GEOMETRIA DESCRIPTIVA

1 1

4 4

KGHCGVTÃA FG^NTE\VE_A KGHCGVTÃA FG^NTE\VE_A

 \th`edefa ia tg|thfwnneþj vhvai h |atneai fg g~va hdta  \th`edefa ia tg|thfwnneþj vhvai h |atneai fg g~va hdta  |ht nwaiqwegt cgfeh) ~ej awvhte}aneþj g~nteva fg ih~  |ht nwaiqwegt cgfeh) ~ej awvhte}aneþj g~nteva fg ih~

awvhtg~* awvhtg~*

 FGTGN@H^ TG^GT_AFH^ ¥ 4<1<) tg~|gnvh a ia  FGTGN@H^ TG^GT_AFH^ ¥ 4<1<) tg~|gnvh a ia  |tecgta gfeneþj gj g~|añhi |ht GFEVHTG^ GI  |tecgta gfeneþj gj g~|añhi |ht GFEVHTG^ GI

CHTHNHN@AJH* CHTHNHN@AJH*

 Fe~gñh fg nwdegtva= Keicgt Aeig~ @*  Fe~gñh fg nwdegtva= Keicgt Aeig~ @*  Ec|tg~h gj \gtý „ \tejvgf ej \gtweaj*  Ec|tg~h gj \gtý „ \tejvgf ej \gtweaj*

 A ih~ qwg fg~ggj hdvgjgt wja nh|ea gignvtþjena gj ohtcavh [htf) \FO ý hvth)  A ih~ qwg fg~ggj hdvgjgt wja nh|ea gignvtþjena gj ohtcavh [htf) \FO ý hvth)  |wgfgj nhcwjenat~g nhj gi awvht ãa g#caei h vgiåohjh* Vacdeåj ~e tgqwegtgj  |wgfgj nhcwjenat~g nhj gi awvht ãa g#caei h vgiåohjh* Vacdeåj ~e tgqwegtgj

a~g~htãa gj Fedwmh Vånjenh) Fedwmh Cgnájenh) Kghcgvtãa Fg~nte|vea) gvn* a~g~htãa gj Fedwmh Vånjenh) Fedwmh Cgnájenh) Kghcgvtãa Fg~nte|vea) gvn*

4 4

KGHCGVTÃA FG^NTE\VE_A KGHCGVTÃA FG^NTE\VE_A

 \th`edefa ia tg|thfwnneþj vhvai h |atneai fg g~va hdta  \th`edefa ia tg|thfwnneþj vhvai h |atneai fg g~va hdta  |ht nwaiqwegt cgfeh) ~ej awvhte}aneþj g~nteva fg ih~  |ht nwaiqwegt cgfeh) ~ej awvhte}aneþj g~nteva fg ih~

awvhtg~* awvhtg~*

 FGTGN@H^ TG^GT_AFH^ ¥ 4<1<) tg~|gnvh a ia  FGTGN@H^ TG^GT_AFH^ ¥ 4<1<) tg~|gnvh a ia  |tecgta gfeneþj gj g~|añhi |ht GFEVHTG^ GI  |tecgta gfeneþj gj g~|añhi |ht GFEVHTG^ GI

CHTHNHN@AJH* CHTHNHN@AJH*

 Fe~gñh fg nwdegtva= Keicgt Aeig~ @*  Fe~gñh fg nwdegtva= Keicgt Aeig~ @*  Ec|tg~h gj \gtý „ \tejvgf ej \gtweaj*  Ec|tg~h gj \gtý „ \tejvgf ej \gtweaj*

 A ih~ qwg fg~ggj hdvgjgt wja nh|ea gignvtþjena gj ohtcavh [htf) \FO ý hvth)  A ih~ qwg fg~ggj hdvgjgt wja nh|ea gignvtþjena gj ohtcavh [htf) \FO ý hvth)  |wgfgj nhcwjenat~g nhj gi awvht ãa g#caei h vgiåohjh* Vacdeåj ~e tgqwegtgj  |wgfgj nhcwjenat~g nhj gi awvht ãa g#caei h vgiåohjh* Vacdeåj ~e tgqwegtgj

a~g~htãa gj Fedwmh Vånjenh) Fedwmh Cgnájenh) Kghcgvtãa Fg~nte|vea) gvn* a~g~htãa gj Fedwmh Vånjenh) Fedwmh Cgnájenh) Kghcgvtãa Fg~nte|vea) gvn*

