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Indian mathematics, Kaye (1915).djvu/49
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INDIAN MATHEMATICS.
33
Date
Circa.
Authority.
Value of
π
{\displaystyle \scriptstyle {\pi }}
A.D. 150
Ptolemy
3
17
120
{\displaystyle \scriptstyle {3{\frac {17}{120}}}}
=
3
⋅
14166.
{\displaystyle \scriptstyle {=3\cdot 14166.}}
„ 263
Liu Hiu
3
7
50
{\displaystyle \scriptstyle {3{\frac {7}{50}}}}
=
3
⋅
14.
{\displaystyle \scriptstyle {=3\cdot 14.}}
„ ?
Puliśa
3
177
1250
{\displaystyle \scriptstyle {3{\frac {177}{1250}}}}
=
3
⋅
1416.
{\displaystyle \scriptstyle {=3\cdot 1416.}}
„ 450
Tsu Ch'ung-chi
3
1
7
{\displaystyle \scriptstyle {3{\frac {1}{7}}}}
=
3
⋅
14286.
{\displaystyle \scriptstyle {=3\cdot 14286.}}
„ 500
Aryabhata
3
{\displaystyle \scriptstyle {3}}
=
3
⋅
{\displaystyle \scriptstyle {=3\cdot }}
"
62832
20000
{\displaystyle \scriptstyle {\frac {62832}{20000}}}
=
3
⋅
1416.
{\displaystyle \scriptstyle {=3\cdot 1416.}}
"
3393
1080
{\displaystyle \scriptstyle {\frac {3393}{1080}}}
=
3
⋅
14166.
{\displaystyle \scriptstyle {=3\cdot 14166.}}
„ 628
Brahmagupta
3
{\displaystyle \scriptstyle {3}}
=
3
⋅
{\displaystyle \scriptstyle {=3\cdot }}
"
10
=
3
1
7
{\displaystyle \scriptstyle {{\sqrt {10}}=3{\frac {1}{7}}}}
=
3
⋅
14286.
{\displaystyle \scriptstyle {=3\cdot 14286.}}
"
10
=
721
228
{\displaystyle \scriptstyle {{\sqrt {10}}={\frac {721}{228}}}}
=
3
⋅
16228.
{\displaystyle \scriptstyle {=3\cdot 16228.}}
„ 800
M. ibn Musa
10
{\displaystyle \scriptstyle {\sqrt {10}}}
=
?
{\displaystyle \scriptstyle {={\text{?}}}}
„ ?
Māhavīra
3
{\displaystyle \scriptstyle {3}}
=
3
⋅
{\displaystyle \scriptstyle {=3\cdot }}
"
10
{\displaystyle \scriptstyle {\sqrt {10}}}
=
?
{\displaystyle \scriptstyle {={\text{?}}}}
„ 1020
Srīdhara
3
{\displaystyle \scriptstyle {3}}
=
3
⋅
{\displaystyle \scriptstyle {=3\cdot }}
"
10
{\displaystyle \scriptstyle {\sqrt {10}}}
=
?
{\displaystyle \scriptstyle {={\text{?}}}}
"
3
1
6
{\displaystyle \scriptstyle {3{\frac {1}{6}}}}
=
3
⋅
1666.
{\displaystyle \scriptstyle {=3\cdot 1666.}}
„ 1150
Bhāskara
3
{\displaystyle \scriptstyle {3}}
=
3
⋅
{\displaystyle \scriptstyle {=3\cdot }}
"
3
1
7
{\displaystyle \scriptstyle {3{\frac {1}{7}}}}
=
3
⋅
14286.
{\displaystyle \scriptstyle {=3\cdot 14286.}}
"
3
17
120
{\displaystyle \scriptstyle {3{\frac {17}{120}}}}
=
3
⋅
14166.
{\displaystyle \scriptstyle {=3\cdot 14166.}}
"
3
177
1250
{\displaystyle \scriptstyle {3{\frac {177}{1250}}}}
=
3
⋅
1416.
{\displaystyle \scriptstyle {=3\cdot 1416.}}
Approximately correct value ..
3
⋅
14159.
{\displaystyle \scriptstyle {\ 3\cdot 14159.}}