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07. Nisbatoun ka bayan.

 *Alnasb -ul- arb’a (Nisbton ka bayaan )*

Meeraas key masaail ko hal karne key liye chaar nisbton ka janna bohat zaroori hai kyunkay yeh asal masla ki tasheeh key amal mein bunyadi haisiyat rakhti hain. yeh darj zail hain .

 

At-tmaasul

At-tdaakhul

At-tbaayun

At-twaafuq

 

*At-tmaasul*

 

Agar do Adad masaawi hon to un key darmiyaan tmaasul ki nisbat paayi jati hai. (5.5) ( 3.3 ) ( 2.2 )

 

*At-tdaakhul*

 

Do adadob mein se aik chhota ho aur dosra bada lekin is terhan keh chhota Adad badhy Adad ko poora poora taqseem kar day aur baqi kuch nah bachay to un ke darmiyaan tdaakhul ki nisbat paayi jati hai. maslan ( 3 aur 6) is mein ( 3 ) apne se badhy Adad ( 6 ) ko poora poora taqseem kar deta hai is terhan ( 4 ) aur ( 8 ) is mein ( 4 ) apne se badhy Adad ( 8 ) ko poora poora taqseem kar deta hai .

 

*At-tbaayun*

 

Aisay do Adad jin mein chhota Adad badhy Adad ko poora poora taqseem nah kere. aur nah hi koi teesra Adad un ko poora poora taqseem kere. to un ke darmiyaan tbaaeen ki nisbat paayi jati hai .

 

*At-twaafuq*

 

Do Adad aisay hon keh chhota Adad apne se badhy Adad ko poora poora taqseem nah kere, lekin koi teesra Adad un dono ko poora poora taqseem kar day. maslan (8) aur ( 12 ) un dono ko ( 4 ) poora poora taqseem karta hai isi terhan ( 6 aur 8) un ko ( 2 ) taqseem karta hai. agar un do adadon ko ( 2 ) taqseem kry to kehte hain ke un key darmiyaan tawafuq bin nisaf hai. agar dono ko ( 3 ) taqseem kry to kehte hain ke un key darmiyaan tawafuq bis sulus hai. aur agar ( 5 ) taqseem kre to tawafuq bil khumus kehte hain waghera waghera .

 

*Note*

At-tdaakhul ki nisbat mein jab chhota Adad apne se badhy Adad ko poora poora taqseem kar deta hai to usay bhi twaafuq mein shumaar karte hain maslan ( 6 aur 12 ) mein ( 6 ) badhy Adad ( 12 ) ko poora poora taqseem kar deta hai is liye kaha jaata hai keh un ke darmiyaan tawafuq bis sudus hai .

 

*Baab -ut- tasheeh ( masaail ki tasheeh )*

 

waraasat key ba’az masaail mein kabhi kabhi aisa hota hai keh wasarison ko jo hissa asal masla main aata hai woh un ke Adad -e- ruoos par poora poora taqseem nahi hota balkay un key hisson mein kasar waqay ho jati hai. is kasar ko rafa karne key liye hum asal masla ko kisi munaasib Adad se zarb day kar dosra naya asal masla daryaaft karte hain jis se har waaris apna apna hissa baghair kasar wusool karta hai. is amliyah ko tasaheeh kehte hain .


*Misaal*

 

Aik aadmi apni do biwion aur do ‘Aini bhaaiyon ko zinda chode kar faut ho gaya .

 

*Hal*

Asal masla ( 4 ) hai do biwion ko (1 / 4 ) ( 1 ) mila, do bhaayion ko baqi ( 3 ) miley. biwion aur bhaaiyon ka hissa un key ruoos par poora poora taqseem nahi ho raha. is liye hamein masla key asal ( 4 ) ki tasheeh ki zaroorat hai .

