÌÂÓ· Û ¯·ÚÙ›.¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ∏ ‰È·‰Èηۛ· ·Ó··Ú¿ÛÙ·Û˘ ÙÔ˘ ÛÙÂÚÂÔ‡ ÛÙÔ Â›Â‰Ô ‰ÂÓ Â›Ó·È ÌÔÓ·‰È΋. ŒÓ·˜ ·fi ÙÔ˘˜ ÙÚfi-Ô˘˜ Ì ÙÔ ÔÔ›Ô ÌÔÚԇ̠ӷ ÙËÓ ÚÔÛÂÁÁ›ÛÔ˘ÌÂ Â›Ó·È Ù· ·Ó·Ù‡ÁÌ·Ù·. ªÂÁ¿ÏÔ ÂӉȷʤÚÔÓ ı·Â›¯Â ÁÈ· ÙÔ˘˜ Ì·ıËÙ¤˜ Î·È Ë ·ÓÙ›ÛÙÚÔÊË ‰È·‰Èηۛ·: ¤Ú·ÛÌ· ·fi ÙÔ Â›Â‰Ô ÛÙÔ ¯ÒÚÔ. ¢Ú·ÛÙËÚÈfiÙËÙ· 1Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ ·ÓÙÈÏ·Ì‚¿ÓÔÓÙ·È Ì Ú·ÎÙÈÎfi ÙÚfiÔ Î·È Ì¤Û· ·fi ‰Ú·ÛÙËÚÈfi-ÙËÙ˜ Ù˘ ηıËÌÂÚÈÓ‹˜ ˙ˆ‹˜ ÙȘ ·Î̤˜ Î·È ÙȘ ÎÔÚ˘Ê¤˜ ÙÔ˘ ·‚Ô˘. ™˘Ó¯›˙ÔÓÙ·˜ ÛÙË ‰Ú·ÛÙËÚÈfiÙËÙ·Û˘ÁÎÚ›ÓÔ˘Ó ÙÔÓ Î‡‚Ô Ì ÙÔ ÔÚıÔÁÒÓÈÔ ·Ú·ÏÏËÏÂ›Â‰Ô Î·È ‰È·ÈÛÙÒÓÔ˘Ó fiÙÈ ˘¿Ú¯ÂÈ Ô ›‰ÈÔ˜ ·ÚÈı-Ìfi˜ ·fi «Ú·Ê¤˜» Î·È «ÊÔ‡ÓÙ˜». ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ ηٷÛ΢¿˙Ô˘Ó ÙÔ ÌÔÓÙ¤ÏÔ ÙÔ˘ ·‚Ô˘ Î·È ÙÔ˘ ÔÚıÔÁÒÓÈÔ˘·Ú·ÏÏËÏÂÈ¤‰Ô˘ Î·È ‰È·ÈÛÙÒÓÔ˘Ó Ì Ú·ÎÙÈÎfi ÙÚfiÔ ÙÔÓ ·ÚÈıÌfi ÙˆÓ ·ÎÌÒÓ Î·È ÙÔÓ ·ÚÈıÌfi ÙˆÓÎÔÚ˘ÊÒÓ ÛÙÔÓ Î‡‚Ô Î·ıÒ˜ Â›Û˘ ÙÔÓ ·ÚÈıÌfi ÙˆÓ ‰È·ÊÔÚÂÙÈÎÒÓ ·ÎÌÒÓ Î·È ÎÔÚ˘ÊÒÓ ÛÙÔ ÔÚıÔÁÒÓÈÔ·Ú·ÏÏËÏÂ›‰Ô. ∆¤ÏÔ˜, Û˘ÁÎÚ›ÓÔ˘Ó ÙȘ ‰‡Ô ηٷÛ΢¤˜ Î·È Û˘ÌÂÚ·›ÓÔ˘Ó fiÙÈ Î·È ÔÈ ‰‡Ô ¤¯Ô˘ÓÙÔÓ ›‰ÈÔ ·ÚÈıÌfi ·ÎÌÒÓ Î·È ÎÔÚ˘ÊÒÓ.∫·ÓfiÓ·˜ Î·È ·Ú·‰Â›ÁÌ·Ù· ™ÙÔÓ Î·ÓfiÓ· ·Ó·Ê¤ÚÔÓÙ·È ÔÈ fiÚÔÈ «·Î̤˜» Î·È «ÎÔÚ˘Ê¤˜». ªÔÏÔÓfiÙÈ ÔÈ ¤ÓÓÔȘ ·˘Ù¤˜ Â›Ó·È ÁÓˆ-ÛÙ¤˜ Î·È Â‡ÎÔÏ· ηٷÓÔËÙ¤˜ ·fi Ù· ·È‰È¿, Ë Û¯¤ÛË ÙÔ˘˜ ‰ÂÓ Â›Ó·È ÙfiÛÔ ÚÔÊ·Ó‹˜. ∏ ηıÂÙfiÙËÙ·ÙÚÈÒÓ Â˘ıÂÈÒÓ Û Â›‰· οıÂÙ· ÌÂٷ͇ ÙÔ˘˜ Â›Ó·È ÔˆÛ‰‹ÔÙ ‰‡ÛÎÔÏÔ Ó· Á›ÓÂÈ Î·Ù·ÓÔËÙ‹. ∏ÔÙÈÎÔÔ›ËÛË ÙˆÓ Û¯¤ÛÂˆÓ ÙˆÓ ·ÎÌÒÓ Î·È ÙˆÓ ÎÔÚ˘ÊÒÓ ‚ÔËı¿ ÛÙËÓ Î·Ù·ÓfiËÛË Ôχ ÂÚÈÛÛfiÙÂÚÔ·fi fi,ÙÈ Ë ÌÂϤÙË ÙÔ˘ ÛΛÙÛÔ˘ ÛÙÔ ·Ú¿‰ÂÈÁÌ· ÙÔ˘ ‚È‚Ï›Ô˘. TETPA¢IO EP°A™IøNÕÛÎËÛË 1Ë ∏ χÛË ·ÂÈÎÔÓ›˙ÂÙ·È ÛÙÔ ‰ÈÏ·Ófi Û¯‹Ì·.ÕÛÎËÛË 2Ë ∏ χÛË ·ÂÈÎÔÓ›˙ÂÙ·È ÛÙÔ ‰ÈÏ·Ófi Û¯‹Ì·. ∂ÌÊ·Ó›˙ÔÓÙ·ÈÌfiÓÔ ÔÈ ‚·ÛÈΤ˜ ·Î̤˜ Ì ·ÚÈıÌÔ‡˜ ÛÙȘ ÙÔ̤˜ ÙÔ˘˜. √È˘fiÏÔÈ˜ Â›Ó·È ·Ïfi Ó· ‚ÚÂıÔ‡Ó. 157