> >

 ÃJFENG 

 ÃJFENG 

  \TGOANEH   \TGOANEH NA\ÃVWIH NA\ÃVWIH E= E= GI GI \WJVH \WJVH 1>1> 1*1* 1*1*   Gi Gi |wjvh |wjvh 1*4* 1*4*   \thugnneþj \thugnneþj fg fg wj wj |wjvh |wjvh 1>1> 1*>*

1*>*   \iajh~ \iajh~ |tejne|aig~ |tejne|aig~ fg fg |thugnneþj |thugnneþj 1; 1;  1*6*

1*6* Nhva) Nhva) aigmacegjvh aigmacegjvh u u a|atvacegjvh a|atvacegjvh 1010 1*7*

1*7*   Fg|wtafh Fg|wtafh fg fg wj wj |wjvh |wjvh 1010 1*?*

1*?* Ktaoenaneþj Ktaoenaneþj fg fg wj wj |wjvh |wjvh |ht |ht nhhtfgjafa~ nhhtfgjafa~ 1515 1*;*

1*;*   \h~enehjg~ tgiavea~ \h~enehjg~ tgiavea~ fg fg fh~ fh~ |wjvh~ |wjvh~ 4<4< 1*0*

1*0* _e~va~ _e~va~ Awpeieatg~ Awpeieatg~ 4141 1*5*

1*5*   Tgkia~ Tgkia~ fg fg e~edeiefaf e~edeiefaf 4>4> 1*1<*

1*1<*   \thdigca~ \thdigca~

NA\ÃVWIH

NA\ÃVWIH EE= EE= IA IA TGNVA TGNVA 6>6> 4*1*

4*1* Fgoejeneþj Fgoejeneþj 6>6>

4*4*

4*4* \thugnneþj \thugnneþj fg fg wja wja tgnva tgnva 6>6> 4*>*

4*>* \h~enehjg~ \h~enehjg~ |atvenwiatg~ |atvenwiatg~ fg fg wja wja tgnva tgnva 6666

  Tgnva

  Tgnva @hte}hjvai @hte}hjvai

  Tgnva

  Tgnva Othjvai Othjvai

  Tgnva

  Tgnva fg fg \gtoei \gtoei 6767

  Tgnva

  Tgnva _gtvenai _gtvenai

  Tgnva

  Tgnva Jhtcai Jhtcai

  Tgnva

  Tgnva Htvh|gtoei Htvh|gtoei 4*6*

4*6* \wjvh \wjvh qwg qwg |gtvgjgng |gtvgjgng a a wja wja tgnva tgnva 6; 6;  4*7*

4*7* _gtfafgta _gtfafgta Cakjevwf Cakjevwf fg fg wja wja tgnva tgnva 6; 6;  4*?*

4*?* _e~va _e~va fg fg |wjva |wjva fg fg wja wja tgnva tgnva 6060 4*;*

4*;* Htegjvaneþj Htegjvaneþj h h twcdh twcdh fg fg wja wja tgnva tgnva 6565 4*0*

4*0* Ejniejaneþj Ejniejaneþj h h |gjfegjvg |gjfegjvg fg fg wja wja tgnva tgnva 6565 4*5*

4*5* \h~enehjg~ \h~enehjg~ tgiavea~ tgiavea~ gjvtg gjvtg fh~ fh~ tgnva~ tgnva~ 7<7<

  Tgnva~

6

  Tgnva~ |ataigia~ 7<

  Tgnva~ |gt|gjfenwiatg~ 71

  Tgnva~ qwg ~g ntw}aj 74

4*1< \thdigca~ 74

NA\ÃVWIH EEE= GI \IAJH ;7

>*1* Fgvgtcejaneþj fg wj |iajh ;7

>*4* \wjvh u tgnva |gtvgjgnegjvg~ a wj |iajh ;7 >*>* \h~enehjg~ |atvenwiatg~ fg wj |iajh ;? 