 

4

1 do biwiyan 1/4

3 do ‘Aini bhaai ain


*Asal ki tasheeh karne ka tareeqa*


*Qaaida#1*

 

Agar kisi masla mein waarison key sirf aik fareeq ka hissa un key ruoos par poora poora taqseem nah hota ho, to un ke ruoos aur un key hissay ke darmiyaan chaar nisbton mein se aik nisbat zaroor paayi jaye gi .

 

*(ا)*

 

Agar ruoos aur un key hissa key darmiyaan tabaaeen ki nisbat ho to ruoos ki tadaad ko asal masla se zarb den ge haasil zarb is masla ki tasheeh ho gi. phir ruoos ki ta’daad ko har waaris key hissa mein zarb day kar jawab har fareeq key saamnay tasheeh key neechay tehreer karen ge .

 

*Misaal*

Biwi faut ho gayi. apna khaawand, teen betiyan aur ‘Aini bhaai ko zindah choda .

 

*Hal*

Asal masla ( 12 ) hai. khaawand ko (1 /4 ) (3 ) miley.3 baitiyon ko (2 / 3) (8) miley baqi (1) bhaai ko bator -e- asbah mila. 3 baitiyon ka hissa ( 8 ) un key ruoos par poora poora taqseem nahi ho raha. (3 ) aur (8) key darmiyaan tabaaeen ki nisbat hai lehaza ( 3 ) ko asal masla ( 12 ) se zarb di ( ٣x١٢ = ۳٦ ) haasil zarb ( 36 ) is masla ki tasheeh hai. aur phir ( 3 ) ko khaawand, baitiyon aur bhaai key hisson se zarb diya. is ke nateeja mein khaawand ko ( 9 ), 3 baityon ko ( 24 ) har aik ko ( 8 ) aur ‘Aini bhaai ko ( 3 ) miley .

 

36 = 12×3

9 = 3×3 khaawand 1/4

24 = 3×8 betiyan 2/3

3 = 1×1 bhai ain

 

*(ب )*

 

Agar kisi aik fareeq key ruoos aur is key hissa key darmiyaan tawaafuq ki nisbat ho to ruoos ki ta’daad ko un key tawaafuq se taqseem karte hain. is key jawab ko asal masla mein zarb dete hain aur haasil -e- zarb is masla ki tasheeh hogi. phir is tawaafuq se har waaris key hissa se zarb dete hain .


*Misaal*

Aik aurat faut ho gayi aur apna khaawand, 6 baitiyan aur chacha ko zindah choda .

 

*Hal*

Asal masla ( 12 ) hai. khawand ko ( 1 /4 ) ( 3 ) miley, 6 baitiyon ko ( 2/3 ), ( 8 ) miley chacha ko baqi ( 1 ) mila. baitiyon key ruoos ( 6 ) aur un key hissa ( 8 ) key darmiyaan tawaafuq bin nisaf hai. lehaza ( 6 ) ko ( 2 ) se taqseem kiya. ( 6÷2= 3 ) haasil -e- taqseem ( 3 ) ko asal masla ( 12 ) se zarb diya ( 12×3 = 36 ) haasil zarb ( 36 ) masla ki tasheeh hai. phir har waaris key hisson ko ( 3 ) se zarb diya. chunancha khaawand ko ( 9 ) miley. 6 baitiyon ko ( 24 ) har aik ko ( 4 ) miley aur chacha ko ( 3 ) miley .

 

*( ج )*

 

Agar kisi aik fareeq key ruoos aur un key hissa key darmiyaan tadaakhul ki nisbat ho to usay hal karne key liye tawaafuq ki nisbat wala amal hi kiya jaaye ga.


*Misaal*

1 shakhs faut ho gaya. maa, 8 betiyan aur bhaai ko zind choda .

