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Vol. IV, No. 3.] Notes on Indian Mathematics. 119 
[N.S.] 
Approximate length in 
Daktulos. Pexus. Orguia. English measures 
Daktulos ... 1 a ct ‘75 inches. 
Pexus Spe 24 1 me 18°00, 
Orguia a 96 4 1 72°00 
he approximate lengths in the first table are oniouleped from 
the length of the yaana given by Dr. Fleet, and in the seco 
taken from Dr. Smith’s Classical Dictionary. Other Hindu ‘abies 
o not agree so closely with Aryabhata. 
square is a figure having iy the four sides equal and its 
area ts the product of two equal number 
The product of three equal nanbere is a cube and it also has 
twelve edges. 
Euclid, in his seventh book, gives the following definitions :— 
“Two numbers multiplied together produce another which 
is called a i te in number, while the numbers thigh, were multi- 
plied together are called sides. 
‘Three numbers multiplied together produce another which 
is called a solid number, while the numbers which were multiplied 
together are called sides.” (11., 187 Heiberg et Menge.) 
4, Square having been subtracted from square always the non- 
square iene be divided by double the square root. The quotient in a 
place set apart is the roo 
To this and the oe rule, Rodet attached undue im- 
portance. He was led to think that the rule implies a knowledge 
our modern ae: of arithmetical notation ; but he was led to 
this conclusion by the commentators of the Lildavati, and by 
the practice followed by Hindu mathematicians in the fifteenth 
century. he ab as it stands, is perfectly general and applies to 
very accurate results in the extraction of square roots. 
Brahmagupta does not give this rule at all, although he aa 
the next one, relating.to cube-roots, word for word. It 
rep ae also that Bhaskara does not usually employ = general 
rule is examples are as follows: First “Squ - 
5. Answers—81; 196; 88209; 100100035. Then, * Find 
the square roots of 4; 9; 81; 196; 88209 : 100100025. Answers: 
97; 10005. : 
To the present day those Hindus, who are taught on purely 
indigenous lines, learn tables of squares to a prodigious extent. 
These enormous tables are a relic of the a see: the gia 
* place-value’ a was unknown. (See Journ, Asiatic Soc 
Bengal, 1907, p. 495.) 
ie ane henge ee 
ppeared to modify his views afterw: ards. ee asks (Journ. Asia 
tique oe “ Arvabhata effectuait-il encore ses calcu sur Vabaque 
The answer is‘ ‘Nor The Hindus did not Semanelly use che tts e eg cideans pore 
was and is almost unknown to them except as a recent foreign introd: 