™Ùã T¿ÍË BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ KÂÊ¿Ï·ÈÔ 68Ô ∫‡ÏÈÓ‰ÚÔ˜ Να το τυλίξω; √È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ۯ‰ȿ˙ÂÈ ÙÔ ·Ó¿Ù˘ÁÌ· Î·È Ó· ηٷÛ΢¿˙ÂÈ Î‡ÏÈÓ‰ÚÔ. ✒ ¡· ηٷÓÔ‹ÛÂÈ ÙË ‰È·‰Èηۛ· ‡ÚÂÛ˘ ÙÔ˘ ÂÌ‚·‰Ô‡ ÙˆÓ ‚¿ÛˆÓ, Ù˘ ·Ú¿Ï¢Ú˘ Î·È Ù˘ ÔÏÈ΋˜ ÂÈÊ¿ÓÂÈ·˜ ÙÔ˘ Î˘Ï›Ó‰ÚÔ˘. ✒ ¡· ۯ‰ȿ˙ÂÈ Î‡ÏÈÓ‰ÚÔ Û Â›Â‰Ë ÂÈÊ¿ÓÂÈ·. √ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ۯ‰ȿ˙ÂÈ ÙÔ ·Ó¿Ù˘ÁÌ·, Ó· ˘ÔÏÔÁ›˙ÂÈ ÙÔ ÂÌ‚·‰fi (‚¿ÛÂˆÓ Î·È ·Ú¿Ï¢Ú˘ ÂÈÊ¿- ÓÂÈ·˜) Î·È Ó· ۯ‰ȿ˙ÂÈ Î‡ÏÈÓ‰ÚÔ Û ¯·ÚÙ›. ¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ∏ ηٷÛ΢‹ Î·È Ë Ì¤ÙÚËÛË ÙÔ˘ ·Ó·Ù‡ÁÌ·ÙÔ˜ ÙˆÓ ÛÙÂÚÂÒÓ Ì ٷ ÔÔ›· ·Û¯ÔÏ‹ıËÎ·Ó Ì¤¯ÚÈ ÙÒÚ· Ù· ·È‰È¿ Û¯ÂÙ›˙ÔÓÙ·Ó Ì ÂÈÊ¿ÓÂȘ Â›‰˜ fiÔ˘ ÔÈ ‰È·ÛÙ¿ÛÂȘ ‹Ù·Ó ‡ÎÔÏ· ÌÂÙÚ‹ÛÈ̘. ™ÙËÓ ÂÚ›ÙˆÛË ÙÔ˘ Î˘Ï›Ó‰ÚÔ˘ fï˜ ÔÈ ‰˘ÛÎÔϛ˜ Ô˘ ·ÚÔ˘ÛÈ¿˙ÔÓÙ·È Û¯ÂÙ›˙ÔÓÙ·È Ì ÙÔ ÁÂÁÔÓfi˜ fiÙÈ Ù· ·È‰È¿ ‰ÂÓ ÌÔÚÔ‡Ó Ó· ÌÂÙÚ‹ÛÔ˘Ó Â‡ÎÔÏ· ÙËÓ ÂÈÊ¿ÓÂÈ·, ηıÒ˜ ÂÌϤÎÂÙ·È Ô Î‡ÎÏÔ˜ Î·È Î·Ù¿ Û˘Ó¤ÂÈ· Ô ·ÚÈıÌfi˜ . ∞˘Ùfi οÓÂÈ ‰‡ÛÎÔÏÔ ÙÔ ¯ÂÈÚÈÛÌfi ÙÔ˘ Î˘Ï›Ó‰ÚÔ˘ Î·È ··ÈÙ› ÌÂÁ·Ï‡ÙÂÚË ÚÔÛ¿ıÂÈ· ÛÙËÓ Î·Ù·ÓfiËÛË ÙˆÓ Û¯¤ÛÂˆÓ Ô˘ ‰È¤Ô˘Ó ÙȘ ‚¿ÛÂȘ Î·È ÙËÓ ·Ú¿Ï¢ÚË ÂÈÊ¿ÓÂÈ¿ ÙÔ˘. ¢Ú·ÛÙËÚÈfiÙËÙ· 1Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ Ì ηıËÌÂÚÈÓ¿ ·ÓÙÈΛÌÂÓ· (ÎÔ˘Ù› ·Ó·„˘ÎÙÈÎÔ‡, ÎÔ˘Ù› ·fi Û˘Ì˘Îӈ̤ÓÔ Á¿Ï· Î.Ï.) ÚÔÛÂÁÁ›˙Ô˘Ó ÙȘ ¤ÓÓÔȘ «·Ú¿Ï¢ÚË ÂÈÊ¿ÓÂÈ·» Î·È «·Ó¿Ù˘ÁÌ· Î˘Ï›Ó‰ÚÔ˘». ™ËÌÂÈÒÓÂÙ·È ˆ˜, ÂÂȉ‹ Â›Ó·È ‰‡ÛÎÔÏÔ Ó· Ê·ÓÙ·ÛÙÔ‡Ó ÙÔÓ Î‡ÏÈÓ‰ÚÔ ·Ê·ÈÚÂÙÈο, ı· ‹Ù·Ó ηÏfi Ó· ¤¯ÂÈ Ô Î·ı¤Ó·˜ ·fi ¤Ó· ΢ÏÈÓ‰ÚÈÎfi ÎÔ˘Ù› ÒÛÙ ·Ó ı¤ÏÂÈ Ó· ÙÔ ÓÙ‡ÛÂÈ Á‡Úˆ Ì ¯·ÚÙ› Î·È Ó· ÙÔ ÍÂÙ˘Ï›ÍÂÈ Î·ÙfiÈÓ ÁÈ· Ó· ‰ÂÈ ÙÔ Û¯‹Ì·. √ ‰¿ÛηÏÔ˜ Ú¤ÂÈ Ó· ·ÔʇÁÂÈ ÙËÓ ÚfiˆÚË «Ì·ıËÌ·ÙÈÎÔÔ›ËÛË» Î·È Ó· ˙ËÙ‹ÛÂÈ ·fi ÙÔ˘˜ Ì·ıËÙ¤˜ Ó· ÌÂÙÚ‹ÛÔ˘Ó ÙÔ˘˜ ·ÎÏÔ˘˜ ÙˆÓ ‚¿ÛˆÓ. ™ÙËÓ ÂÚÒÙËÛË «·Ó ·ÓÙÈÁÚ¿„ÂȘ ÙÔ ·Ó¿Ù˘ÁÌ· Ô˘ ¤ÊÙȷ͘ Û ¯·ÚÙ› Î·È ÙÔ Îfi„ÂȘ, ı· Á›ÓÂÈ Î‡ÏÈÓ- ‰ÚÔ˜;» οÔÈ· ·È‰È¿ ı· ··ÓÙ‹ÛÔ˘Ó ıÂÙÈο Î·È Î¿ÔÈ· ·ÚÓËÙÈο. ™˘ÓÈÛÙ¿Ù·È Ó· ÙÔ ‰ÔÎÈÌ¿ÛÔ˘Ó ÁÈ· Ó· ·Ó·Î·Ï‡„Ô˘Ó fiÙÈ ÁÈ· Ó· ÌÔÚ› ÙÔ ·Ó¿Ù˘ÁÌ· Ô˘ ۯ‰›·Û·Ó Ó· Á›ÓÂÈ Î‡ÏÈÓ‰ÚÔ˜, Ú¤ÂÈ ÙÔ Ì‹ÎÔ˜ ÙÔ˘ ·ÎÏÔ˘ (Ë ‚¿ÛË) Ó· Â›Ó·È ›ÛË Ì ÙÔ Ï¿ÙÔ˜ Ù˘ ·Ú¿Ï¢Ú˘ ÂÈÊ¿ÓÂÈ·˜ (ÂÙÈΤٷ˜ ÛÙÔ ÎÔ˘Ù›). ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ ÚÔÛ·ıÔ‡Ó Ó· ˘ÔÏÔÁ›ÛÔ˘Ó ÙÔ ÂÌ‚·‰fi ÙÔ˘ ·Ó·Ù‡ÁÌ·ÙÔ˜ ÙÔ˘ Î˘Ï›Ó‰ÚÔ˘. ™˘ÌÂÚ·›ÓÔ˘Ó ˆ˜ Ú¤ÂÈ Ó· ˘ÔÏÔÁ›ÛÔ˘Ó ÙÔ ÂÌ‚·‰fi Ù˘ ·Ú¿Ï¢Ú˘ ÂÈÊ¿- ÓÂÈ·˜ Î·È ÙÔ ÂÌ‚·‰fi ÙˆÓ ‰‡Ô ‚¿ÛˆÓ. ™ÙÔ Ù¤ÏÔ˜ Ù˘ ‰Ú·ÛÙËÚÈfiÙËÙ·˜ ˙ËÙÂ›Ù·È ·fi ÙÔ˘˜ Ì·ıËÙ¤˜ Ó· ÂÎÊÚ¿ÛÔ˘Ó ÙÔÓ ˘ÔÏÔÁÈÛÌfi ÙÔ˘ ÂÌ‚·‰Ô‡ Û ·Ê·ÈÚÂÙÈÎfi Â›Â‰Ô (¯ˆÚ›˜ Ó· ‚ϤÔ˘Ì ÙÔ ·Ó¿- Ù˘ÁÌ¿ ÙÔ˘). TETPA¢IO EP°A™IøN ¶Úfi‚ÏËÌ· 3Ô ∫¿ı η¤ÏÔ ¯ÚÂÈ¿˙ÂÙ·È ÙÔ ·Ú¿Ï¢ÚÔ ÂÌ‚·‰fi Û˘Ó ÙÔ ÂÌ‚·‰fi ÙÔ˘ ÌÂÁ¿ÏÔ˘ ·ÎÏÔ˘ (30 ÂÎ). ¶ÂÚ›ÌÂÙÚÔ˜ η¤ÏÔ˘: 14 . 3,14 = 43,96, 43,96 . 15 = 659,4 Ù.ÂÎ. ∂Ì‚·‰fi ·ÎÏÔ˘ 15 . 15 . 3,14 = 706,5. ™˘ÓÔÏÈÎfi ÂÌ‚·‰fi ¯·ÚÙÈÔ‡ 706,5 + 659,4 = 1365,9 Ù.ÂÎ.158

BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ ™Ùã T¿ÍËKÂÊ¿Ï·ÈÔ 69Ô ŸÁÎÔ˜ – ÈÚËÙÈÎfiÙËÙ· Γέµισε; Χωράω κι εγώ;√È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ηٷÓÔ› ÙÔ Ï›ÙÚÔ ˆ˜ ÌÔÓ¿‰· ¯ˆÚËÙÈÎfiÙËÙ·˜. ✒ ¡· ηٷÓÔ› ÙÔ Î˘‚ÈÎfi ÂηÙÔÛÙfi ˆ˜ ÌÔÓ¿‰· fiÁÎÔ˘ Î·È Ó· Ì¿ıÂÈ ÙË Û¯¤ÛË ÙÔ˘ Ì ٷ ÔÏÏ·Ï¿- ÛÈ¿ ÙÔ˘. ✒ ¡· ÂÎÊÚ¿˙ÂÈ ÙȘ ÌÂÙÚ‹ÛÂȘ fiÁÎÔ˘ ÌÂ Ê˘ÛÈÎÔ‡˜, ‰Âη‰ÈÎÔ‡˜ Î·È Û˘ÌÌÈÁ›˜ ·ÚÈıÌÔ‡˜. ✒ ¡· χÓÂÈ ÚÔ‚Ï‹Ì·Ù· Ô˘ ·Ó·Ê¤ÚÔÓÙ·È Û fiÁÎÔ˘˜.√ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ÌÂÙÚ¿ fiÁÎÔ˘˜ Î·È ¯ˆÚËÙÈÎfiÙËÙ˜ Î·È Ó· χÓÂÈ Û¯ÂÙÈο ÚÔ‚Ï‹Ì·Ù·.¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ∆Ô ¤Ú·ÛÌ· ·fi ÙÔÓ fiÁÎÔ ÛÙË ¯ˆÚËÙÈÎfiÙËÙ· Â›Ó·È ¤Ó· Ôχ ‰‡ÛÎÔÏÔ ‚‹Ì· ÁÈ· ÙÔ˘˜ Ì·ıËÙ¤˜ ·˘Ù‹˜Ù˘ ËÏÈΛ·˜. √ Ì·ıËÙ‹˜ ¤¯ÂÈ Î·Ù·ÎÙ‹ÛÂÈ ÙȘ ¤ÓÓÔȘ «Î˘‚ÈÎfi ÂηÙÔÛÙfi», «Ì¤ÙÚËÛË fiÁÎÔ˘ ·‚Ô˘» ηȫ̤ÙÚËÛË fiÁÎÔ˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘» Ì ÙË ¯Ú‹ÛË ÙÔ˘ ΢‚ÈÎÔ‡ ÂηÙÔÛÙÔ‡, ÌÈ·˜ ÌÔÓ¿‰·˜ ΢‚È΋˜ ÌÂÙËÓ ÔÔ›· ‡ÎÔÏ· ÌÔÚԇ̠ӷ Û¯ËÌ·Ù›ÛÔ˘Ì ÌÂÁ·Ï‡ÙÂÚÔ˘˜ ·‚Ô˘˜ ‹ ·Ú·ÏÏËÏÂ›‰·. ™ÙËÓ ÂÚ›-ÙˆÛË Ù˘ ¯ˆÚËÙÈÎfiÙËÙ·˜ Ë ¤ÓÓÔÈ· Ù˘ ¯ˆÚËÙÈÎfiÙËÙ·˜ ÂÓfi˜ ‰Ô¯Â›Ô˘, Ô fiÁÎÔ˜ ÙÔ˘ ‰Ô¯Â›Ô˘ Î·È Ô fiÁÎÔ˜ÙÔ˘ ˘ÁÚÔ‡ Â›Ó·È ¤ÓÓÔȘ Ô˘ Ù· ·È‰È¿ Û˘Á¯¤Ô˘Ó. ¢Ú·ÛÙËÚÈfiÙËÙ˜ Ì ÔÁÎÔÌÂÙÚÈÎÔ‡˜ Î˘Ï›Ó‰ÚÔ˘˜ ηȯÂÈÚÈÛÌfi˜ ÙÔ˘˜ ˆ˜ ‰È·‰Èηۛ· ÂϤÁ¯Ô˘ Û ˘ÔÏÔÁÈÛÌÔ‡˜ fiÁÎÔ˘ ı· ‰ÒÛÂÈ ÛÙÔ˘˜ Ì·ıËÙ¤˜ ÙËÓ ··Ú·›-ÙËÙË ÔÙÈ΋ ‰È¿ÛÙ·ÛË ÙˆÓ ÂÓÓÔÈÒÓ Ô˘ ‰È·Ú·ÁÌ·Ù‡ÔÓÙ·È. ∂›Û˘ ¯ÚÂÈ¿˙ÂÙ·È Ó· Û˘˙ËÙËı› Ë ÔÏ˘-ÏÔÎfiÙËÙ· Ù˘ ¤ÓÓÔÈ·˜ ÙÔ˘ fiÁÎÔ˘. ∂Ó‰ÂÈÎÙÈο ÌÔÚԇ̠ӷ ˘Ô‚¿ÏÏÔ˘Ì ÙȘ ·ÎfiÏÔ˘ı˜ ÂÚˆÙ‹ÛÂȘ:«ÙÈ Â›Ó·È Ë ¯ˆÚËÙÈÎfiÙËÙ·;», «ÙÈ Û˘Ì‚·›ÓÂÈ ·Ó ¤Ó· ‰Ô¯Â›Ô ¤¯ÂÈ ¯ÔÓÙÚ¿ ÙÔȯÒÌ·Ù·;», «ÙÈ Û˘Ì‚·›ÓÂÈ ·Ó ¤Ó·ÛÙÂÚÂfi Â›Ó·È Û˘Ì·Á¤˜ ‹ ÎÔ‡ÊÈÔ;», «ÙÈ Û˘Ì‚·›ÓÂÈ ·Ó ¤Ó· ÔÙ‹ÚÈ Â›Ó·È ·ÓÔÈÎÙfi ‹ ¤¯ÂÈ Î·¿ÎÈ;», «Ò˜Û˘Ó‰¤ÂÙ·È Ë ¤ÓÓÔÈ· ÙÔ˘ fiÁÎÔ˘ Ì ÙÔ ÂÎÙÔÈ˙fiÌÂÓÔ ˘ÁÚfi fiÙ·Ó ‚˘ı›ÛÔ˘Ì ÙÔ ÛÙÂÚÂfi;» ¢Ú·ÛÙËÚÈfiÙËÙ· 1Ë™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ ı· ͯˆÚ›ÛÔ˘Ó ÙȘ ¤ÓÓÔȘ «¯ˆÚËÙÈÎfiÙËÙ·» Î·È «‚¿ÚÔ˜». ◊‰Ë ÁÓˆ-Ú›˙Ô˘Ó fiÙÈ ‰È·ÊÔÚÂÙÈο ˘ÁÚ¿, ·Ó Î·È Î·Ù·Ï·Ì‚¿ÓÔ˘Ó ÙÔÓ ›‰ÈÔ fiÁÎÔ, ¤¯Ô˘Ó ‰È·ÊÔÚÂÙÈÎfi ‚¿ÚÔ˜ (Ì¿˙·). ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ ÌÂÏÂÙÔ‡Ó ÙË ÌÔÓ¿‰· ̤ÙÚËÛ˘ ÙÔ˘ fiÁÎÔ˘ Î·È ¯Ù›˙ÔÓÙ·˜ ¤Ó·Ó‡ÚÁÔ ·fi 3-4 ΢‚Èο ÂηÙÔÛÙ¿ ‰È·ÈÛÙÒÓÔ˘Ó ˆ˜ Ô ‡ÚÁÔ˜ ÙÔ˘˜ ηٷϷ̂¿ÓÂÈ Î¿ÔÈÔ ¯ÒÚÔ, ¤¯ÂȉËÏ·‰‹ fiÁÎÔ. ∞ÓÂÍ¿ÚÙËÙ· ·fi ÙÔ Û¯‹Ì· Ù˘ ηٷÛ΢‹˜ Ô fiÁÎÔ˜ ·Ú·Ì¤ÓÂÈ ÛÙ·ıÂÚfi˜. ∞Ó ÁÂÌ›˙·ÌÂÓÂÚfi ÙÔ Î˘‚ÈÎfi ÂηÙÔÛÙfi Ô˘ ηٷÛ΢¿Û·Ì ı· ›¯Â ¯ˆÚËÙÈÎfiÙËÙ· ›ÛË Ì 1 ΢‚ÈÎfi ÂηÙÔÛÙfi.∂‡ÎÔÏ· (Ì ‚¿ÛË ÙËÓ ÂÌÂÈÚ›· ÙÔ˘˜ Î·È ÙȘ ÚÔËÁÔ‡ÌÂÓ˜ ÁÓÒÛÂȘ) ı· ηٷϋÍÔ˘Ó fiÙÈ ÙÔ 1 Ï›ÙÚÔÓÂÚfi Â›Ó·È 1000 Î.ÂÎ.∫·ÓfiÓ·˜ Î·È ·Ú·‰Â›ÁÌ·Ù· ™ÙÔÓ Î·ÓfiÓ· ·Ó·Ê¤ÚÔÓÙ·È ÔÈ fiÚÔÈ «Î˘‚ÈÎfi ̤ÙÚÔ», «Î˘‚ÈÎfi ‰ÂηÙfiÌÂÙÚÔ» Î·È «Î˘‚ÈÎfi ÂηÙÔÛÙfi»(‹ ÂηÙÔÛÙfiÌÂÙÚÔ). ∞Ó Î·È ÔÈ ¤ÓÓÔȘ ·˘Ù¤˜ Â›Ó·È ÁÓˆÛÙ¤˜ ÛÙ· ·È‰È¿, Ë Û¯¤ÛË ÙÔ˘˜ ‰ÂÓ Â›Ó·È ÙfiÛÔÚÔÊ·Ó‹˜. √ÙÈÎÔÔ›ËÛË ÙˆÓ ÌÔÓ¿‰ˆÓ Ì ˘ÏÈÎfi Ô˘ ˘¿Ú¯ÂÈ ‹ ı· ÊÙÈ¿ÍÔ˘Ó Ù· ·È‰È¿ ı· ‚ÔËı‹ÛÂÈÙË ÛˆÛÙ‹ ‰È·¯Â›ÚÈÛË ÙˆÓ ˘ԉȷÈÚ¤ÛÂˆÓ Î·ıÒ˜ οı ˘ԉȷ›ÚÂÛË Î·Ù·Ï·Ì‚¿ÓÂÈ 3 ‰Âη‰ÈΤ˜ı¤ÛÂȘ ˘Ô¯ÚˆÙÈο (2.570.050 Î.ÂÎ. = 2,57005 Î.Ì. = 2 Î.Ì. 570 Î.‰ÂÎ. 50 Î.ÂÎ.). TETPA¢IO EP°A™IøN 159¶Úfi‚ÏËÌ· 2Ô 2 . 32 (64 ·‚ÔÈ Û 1 ÛÂÈÚ¿), 2 . 2 . 16 (2 ÛÂÈÚ¤˜ ÙˆÓ 32 ·‚ˆÓ) 2 . 4 . 8 (4 ÛÂÈÚ¤˜ ÙˆÓ 16 ·‚ˆÓ).