 

*Hal*

Asal masla ( 6 ) hai maa ko ( 1 / 6 ) ( 1 ) mila 8 baitiyon ko ( 2/3 ) ( 4 ) miley bhaai asbah hai usay baqi ( 1 ) mila. 8 baitiyon aur un

key hissa ( 4 ) key darmiyaan tawaafuq bir rubo’u hai lehaza baitiyon key ruoos ( 8 ) ko ( 4 ) se taqseem kiya. ( 8÷4 = 2) haasil taqseem ( 2 ) ko asal masla ( 6 ) se zarb diya. ( 2×6 = 12 ) haasil zarb ( 12 ) masla ki tasheeh hai. neez har waaris key hissa ko bhi ( 2 ) se zarb diya. chunancha maa ko ( 2 ), 8 baityon ko ( 8 ) har aik ko ( 1 ) aur bhaai ko ( 2 ) miley .

 

12 = 6×2

2 = 2×1 Maa 1/6

8 = 2×4 baitiyan 2/3

2 = 1×2 bhaai ain


*Qaida*

 

Agar kisi masla mein aik se ziyaada fareeqon key hissay un ke ruoos par pooray pooray taqseem nah hotay hon to un key asal masla ki tasheeh key liye do tareeqay hain. pehla tareeqa meeras ki kitaabon mein mojood hai aur chaar nisbton key zariye asal masla ki tasheeh ki jati hai. jo darj zail hai .

 

*(ب)*

 

jab kisi masla mein do ya do se ziyaada fareeqon key ruoos par un key hissay pooray pooray taqseem nah hotay hon aur sab fareeqon ke ruoos key darmiyaan tamaasul ki nisbat ho to kisi aik fareeq key adad ruoos ko asal masla se zarb den ge. aur haasil zarb asal masla ki tasheeh ho gayi. phir isi adad se har fareeq key hisson se bhi zarb den gaye .

 

*Misaal*

1 shakhs faut ho gaya. apni 3 biwiyaan, 3 betiyaan aur 3 chacha zindah chody .

 

*Hal*

Asal masla ( 24 ) hai. 3 biwion ko (1/8 )

( 3 ) miley. 3 baityon ko ( 2/3 ) (16 ) miley aur chachay asbah hein inhen baqi ( 5 ). baityon aur chchaon key hissay unkay ruoos par pooray pooray taqseem nahi hotay. biwi, baityon aur chchaon key ruoos key darmiyan tamaasul ki nisbat hai. lehaza ( 3 ) se asal masla (24) mein zarb den gaye. (3 x 24= 72 ) haasil zarb ( 72 ) masla ki tasheeh hai. phir har fareeq key hissa ko bhi ( 3 ) se zarb den ge. is terhan 3 biwion ko ( 9 ) miley har aik ko (3), 3 baityon ko (48) miley har beti ko ( 16 ) aur 3 chchaon ko ( 15 ) miley. har aik ko ( 5 ) .

 

72 = 3×24

9 = 3×3 (3)biwiyan 1/8

48= 12×3 (3) baitiyan 2/3

15 = 5×3 chacha ain

 

*( ب )*

 

Agar sab fareeqon key ruoos ke darmiyaan tadaakhul ki nisbat ho to sab se bady Adad ko asal masla se zarb den ge. aur haasil zarb masla ki taseeh ho gayi neez isi Adad se har fareeq key hissa se bhi zarb den ge .


*Misaal*

Aik aadmi faut hogaya aur apni ( 4 ) biwion, 3 Akhiyaafi behnon aur ( 12 ) ‘Aini bhaaiyon ko zindah choda .

 

*Hal*

Asal masla ( 12 ) hai. 4 biwion ko ( 3 ) miley, 3 Akhiyaafi behnon ko ( 4 ) miley aur ( 12 ) bhaaiyon ko baqi ( 5 ) miley. is misaal mein har fareeq key ruoos par un key hisson ki taqseem mein kasar waqay hui hai. lekin un key ruoos 3, 4 aur 12 key darmiyaan tdaakhul ki nisbat hai. is liye un mein se bady Adad ( 12 ) se asal masla ( 12 ) ko zarb den ge ( 12×12 = 144 ) haasil zarb ( 144 ) masla ki tasheeh hai is terhan ( 4 ) biwion ko ( 36 ) miley har biwi ko ( 9 ) 3 akhiyaafi behnon ko ( 48 ) miley har behan ko ( 16 ) aur ( 12 ) bhaiyon key ( 60 ) miley har bhaai ko ( 5 ) .