  \iajh @hte}hjvai ;?    \iajh Othjvai ;;    \iajh fg \gtoei ;;    \iajh _gtvenai ;0   \iajh Jhtcai ;0   \iajh Htvh|gtoei ;5

>*6* Tgnva~ jhvadig~ gj gi |iajh ;5

  Tgnva @hte}hjvai fgi |iajh ;5

  Tgnva Othjvai fgi \iajh 0<

  Tgnva fg \gtoei fgi \iajh 0<

>*7* Htegjvaneþj fg wj |iajh 0<

>*?* \iajh fg najvh 01

>*;* _gtfafgta cakjevwf fg wj |iajh 04

>*0* Tgnva fg cápeca |gjfegjvg 04

>*5* Ejniejaneþj u |gjfegjvg fgi |iajh 0>

>*1<* \thdigca~ 06

NA\ÃVWIH E_= \ATAIGIE^CH U \GT\GJFENWIATEFAF 111 6*1* Nhjfenehjg~ fg |ataigie~ch gjvtg tgnva~ u |iajh~ 111

  Tgnva |ataigia a wj |iajh 111

  \iajh~ \ataigih~ 114

6*4* Nhjfenehjg~ fg |gt|gjfenwiatefaf 11>

  Tgnva |gt|gjfenwiat a wj |iajh 11>

7

6*6* \iajh~ |gt|gjfenwiatg~ 116

6*7* \iajh cgfeavte} 11? 

6*?* \ht wj |wjvh vta}at wj |iajh |gt|gjfenwiat a wj |iajh fafh u a wja tgnva

fafa 11? 

6*;* Fe~vajnea cá~ nhtva fg~fg wj |wjvh a wja tgnva 11; 

6*0* \thdigca~ 11; 

NA\ÃVWIH _= EJVGT^GNNEHJG^ 115

7*1* Ejvgt~gnneþj gjvtg tgnva u |iajh 115

7*4* Cåvhfh~ fg ~hiwneþj 14< Cåvhfh \iajh fg Najvh 14< Cåvhfh \iajh Nhtvajvg 141   Tgkia~ fg _e~edeiefaf 141 7*>* Ejvgt~gnneþj fg fh~ |iajh~ 144 7*6* Cåvhfh~ fg ~hiwneþj 144 Cåvhfh fg |iajh~ nhtvajvg~ 144 Cåvhfh fg |iajh~ eiecevafh~ 14> 7*7* \thdigca~ 146   DEDIEHKTAOÃA   AJGPH^

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 \TGOANEH

  Gi Vgpvh fg Kghcgvtãa Fg~nte|vea ~g |tg~gjva) nhch wja cajgta fg nhjvtedwet nhj gi  nhjhnecegjvh u a|tgjfe}amg fgi ajáie~e~ vtefecgj~ehjai) qwg g~ wj tgqwe~evh |ata gi fe~gñh  |ata ih~ g~vwfeajvg~ fg ih~ Ej~vevwvh~ Vgnjhiþkenh~ ^w|gtehtg~) Wjegt~evateh~ u fgi jegi   ~gnwjfateh*

  Gj g~va |tecgta gfeneþj ~g nwdtgj vhfh~ ih~ a~|gnvh~ jgng~ateh~ qwg aj fg~fg gi  nhjhnecegjvh fg ih~ |tejne|eh~ owjfacgjvaig~ fg ia a|ienaneþj fg ia~ |thugnnehjg~ a ia Kghcgvtãa Fg~nte|vea) `a~va gi nhjhnecegjvh fg ih~ cåvhfh~ fg ejvgt~gnneþj u hvth~) qwg   |gtcevetáj cá~ afgiajvg) ejvthfwnet a ih~ g~vwfeajvg~ ai nhjhnecegjvh fgi fe~gñh