™Ùã T¿ÍË BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ KÂÊ¿Ï·ÈÔ 70Ô ŸÁÎÔ˜ ·‚Ô˘ Î·È ÔÚıÔÁÒÓÈÔ˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘ Κύβοι και κιβώτια √È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ηٷÓÔ› ÙË ‰È·‰Èηۛ· ˘ÔÏÔÁÈÛÌÔ‡ ÙÔ˘ fiÁÎÔ˘ ·‚Ô˘ Î·È ÔÚıÔÁÒÓÈÔ˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘. ✒ ¡· ˘ÔÏÔÁ›˙ÂÈ ÙÔÓ fiÁÎÔ Î‡‚Ô˘ Î·È ÔÚıÔÁÒÓÈÔ˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘ Ì هÔ. ✒ ¡· χÓÂÈ ÚÔ‚Ï‹Ì·Ù· Ì fiÁÎÔ˘˜ ·‚ˆÓ Î·È ÔÚıÔÁÒÓÈˆÓ ·Ú·ÏÏËÏÂÈ¤‰ˆÓ. √ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ÌÂÙÚ¿ fiÁÎÔ˘˜ ·‚Ô˘ Î·È ÔÚıÔÁÒÓÈÔ˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘ Î·È Ó· χÓÂÈ Û¯ÂÙÈο ÚÔ‚Ï‹Ì·Ù·. ¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ OÈ Ì·ıËÙ¤˜ ÈÛÙÂ‡Ô˘Ó ˆ˜ ‰ÈÏ·ÛÈ·ÛÌfi˜ ÙˆÓ ‰È·ÛÙ¿ÛÂˆÓ ÂÓfi˜ ÛÙÂÚÂÔ‡ (.¯. ÂÓfi˜ ÔÚıÔÁˆÓ›Ô˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘), ÛËÌ·›ÓÂÈ Î·È ‰ÈÏ·ÛÈ·ÛÌfi ÙÔ˘ fiÁÎÔ˘ ÙÔ˘. ¢Ú·ÛÙËÚÈfiÙËÙ· 1Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ Ì Ú·ÎÙÈÎfi ÙÚfiÔ (.¯. ÁÂÌ›˙ÔÓÙ·˜ Ì ¿ÌÌÔ) ı· ·Ó·Î·Ï‡- „Ô˘Ó fiÙÈ, ÂÓÒ ¤¯Ô˘Ó ÚÔÛ‰ÈÔÚÈṲ̂ÓË ÌÔÓ¿‰· ̤ÙÚËÛ˘ ÙÔ˘ fiÁÎÔ˘, ÙÔ ÂÚÁ·ÏÂ›Ô ·˘Ùfi ‰ÂÓ Â›Ó·È Ú·- ÎÙÈο ÂÊ·ÚÌfiÛÈÌÔ, ηıÒ˜ ÔÈ ÌÂÙÚ‹ÛÂȘ ‰ÂÓ ÌÔÚÔ‡Ó Ó· Â›Ó·È ·ÎÚȂ›˜ ‹ ÔÈ ÌÈÎÚfiÙÂÚ˜ ÌÔÓ¿‰Â˜ Â›Ó·È ‰‡ÛÎÔϘ ÛÙÔ ¯ÂÈÚÈÛÌfi ·fi ÙÔ˘˜ Ì·ıËÙ¤˜ ÏfiÁˆ ÙÔ˘ Ôχ ÌÂÁ¿ÏÔ˘ ·ÚÈıÌÔ‡ ÙÔ˘˜. ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë OÈ Ì·ıËÙ¤˜ ÂÍÂÙ¿˙Ô˘Ó ¤Ó· ·‚Ô Ô˘ ηٷÛ΢¿˙Ô˘Ó Ì ·‚Ô˘˜ ÂÓfi˜ ÂηÙÔÛÙÔ‡. ¢È·ÈÛÙÒÓÔ˘Ó ˆ˜ ÌÔÚÔ‡Ó Ó· ‚ÚÔ˘Ó ÙÔÓ fiÁÎÔ ÙÔ˘ Ì ‰È·ÊÔÚÂÙÈÎÔ‡˜ ÙÚfiÔ˘˜ Î·È Û˘ÌÏËÚÒÓÔÓÙ·˜ ÙÔ˘˜ ›Ó·Î˜ Û˘ÛÙËÌ·ÙÔÔÈÔ‡Ó ÙȘ ·Ú·ÙËÚ‹ÛÂȘ ÙÔ˘˜ ÁÈ· ÙȘ Ú¿ÍÂȘ Ô˘ Ì·˜ ‰›ÓÔ˘Ó ÙÔÓ fiÁÎÔ ÙÔ˘ ·‚Ô˘. ¢ÔÎÈ- Ì¿˙Ô˘Ó ÛÙË Û˘Ó¤¯ÂÈ· ÙȘ ›‰È˜ Ú¿ÍÂȘ Û ¿ÏÏÔ˘˜ Û˘Ó‰˘·ÛÌÔ‡˜ Ì ÙÔ˘‚Ï¿ÎÈ· Î·È ‰È·ÈÛÙÒÓÔ˘Ó fiÙÈ ÌÔÚÔ‡Ó Ó· ηٷϋÍÔ˘Ó Û ηÓfiÓ· ÁÈ· ÙËÓ Â‡ÚÂÛË ÙÔ˘ fiÁÎÔ˘ ÔÚıÔÁÒÓÈˆÓ ·Ú·ÏÏËÏÂÈ¤‰ˆÓ. TETPA¢IO EP°A™IøN ÕÛÎËÛË 2Ë √È Û˘Ó‰˘·ÛÌÔ› ÌÔÚ› Ó· Â›Ó·È 3 . 5 . 22 ‹ 6 . 5 . 11 ‹ 3 . 10 . 11 ‹ ¿ÏÏÔ˜ Û˘Ó‰˘·ÛÌfi˜ Ô˘ ‰›ÓÂÈ ·˘Ùfi ÙÔ ÁÈÓfiÌÂÓÔ. ÕÛÎËÛË 3Ë ∏ ¯ˆÚËÙÈÎfiÙËÙ· ÙÔ˘ ÌÂÁ¿ÏÔ˘ ÎÔ˘ÙÈÔ‡ Â›Ó·È 70 . 