 

12×12 = 144

12×3 = 36 chaar biwiyaan 1/4

12×4 = 48 teen akhiyaafi behnain 1/3

12×5= 60 ( ۱۲ ) ‘Aini bhaai ain

 

*( ج )*

 

Agar sab fareeqon key Adad ruoos ke darmiyaan tawaafuq ki nisbat ho to aik fareeq key Adad ke tawaafuq ko dosray fareeq ke kul Adad ke sath zarb den ge. phir agar haasil zarb aur teesray fareeq key Adad ruoos key darmiyaan tawaafuq ki nisbat ho to haasil zarb ko teesray fareeq key Adad ruoos ke tawaafuq se zarb den ge aur agar Tabaayun ki nisbat ho to teesray fareeq key kul Adad ruoos key sath zarb den ge. phir isi terhan chouthay aur paanchwin fareeq key ruoos key sath amal dohraayen ge. phir un sab ki haasil zarb ko asal masla se zarb den ge. aur haasil zarb masla ki tasheeh hogi. phir sab ki haasil zarb ko dobarah har fareeq key hissay ke sath bhi zarb den ge .


*Misaal*

Aik aadmi faut ho gaya. apni 4 biwiyon, 6 baitiyon aur 10 ‘Aini behnon ko zindah choda .

 

*Hal*

Asal masla ( 24 ) hai. 4 biwion ko ( 3 ) miley. 6 baitiyon ko ( 16 ) miley aur 10 ‘Aini behnon ko ( 5 ) miley is masla mein har fareeq key ruoos par un ki hisson ki taqseem mein kasar waqay hui hai aur sab fareeqon key Adad ruoos 4, 6, 10 key darmiyaan tawaafuq ki nisbat paayi jati hai. lehaza ( 10 ) aur ( 6 ) key darmiyaan tawaafuq bin nisaf hai. ( 10 ) ka tawaafuq ( 5 ) hai. usay ( 6 ) se zarb di ( 5×6 = 30 ) haasil zarb ( 30 ) hai, ab ( 30 ) aur ( 4 ) key darmiyaan bhi tawaafuq bin nisaf hai. ( 30 ) ka tawaafuq ( 15 ) hai usay ( 4 ) se zarb diya ( 15×4 = 60 ) haasil zarb ( 60 ) hai. ab ( 60) ko asal masla ( 24؍ ) se zarb diya. ( 24×60 = 1440 ). haasil zarb ( 1440 ) hai jo masla ki sahih hai. ab dobarah ( 60 ) ko har fareeq key hissa se zarb diya. is terhan 4 biwion ko ( 180 ) miley har biwi ko ( 45 ) miley. 6 baitiyon ko ( 960 ) miley har beti ko ( 160 ) miley aur ( 10 ) ‘Aini behnon ko ( 300 ) miley har behan ko ( 30 ) miley .

 

24×60 = 1440

3×60 = 180 chaar biwiyaan 1/8

16×60 = 960 baitiyan 2/3

5×60 = 300 (10) ‘aini behnain ain

 

*( ا)*

 

Agar sab fareeqon key Adad ruoos key darmiyaan Tabaayun ki nisbat paayi jaati ho to pehlay fareeq key Adad ruoos ko dosray fareeq ke Adad ruoos se zarb den ge. phir is ki haasil zarb ko teesray fareeq key adad ruoos se zarb den ge. aur isi terhan is haasil zarb ko chouthay phir paanchwin fareeq key adad ruoos key sath amal dohrayen ge. aur aakhri haasil zarb ko asal masla key sath zarb den ge. aur haasil key sath zarb den ge zarb is ki masla ki tasheeh hogi.