ejfw~vteai*

 \ht ta}hjg~ fg nhchfefaf) g~vg vgpvh g~vá htkaje}afh gj nejnh na|ãvwih~* Gi N  A\ÃVWIH  E) fgjhcejafh GI \WJVH vtava ~hdtg A|ienaneþj fg ih~ |tejne|eh~ fg ia |thugnneþj htvhkhjai a ia kghcgvtãa fg~nte|vea= Fg|wtafh fgi |wjvh* Ktaoenaneþj fg wj |wjvh |ht  nhhtfgjafa~* \h~enehjg~ tgiavea~ fg fh~ |wjvh~* \h~enehjg~ ~wng~ea~ fg wj |wjvh h fg  ~þiefh~* Tgkia~ fg e~edeiefaf*

 Gi NA\ÃVWIH EE fgjhcejafh IA TGNVA vtava* \h~enehjg~ |atvenwiatg~ fg wja tgnva= `h# te}hjvai) othjvai) fg |gtoei) gtvenai) jhtcai u htvh|gtoãi) \h~enehjg~ tgiavea~ gjvtg fh~ tgnva~= Tgnva~ qwg ~g ntw}aj) |ataigia~) u |gt|gjfenwiatg~* Htegjvaneþj* _gtfafgta cakjevwf* Cåvhfh~= nhj e~va awpeieat u feogtgjnea fg nhva~* \gjfegjvg* _e~va fg |wjva fg ia tgnva**

 Gi NA\ÃVWIH EEE   ) g~vwfea GI \IAJH g~vwfea= \h~enehjg~ |atvenwiatg~ fg wj |iajh= `hte}hjvai) othjvai) fg |gtoei) jhtcai) gtvenai u htvh|gtoei*   Tgnva~ jhvadig~ gj gi |iajh* Htegjvaneþj* _e~va fg najvh u gtfafgta cakjevwf fgi |iajh* Tgnva fg cápeca |gjfegjvg*  \gjfegjvg fgi |iajh*

 Gi NA\ÃVWIH E_) g~vwfea \ataigie~ch u \gt|gjfenwiatefaf= Nhjfenehjg~ fg |ataigie~ch  u |gt|gjfenwiatefaf gjvtg tgnva~ u |iajh~* \ht wj |wjvh vta}at wj |iajh |gt|gjfenwiat a

;

wja tgnva fafa* \iajh cgfeavte}* \ht wj |wjvh vta}at wj |iajh |gt|gjfenwiat a wj |iajh fafh u |ataigih a wja tgnva fafa* Fe~vajnea cá~ nhtva fg~fg wj |wjvh a wja tgnva*

 Gi NA\ÃVWIH _ = fgjhcejafh EJVGT^GNNEHJG^) g~vwfea Ejvgt~gnneþj gjvtg tgnva u   |iajh* Na~h~= Tgnva hdienwa u fg |gtoei* Cåvhfh~ fg ~hiwneþj= \iajh fg najvh) |iajh

nhtvajvg* Tgkia~ fg e~edeiefaf* Ejvgt~gnnehjg~ fg fh~ |iajh~* Na~h kgjgtai u |atvenwiat* Cåvhfh~ fg ~hiwneþj= _e~va awpeieat u |iajh nhtvajvg* Tgkia~ fg e~edeiefaf*

 Ih~ awvhtg~ aktafgngj a vhfh~ qwegjg~ `aj `gn`h |h~edig ia |wdienaneþj fg g~va hdta) a ia~ |gt~hja~ qwg `aj |th|htnehjafh auwfa) a~ã nhch nhj~gmh~ cwu aieh~h~* Ih~ nhcgjvateh~ a g~va gfeneþj ~gtáj degj tgnedefh~*

0

NA\ÃVWIH E= GI \WJVH

1*1* GI \WJVH

Gi |wjvh g~ wja efga) qwg fava fg~fg ia ajvekùgfaf u qwg ~g wveie}a |ata tg|tg~gjvat  wj hdmgvh wdenafh gj gi g~|aneh* Nhj g~vh |hfgch~ ~ec|ieoenat gi ajáie~e~ |ata tg~higt nwaiqwegt ~evwaneþj oã~ena u kghcåvtena*