50 . 30 = 105.000 Î.ÂÎ., ÂÓÒ Ô fiÁÎÔ˜ ÙÔ˘ ÌÈÎÚÔ‡ ÎÔ˘ÙÈÔ‡ 105 Î.ÂÎ. 105.000 : 105 = 1000 ÎÔ˘ÙÈ¿. ∂Ó·ÏÏ·ÎÙÈο ÛÙÔ ÌÂÁ¿ÏÔ ÎÔ˘Ù› ÌÔÚÒ Ó· ‚¿Ïˆ 10 x 10 ÎÔ˘ÙÈ¿ Û οı ÛÂÈÚ¿ Î·È Û˘ÓÔÏÈο 10 ÛÂÈÚ¤˜ 10 . 100 = 1000. ¶Úfi‚ÏËÌ· 1Ô £· ÓÔ›ÎÈ·˙˜ 4 ÎÔÓÙ¤ÈÓÂÚ (4 . 40 = 160 Î.Ì.) ÚÔ˜ 300 ú ÙÔ ¤Ó· Î·È ı· Ï‹ÚˆÓ˜ Â›Û˘ 20 . 11 = 220 ú ÁÈ· Ù· ˘fiÏÔÈ·. ™˘ÓÔÏÈο ı· Ï‹ÚˆÓ˜ 1.420 ú. ¶Úfi‚ÏËÌ· 2Ô °È· Ù· ÌÈÎÚ¿ ÎÈ‚ÒÙÈ· ¯ÚÂÈ¿˙ÂÙ·È 812 Ù.ÂÎ. ˘ÏÈÎfi, ÂÓÒ ÁÈ· Ù· ÌÂÁ¿Ï· 3.248 Ù. ÂÎ., ‰ËÏ·‰‹ 4 ÊÔÚ¤˜ ÂÚÈÛÛfiÙÂÚÔ. ÕÚ· ı· Ô˘Ï‹ÛÂÈ Ù· ÌÂÁ¿Ï· ÎÈ‚ÒÙÈ· 1,5 . 4 = 6 ú ¶Úfi‚ÏËÌ· 3Ô √ fiÁÎÔ˜ ÙÔ˘ ·¤Ú· Â›Ó·È 42 ΢‚Èο Î·È Â·ÚΛ ÁÈ· 7 ÒÚ˜.160

BÈ‚Ï›Ô ÂÎ·È‰Â˘ÙÈÎÔ‡ ™Ùã T¿ÍËKÂÊ¿Ï·ÈÔ 71Ô ŸÁÎÔ˜ Î˘Ï›Ó‰ÚÔ˘ Τύπος συντηρητικός!√È ÂÈ̤ÚÔ˘˜ ÛÙfi¯ÔÈ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ·˘ÙÔ‡ ÁÈ· ÙÔ Ì·ıËÙ‹ Â›Ó·È ÔÈ ÂÍ‹˜: ✒ ¡· ηٷÓÔ› ÙË ‰È·‰Èηۛ· ˘ÔÏÔÁÈÛÌÔ‡ ÙÔ˘ fiÁÎÔ˘ ÙÔ˘ Î˘Ï›Ó‰ÚÔ˘. ✒ ¡· ˘ÔÏÔÁ›˙ÂÈ ÙÔÓ fiÁÎÔ ÙÔ˘ Î˘Ï›Ó‰ÚÔ˘ Ì هÔ. ✒ ¡· χÓÂÈ ÚÔ‚Ï‹Ì·Ù· Ì fiÁÎÔ˘˜ Î˘Ï›Ó‰ÚˆÓ.√ Ì·ıËÙ‹˜ ·Ó·Ì¤ÓÂÙ·È: ✒ ¡· ÌÂÙÚ¿ ÙÔÓ fiÁÎÔ ÙÔ˘ Î˘Ï›Ó‰ÚÔ˘ Î·È Ó· χÓÂÈ Û¯ÂÙÈο ÚÔ‚Ï‹Ì·Ù·.¶Èı·Ó¤˜ ‰˘ÛÎÔϛ˜ ÙÔ˘ ÎÂÊ·Ï·›Ô˘ ∏ ̤ÙÚËÛË ÙÔ˘ fiÁÎÔ˘ ÙˆÓ ÛÙÂÚÂÒÓ Ì ٷ ÔÔ›· ·Û¯ÔÏ‹ıËÎ·Ó Ì¤¯ÚÈ ÙÒÚ· Ù· ·È‰È¿ ‚·ÛÈ˙fiÙ·Ó ÛÙ˯ڋÛË ÙÔ˘ ΢‚ÈÎÔ‡ ÂηÙÔÛÙÔ‡, ÌÈ·˜ ΢‚È΋˜ ÌÔÓ¿‰·˜ Ì ÙËÓ ÔÔ›· ‡ÎÔÏ· ÌÔÚÔ‡Û·Ì ӷ Û¯ËÌ·Ù›-ÛÔ˘Ì ÌÂÁ·Ï‡ÙÂÚÔ˘˜ ·‚Ô˘˜ ‹ ·Ú·ÏÏËÏÂ›‰·. ™ÙËÓ ÂÚ›ÙˆÛË ÙÔ˘ Î˘Ï›Ó‰ÚÔ˘ fï˜ ÔÈ ‰˘ÛÎÔϛ˜Ô˘ ·ÚÔ˘ÛÈ¿˙ÔÓÙ·È Û¯ÂÙ›˙ÔÓÙ·È Ì ÙÔ ÁÂÁÔÓfi˜ fiÙÈ Ù· ·È‰È¿ ‰ÂÓ ÌÔÚÔ‡Ó Ó· Ê·ÓÙ·ÛÙÔ‡Ó ÙË ÌÔÓ¿‰·Ì¤ÙÚËÛ˘ (Î.ÂÎ.) Ó· «ÁÂÌ›˙ÂÈ» Ï‹Úˆ˜ ¤Ó·Ó ·ÏÈÓ‰ÚÔ. ¢Ú·ÛÙËÚÈfiÙËÙ· 1Ë ™ÙË ‰Ú·ÛÙËÚÈfiÙËÙ· ·˘Ù‹ ÔÈ Ì·ıËÙ¤˜ ‰È·ÈÛÙÒÓÔ˘Ó fiÙÈ ¤Ó· ·Ú·ÏÏËÏÂ›Â‰Ô Î·È ¤Ó·˜ ·ÏÈÓ‰ÚÔ˜¤¯Ô˘Ó Ù· ÂÍ‹˜ ÎÔÈÓ¿ ¯·Ú·ÎÙËÚÈÛÙÈο: Â›Ó·È ÛÙÂÚ¿ ÛÒÌ·Ù·, ¤¯Ô˘Ó 3 ‰È·ÛÙ¿ÛÂȘ Î·È fiÁÎÔ. øÛÙfiÛԉȷʤÚÔ˘Ó ÛÙÔ fiÙÈ ÔÈ ‰È·ÛÙ¿ÛÂȘ ÙÔ˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘ ‰È·ÎÚ›ÓÔÓÙ·È ÈÔ Â‡ÎÔÏ·, (.