*Misaal*

Aik aadmi faut ho gaya aur apni 2 biwiyon, 5 baitiyon aur 3 bhaaiyon ko zindah choda .

 

*Hal*

Asal masla ( 24 ) hai. 2 biwiyon ko ( 1 / 8 ) ( 3 ) miley. ( 5 ) baityon ko ( 2/3 ) ( 16 ) miley. aur baaqi 3 bhaayion ko miley. is masla mein sab fareeqon key Adad ruoos ( 2 ,5 ,3 ) ke darmiyaan tabaayun ki nisbat hai. pehlay ( 2 ) ko ( 5 ) se zarb den ge. ( 2×5 = 10 ) haasil zarb ( 10 ) ko ( 3 ) se zarb den ge (3×10=30 ) haasil zarb (30 ) ko asal masla ( 24 ) se zarb den ge. (30×24=720 ) haasil zarb ( 720 ) is masla ki tasheeh hai phir har fareeq key hissay ko ( 30 ) se zarb den ge. is terhan ( 20 ) biwiyon ko ( 90 ) har biwi ko ( 45 ) miley. ( 5 ) baitiyon ko ( 480 ) har beti ko ( 96 ) miley aur ( 3 ) bhaaiyon ko ( 150 ) miley har bhaai ko ( 50) miley .

 

30×25=720

30×3=90 Do biwiyaan 1/8

30×16 = 480 ( 5 ) baitiyaan 2/3

30×5 = 150 teen bhaai ain


*Dosra tareeqa*


 

Yeh tareeqa rayazi janne walon key liye bohat aasaan hai. agar kisi masla mein aik se ziyada fareeqon ke hissay un key Adad ruoos par pooray pooray taqseem nah hotay hon. aur sab fareeqon key Adad ruoos ke darmiyaan chaar nisbton mein se koi bhi nisbat paayi jaye. to is masla ki tasheeh karne key liye sab fareeqon key adad ruoos ka zo-az’aaf aqal maloom karen ge phir is se asal masla mein zarb den ge aur haasil zarb is masla ki taseeh ho gayi. phir zo-az’aaf aqal se har fareeq key hissa se zarb den .

 

*Misaal*

Aik aadmi faut ho gaya aur apni 4 biwiyan, 18 betiyan aur 8 chacha zindah chhody .

 

*Hal*

Asal masla ( 24 ) hai. (4) biwion ko ( 1/8 ) ( 16 ) miley aur 8 chachon ko ( 5 ) miley

 

24×72 = 1728

3×72 = 216 (4) biwiyaan 1/8

72×16 = 1152 ( 18 ) betiyaan 2/3

72×5 = 360 (8) chachy ain

 

har fareeq key hissay un ke darmiyaan pooray pooray taqseem nahi hotay. is liye ( 4, 8,18 ) ka zo-az’aaf aqal maloom karen ge


* Zo-az’aaf aqal maloom karne ka tareeqa*


 

2 . 4 .18 .8 .

2 . 2 . 9 . 4

3 . 1 . 9 . 2

3 . 1 . 3 . 2

2 . 1 . 1 . 2

1 . 1 . 1

 

un ka zo-az’aaf aqal ( 72 ) hai

usay asal masla ( 24 ) se zarb den ge ( 24×72 =1728 ) haasil zarb ( 1728 ) is masla ki tasheeh hai phir ( 72 ) ko har fareeq key hissa se zarb diya. nateeja key tor par ( 4 ) biwion ko ( 216 ) miley har biwi ko ( 64 ) miley. ( 18 ) baitiyon ko ( 1152 ) miley har beti ko ( 64 ) miley. aur ( 8 ) chachon ko ( 360 ) miley. har chacha ko ( 45 ) miley.

 

REFERENCE:
Book: “Islam Ka Qanoon-e-Warasaat”
By Salah Uddin Haider Lakhwi.

 

 

sheikh Ubaid ur Rehman muhammadi | islami qanoon e miras | lecture_6 | Ramadan Mubarak 2023
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