1*4* \THUGNNEÞJ FG WJ \WJVH

Wj ~e~vgca fg |thugnneþj g~ wj ~e~vgca  |ht cgfeh fgi nwai |wgfg ~gt fgoejefa ia   |thugnneþj fg wj hdmgvh ~hdtg wja

~w|gtoeneg* Gj vhfh ~e~vgca fg  |thugnneþj ejvgtegjgj nwavth gigcgjvh~

fgjhcejafh~= oek*1*1=

a% Hdmgvh* G~ gi hdmgvh qwg ~g fg~ga tg|tg~gjvat* \wgfg ~gt wj |wjvh) tgnva) |iajh) ~w|gtoeneg) ~þiefh) gvn2 gj oej nwaiqwegt gigcgjvh kghcåvtenh w hdmgvh gj ~ã*

D1

D

< A N A1 N1

F

α F1

d% \wjvh fg hd~gtaneþj* \wjvh fg~fg gi nwai ~g hd~gta gi hdmgvh qwg ~g qwegtg tg|tg~gjvat* G~ wj |wjvh nwaiqwegta fgi g~|aneh*

n% ^w|gtoeneg fg |thugnneþj* G~ ia ~w|gtoeneg ~hdtg ia nwai ~g |thugnvatá gi hdmgvh* Kgjgtaicgjvg g~ wj |iajh2 awjqwg vacdeåj |wgfg ~gt wja ~w|gtoeneg g~oåtena) neiãjftena) nþjena) gvn*

f% Tauh~ \thugnvajvg~* ^hj tgnva~ ecakejatea~ qwg wjgj ih~ |wjvh~ fgi hdmgvh nhj gi |wjvh fg hd~gtaneþj*

Ia |thugnneþj (\+% fg nwaiqwegt |wjvh (\% fgi hdmgvh ~g hdvegjg ejvgtng|vajfh ~w  |thugnvajvg nhj gi |iajh fg |thugnneþj*

5

IH^ ^E^VGCA^ FG \THUGNNEÞJ CÁ^ W^AFH^ ^HJ= a% \thugnneþj neiãjftena* ^g

hdvegjg nwajfh gi |wjvh fg hd~gtaneþj ~g gjnwgjvta a wja fe~vajnea vaj ktajfg fgi hdmgvh) qwg |gtceva nhj~efgtat qwg ia~

 |thugnvajvg~ ~hj |ataigia~ ai ejvgtng|vat~g nhj gi |iajh fg |thugnneþj (oek*1*4%* Ih~  |tejne|aig~ ve|h~ fg |thugnneþj neiãjftena ~hj=

1% \thugnneþj htvhkhjai (Chjkg%* Vacdeåj fgjhcejafa |thugnneþj htvhktáoena* ^g hdvegjg nwajfh ia~ |thugnvajvg~ ~hj |gt|gjfenwiatg~ ai |iajh fg |thugnneþj* Ia   |thugnneþj htvhkhjai g~ cwu wveie}afa gj gi fe~gñh fg |eg}a~ cgnájena~ u

caqwejatea~ oek* a* Ih~ |tejne|aig~ ve|h~ fg |thugnneþj htvhkhjai ~hj=

e% \thugnneþj gj e~va~ cýive|ig~*

Nafa e~va g~ wja |thugnneþj htvhktáoena* \ata hdvgjgt wja e~va ~g nhihna gi |iajh fg |thugnneþj   |tgogtgjvgcgjvg |ataigih a wja fg ia~

nata~ |tejne|aig~ fgi hdmgvh oek*1*>*

Ih~ hdmgvh~ ~g tg|tg~gjvaj kgjgtaicgjvg gj vtg~ e~va~ htvhktáoena~* Ih~ cåvhfh~ wveie}afh~ |ata fgvgtcejat g~va~ e~va~ ~hj=