¯. ÙÔ ÂÌ‚·‰fiÙ˘ ‚¿Û˘ ÙÔ˘ ·Ú·ÏÏËÏÂÈ¤‰Ô˘ ‚Ú›ÛÎÂÙ·È ÈÔ Â‡ÎÔÏ·, ÂÓÒ ÛÙÔÓ Î‡ÏÈÓ‰ÚÔ Ú¤ÂÈ Ó· ÁÓˆÚ›˙Ô˘ÌÂÙËÓ ·ÎÙ›Ó·, ηıÒ˜ ‰ÂÓ Â›Ó·È Â‡ÎÔÏÔ Ó· ÙË ÌÂÙÚ‹ÛÔ˘ÌÂ). ¢Ú·ÛÙËÚÈfiÙËÙ· 2Ë ∞˘Ùfi Ô˘ ¤¯ÂÈ ÛËÌ·Û›· Â›Ó·È Ó· ηٷϿ‚Ô˘Ó ÔÈ Ì·ıËÙ¤˜ ÙËÓ ·Ó¿ÁÎË Ó· ˘ÔÏÔÁ›ÛÔ˘Ó ÙÔ ÂÌ‚·‰fiÙ˘ ‚¿Û˘ ÚÒÙ· Î·È ÛÙÔ Î˘ÏÈÓ‰ÚÈÎfi Û¯‹Ì·. ™ÙË Û˘Ó¤¯ÂÈ· Û˘ÌÂÚ·›ÓÔ˘Ó ˆ˜, ·Ó ¤ÚÂ ӷ ‚ÚÔ˘ÓÙÔÓ fiÁÎÔ ÙˆÓ ·Ú·ÏÏËÏÂ›‰ˆÓ ·˘ÙÒÓ Û¯ËÌ¿ÙˆÓ ı· ¤‚ÚÈÛÎ·Ó ÚÒÙ· ÙÔ ÂÌ‚·‰fi Ù˘ ‚¿Û˘ ηÈÌÂÙ¿ ı· ÙÔ ÔÏÏ·Ï·Û›·˙·Ó Ì ÙÔ ‡„Ô˜. ∫·ÙfiÈÓ ÛÎÂÙfiÌÂÓÔÈ ÁÈ· ÙÔÓ ÙÚfiÔ Ì ÙÔÓ ÔÔ›Ô ·˘Ùfi ı·ÌÔÚÔ‡Û ӷ ÂÊ·ÚÌÔÛÙ› Î·È ÛÙÔÓ Î‡ÏÈÓ‰ÚÔ, ÂÎÙÈÌÔ‡Ó ˆ˜ ÌÔÚÔ‡Ó Ó· ÂÊ·ÚÌfiÛÔ˘Ó ÙËÓ ›‰È·Ì¤ıÔ‰Ô, ·ÚΛ Ó· ÁÓˆÚ›˙Ô˘Ó ÙËÓ ·ÎÙ›Ó· Ù˘ ‚¿Û˘ ÁÈ· Ó· ‚ÚÔ˘Ó ÙÔ ÂÌ‚·‰fi Ù˘. TETPA¢IO EP°A™IøNÕÛÎËÛË 1Ë √ fiÁÎÔ˜ ÛÙËÓ ÚÒÙË ÂÚ›ÙˆÛË Â›Ó·È 10.039,36 Î.ÂÎ. ÂÓÒ ÛÙË ‰Â‡ÙÂÚË 13.863,88 Î.ÂÎ..ÕÛÎËÛË 2Ë √ fiÁÎÔ˜ Â›Ó·È 2.653,3 ΢‚Èο ̤ÙÚ·.¶Úfi‚ÏËÌ· 1Ô ∆Ô ·Ú·ÏÏËÏÂ›Â‰Ô ‰Ô¯Â›Ô ¤¯ÂÈ fiÁÎÔ 15 . 10 . 20 = 3.000 Î.ÂÎ. ÂÓÒ ÙÔ Î˘ÏÈÓ‰ÚÈÎfi 5.024 Î.ÂÎ.¶Úfi‚ÏËÌ· 2Ô √ fiÁÎÔ˜ ÙÔ˘ ıÂÚÌÔÎË›Ô˘ Â›Ó·È ›ÛÔ˜ Ì ÙÔ ÌÈÛfi fiÁÎÔ Î˘Ï›Ó‰ÚÔ˘ Ì ÙȘ ›‰È˜ ‰È·ÛÙ¿ÛÂȘ, ‰ËÏ·‰‹8.478 ΢‚Èο ̤ÙÚ·¶Úfi‚ÏËÌ· 3Ô ∆Ô ¯ÒÌ· Ô˘ ÌÂÙ·ÎÈÓ‹ıËΠ‹Ù·Ó 452.160 ΢‚Èο ̤ÙÚ· Î·È Ù· ÊÔÚÙËÁ¿ ¤Î·Ó·Ó 22.608 ‰ÚÔÌÔÏfiÁÈ·. 161

∫ÚÈÙ‹ÚÈÔ ·ÍÈÔÏfiÁËÛ˘ ÁÈ· ÙË ıÂÌ·ÙÈ΋ ÂÓfiÙËÙ· 6 1. ¶ÔÈÔ ·fi Ù· ·Ú·Î¿Ùˆ Û¯‹Ì·Ù· ¤¯ÂÈ 2. ∞. ¶ÔÈÔ ·fi Ù· ·Ú·Î¿Ùˆ Û¯‹Ì·Ù· ‰ÂÓ Â›Ó·È ÂÌ‚·‰fi 24 Ù.ÂÎ. Î·È ÂÚ›ÌÂÙÚÔ 20 ÂÎ.; ‰˘Ó·Ùfi Ó· ˘¿Ú¯ÂÈ; ·. ÙÂÙÚ¿Ï¢ÚÔ Ì 4 ÔÚı¤˜ ÁˆÓ›Â˜ ‚. ÙÚ›ÁˆÓÔ Ì ›Û˜ Ï¢ڤ˜ Á. ÙÚ·¤˙ÈÔ Ì ‰‡Ô ÔÚı¤˜ ÁˆÓ›Â˜ ‰. ÙÚ›ÁˆÓÔ Ì ‰‡Ô ÔÚı¤˜ ÁˆÓ›Â˜ ∞¿ÓÙËÛË: .................................................. µ. ¶ÔÈÔ ·fi Ù· ·Ú·Î¿Ùˆ Û¯‹Ì·Ù· ¤¯ÂÈ ÌfiÓÔ ‰‡Ô Ï¢ڤ˜ ·Ú¿ÏÏËϘ; 3. ∏ ∞ÁÁÂÏÈ΋ ı¤ÏÂÈ Ó· ÊÙÈ¿ÍÂÈ ¤Ó·Ó ·ÏÈÓ‰ÚÔ 4. ª›· ·fi ÙȘ ÁˆÓ›Â˜ ÂÓfi˜ ÔÚıÔÁÒÓÈÔ˘ ÙÚÈÁÒ- ·fi ¯·ÚÙ›. ¶ÔÈÔ Û˘Ó‰˘·ÛÌfi Û¯ËÌ¿ÙˆÓ ·fi ÓÔ˘ Â›Ó·È 50Ô. ¶fiÛÔ Â›Ó·È Ë ¿ÏÏË; ÙÔ˘˜ ·Ú·Î¿Ùˆ ı· ¯ÚÂÈ·ÛÙ›; ·. 4 ÙÚ›ÁˆÓ· Î·È 1 ÙÂÙÚ¿ÁˆÓÔ ‚. 2 ÙÚ›ÁˆÓ· Î·È 1 ÔÚıÔÁÒÓÈÔ Á. 2 ·ÎÏÔ˘˜ Î·È 1 ÔÚıÔÁÒÓÈÔ ‰. 3 ·ÎÏÔ˘˜ Î·È 1 ÙÂÙÚ¿ÁˆÓÔ ∞¿ÓÙËÛË: ...................................................... 5. ∆Ô Ï¿ÙÔ˜ ÂÓfi˜ ÔÚıÔÁÒÓÈÔ˘ ¯·ÏÈÔ‡ Â›Ó·È 4 ̤ÙÚ·. ∞Ó Ë ÂÚ›ÌÂÙÚfi˜ ÙÔ˘ Â›Ó·È 20 ̤ÙÚ· ÔÈÔ Â›Ó·È ÙÔ ÂÌ‚·‰fi ÙÔ˘; ∞¿ÓÙËÛË: ..................................................................................................................................... 6. ∞˘Ù‹ Â›Ó·È Ë Î¿ÙÔ„Ë ÂÓfi˜ ÂÚÁÔÛÙ·Û›Ô˘. 7. ¶ÔÈ· Â›Ó·È Ë ÏËÛȤÛÙÂÚË ÂÎÙ›ÌËÛË ÁÈ· ÙË ¶fiÛ· ÙÂÙÚ·ÁˆÓÈο ̤ÙÚ· ϷοÎÈ· ¯ÚÂÈ¿- ÁˆÓ›· ÃY∑; ˙ÔÓÙ·È ÁÈ· ÙÔ ‰¿Â- ·. 225Æ ‰Ô; ¶fiÛ· ̤ÙÚ· Â›Ó·È Ë ÂÚ›ÌÂÙÚÔ˜ ‚. 135Æ ÁÈ· Ó· ÙÔÔıÂÙËı› Á. 90Æ ÌÈ· ͇ÏÈÓË Ì·ÚΛ˙·; ‰. 45Æ Â. 10Æ ∞¿ÓÙËÛË: .......................................................162

8. √ fiÁÎÔ˜ ÂÓfi˜ ·‚Ô˘ Â›Ó·È 125 Î.ÂÎ. ¶fiÛ· 9. ŒÓ· ÔÚıÔÁÒÓÈÔ ·Ú·ÏÏËÏÂ›Â‰Ô ‰Ô¯Â›Ô ÂηÙÔÛÙ¿ ÓÔÌ›˙ÂȘ fiÙÈ Â›Ó·È Ë Ì ‰È·ÛÙ¿ÛÂȘ 50 ÂÎ., 30 ÂÎ. Î·È 20 ÂÎ. ·ÎÌ‹ ÙÔ˘; ÁÂÌ›˙ÂÈ ·fi ÌÈ· ‚Ú‡ÛË Ô˘ ÛÙ¿˙ÂÈ. ¶fiÛ· Ï›ÙÚ· ÓÂÚfi ı· ¯ˆÚ¤ÛÂÈ; ·. 12 ÂÎ. ∞¿ÓÙËÛË: ..................................................... ‚. 25 ÂÎ. Á. 6 ÂÎ. ‰. 5 ÂÎ.10. ¶ÔÈÔ ·fi Ù· ·Ú·Î¿Ùˆ ‰ÂÓ Â›Ó·È ·Ó¿Ù˘ÁÌ· ·‚Ô˘;11. ∏ µ·ÁÁÂÏÈÒ ¤ÊÙÈ·Í ¤Ó· ÎÔ˘Ù› Î·È ı¤ÏÂÈ Ó· ÙÔ ÓÙ‡ÛÂÈ Ì ‚ÂÏÔ˘Ù¤ ¯·ÚÙ›. ¶fiÛ· Ù.ÂÎ. ¯·ÚÙ› ı· ¯ÚÂÈ·ÛÙ›;12. ™¯Â‰›·Û ¤Ó· ·ÏÈÓ‰ÚÔ, ‰ÒÛ ÙȘ ‰È·ÛÙ¿ÛÂȘ ÙÔ˘ Î·È ÁÚ¿„ ¤Ó· Úfi‚ÏËÌ· Ô˘ Ó· ˙ËÙ¿ ÙÔÓ fiÁÎÔ ÙÔ˘. ...................................................................................................... ...................................................................................................... ...................................................................................................... 163

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ªÂ ·fiÊ·ÛË Ù˘ ∂ÏÏËÓÈ΋˜ ∫˘‚¤ÚÓËÛ˘ Ù· ‰È‰·ÎÙÈο ‚È‚Ï›· ÙÔ˘ ¢ËÌÔÙÈÎÔ‡, ÙÔ˘ °˘ÌÓ·Û›Ô˘ Î·È ÙÔ˘ §˘Î›Ԣ Ù˘ÒÓÔÓÙ·È ·fi ÙÔÓ √ÚÁ·ÓÈÛÌfi ∂ΉfiÛˆ˜ ¢È‰·ÎÙÈÎÒÓ µÈ‚Ï›ˆÓ Î·È ‰È·Ó¤ÌÔÓÙ·È ‰ˆÚÂ¿Ó ÛÙ· ¢ËÌfiÛÈ· ™¯ÔÏ›·. ∆· ‚È‚Ï›· ÌÔÚ› Ó· ‰È·Ù›ıÂÓÙ·È ÚÔ˜ ÒÏËÛË, fiÙ·Ó Ê¤ÚÔ˘Ó ‚È‚ÏÈfiÛËÌÔ ÚÔ˜ ·fi‰ÂÈÍË Ù˘ ÁÓË- ÛÈfiÙËÙ¿˜ ÙÔ˘˜. ∫¿ı ·ÓÙ›Ù˘Ô Ô˘ ‰È·Ù›ıÂÙ·È ÚÔ˜ ÒÏËÛË Î·È ‰Â ʤÚÂÈ ‚È‚ÏÈfiÛËÌÔ, ıˆÚÂ›Ù·È ÎÏ„›Ù˘Ô Î·È Ô ·Ú·‚¿Ù˘ ‰ÈÒÎÂÙ·È Û‡Ìʈӷ Ì ÙȘ ‰È·Ù¿ÍÂȘ ÙÔ˘ ¿ÚıÚÔ˘ 7 ÙÔ˘ ¡fiÌÔ˘ 1129 Ù˘ 15/21 ª·ÚÙ›Ô˘ 1946 (ºEK 1946, 108, Aã). BIB§IO™HMO∞·ÁÔÚ‡ÂÙ·È Ë ·Ó··Ú·ÁˆÁ‹ ÔÔÈÔ˘‰‹ÔÙ ÙÌ‹Ì·ÙÔ˜ ·˘ÙÔ‡ ÙÔ˘ ‚È‚Ï›Ô˘, Ô˘Î·Ï‡ÙÂÙ·È ·fi ‰ÈηÈÒÌ·Ù· (copyright), ‹ Ë ¯Ú‹ÛË ÙÔ˘ Û ÔÔÈ·‰‹ÔÙ ÌÔÚÊ‹, ¯ˆÚ›˜ÙË ÁÚ·Ù‹ ¿‰ÂÈ· ÙÔ˘ ¶·È‰·ÁˆÁÈÎÔ‡ πÓÛÙÈÙÔ‡ÙÔ˘.

7+1 5 24 6380 * 1+3 - 5 9*ΚωδικόςΒιβλίου:0-10-0174 ISBN 978-960-06-2640-79 426 1 3(01)00000001001747