A% \thugnneþj gj gi Vgtngt Nwaftajvg* W~afh gj ih~ G~vafh~ Wjefh~ u Najafá* oek*1*6*

D% \thugnneþj gj gi \tecgt Nwaftajvg (|tecgt hnvajvg%* W~afh gj vhfh gi cwjfh) gpng|vh gj ih~ G~vafh~ Wjefh~ u Najafá* oek*1*7*

1<

\thugnnehjg~ fg |wjvh~ gj oekwta g~|aneai u fg~nte|vea

Nwaftajvg EE Nwaftajvg E <4 <4 < <4 V << <1 < I V I ό₁ Nwaftajvg EEE ό₄ Nwaftajvg E_ <₁ (Gi |wjvh < g~vá gj gi nwaftajvg E%

Vai nhch g~vá tg|tg~gjvafh gi |wjvh gj ia oekwta g~|aneai u fg~nte|vea |wgfg gpvtagt~g qwg |ata |a~at fg ia oekwta g~|aneai a wja fg~nte|vea fgdgtá adavet~g gi  |iajh ό₄ ~hdtg gi |iajh ό₁ ) vgjegjfh nhch gmg fg keth a ia V (iãjga fg vegtta h fg

 |iegkwg%* Fg g~a cajgta qwgfatáj aiejgafh~ <1„ < „ <4) nhch ~g |wgfg a|tgneat gj ia oekwta fg~nte|vea*

Fgdg fg~vanat~g qwg gj ia tg|tg~gjvaneþj g~|aneai a|atgng gi hdmgvh (<%* Gj ia tg|tg~gjvaneþj fg~nte|vea ~hiacgjvg ~g vtadama nhj gi |iajh ό₄ ua adavefh) u ia~

11 Nwaftajvg EE Nwaftajvg E <1 < <4 V <4 <1 <4 << << I V I ό₁

Nwaftajvg EEE ό₄ Nwaftajvg E_

Gi |wjvh (<% g~vá gj gi nwaftajvg EE ό₄ ό₄ H₁ H1 I << V H< V I όόόό₁ <4 H H4 ό₁

\thugnneþj fgi |wjvh (<% wdenafh gj gi >½ nwaftajvg

ό₄ ό₄ V ό₁ I <1 I <13<4 <4 << ό₁

14

Gj g~vg ýivech na~h) gi aigmacegjvh (fe~vajnea fg < ai |iajh gtvenai% vegjg ia ce~ca ihjkevwf qwg ia nhva (fe~vajnea fg < ai |iajh `hte}hjvai) |ht ih vajvh) gj ia tg|tg~gjvaneþj gj OEKWTA FG^NTE\VE_A <1a|atgng ~w|gt|wg~vh nhj <4*

1*>* \IAJH^ \TEJNE\AIG^ FG \THUGNNEÞJ

Vtg~ ~hj ih~ |iajh~ |tejne|aig~ fg |thugnneþj=

․ Othjvai ․ @hte}hjvai u ․ Fg |gtoei

1>

AO= \thugnneþj fgi |wjvh A ~hdtg gi |iajh fg |thugnneþj Othjvai A@= \thugnneþj fgi |wjvh A ~hdtg gi |iajh fg |thugnneþj @hte}hjvai A\= \thugnneþj fgi |wjvh A ~hdtg gi |iajh fg |thugnneþj Fg \gtoei

1*6* NHVA „ AIGMACEGJVH „ A\ATVACEGJVH

\ata gi g~vwfeh fg ia kghcgvtãa fg~nte|vea) g~ jgng~ateh vgjgt degj fgoejefh ia~ fe~vajnea~ fgi hdmgvh a ih~ |iajh~ |tejne|aig~ fg |thugnneþj* G~vh~ ~hj=

Nhva= Fe~vajnea fgi hdmgvh ai |iajh fg |thugnneþj @hte}hjvai (A „ A@%*

Aigmacegjvh=Fe~vajnea fgi hdmgvh ai |iajh fg |thugnneþj Othjvai (A „ AO%*

A|atvacegjvh= Fe~vajnea fgi hdmgvh ai |iajh fg |thugnneþj Fg \gtoei (A „ A\%*

1*7* FG\WTAFH FG WJ \WJVH

Ai adavet gi \iajh fg |thugnneþj @hte}hjvai u gi \iajh fg |thugnneþj fg \gtoei) vgjegjfh nhch gmg~ fg keth a ia~ iãjga~ fg |iegkwg nhttg~|hjfegjvg~) ~g hdvegjg wj ~hih |iajh* A g~vg |iajh ~g ig fgjhceja Fg|wtafh fg wj \wjvh*

16

1*?* KTAOENANEÞJ FG WJ \WJVH \HT NHHTFGJAFA^

Gj gi gjwjneafh fg ih~ |thdigca~) a gng~ ~g ejfena ia wdenaneþj fg ia~   |thugnnehjg~ fg wj |wjvh |ht cgfeh fg nhhtfgjafa~* ^g |wgfg hdvgjgt ia  |thugnneþj @hte}hjvai u Othjvai fg fen`h |wjvh a |atvet fg fen`a~ nhhtfgjafa~*

Gmgc|ih= Tgaie}at gi fg|wtafh fgi |wjvh A(a)d)n)%*

Gi |tecgt nhc|hjgjvg fg ia nhhtfgjafa) jh~ ýjena ia iãjga fg tgogtgjnea gjvtg ia~  |thugnnehjg~ `hte}hjvai u othjvai fgi |wjvh A*

Gi ~gkwjfh nhc|hjgjvg) jh~ ýjena ia |thugnneþj othjvai fgi |wjvh A) u gi vgtngt  nhc|hjgjvg jh~ wdena ia |thugnneþj `hte}hjvai fgi |wjvh A*

17

1*;* \H^ENEHJG^ TGIAVE_A^ FG FH^ \WJVH^

Ia~ |h~enehjg~ tgiavea~ fg fh~ |wjvh~ gjvtg ~ã) ~g |wgfg hd~gtat nhihnajfh wja  dtýmwia gj gi |iajh fg |thugnneþj `hte}hjvai*

1? Tg~|gnvh fg ia oekwta) ~g feng=

D g~vá a ia fgtgn`a fg A) D g~vá atteda fg A) D g~vá fgiajvg fg A)

u ~þih gj gi |iajh @hte}hjvai= D g~vá `anea gi ^wt fg A) D g~vá `anea gi G~vg fg A) h A g~vá `anea gi Jhtvg fg D) A g~vá `anea gi Hg~vg fg D*

1*0* _E^VA^ AWPEIEATG^

Nwajfh ~g vegjg |thugnnehjg~ qwg jh ~g cwg~vtaj afgnwafacgjvg gj ih~ vtg~ |iajh~  |tejne|aig~ fg |thugnneþj) ~g |wgfgj vta}at |iajh~ awpeieatg~* Gpe~vgj fh~ ve|h~ fg

\iajh~ Awpeieatg~ fg \thugnneþj=

․ \iajh~ Awpeieatg~ \tecateh~ u ․ \iajh~ Awpeieatg~ ^gnwjfateh~*

1;

\IAJH^ AWPEIEATG^ \TECATEH^

10

1*5* TGKIA^ FG _E^EDEIEFAF*

Nwajfh ~g vta}a ia |thugnneþj fg ~þiefh~) aj a gjnhjvtat~g ate~va~ hnwiva~) fen`a~ ate~va~ ~g vta}aj nhj iãjga fg ~gkcgjvh~* @au qwg vgjgt gj nwgjva ia~ ~ekwegjvg~ tgkia~ fg e~edeiefaf*

․ Gi nhjvhtjh fg ia |thugnneþj) ~egc|tg g~ e~edig*

․ Nwajfh wja ate~va qwg nhjnwttg a wj åtveng g~ eje~edig) ia~ fgcá~ ate~va~ qwg

nhjnwttgj a fen`h åtveng) vacdeåj ~gtáj eje~edig~*