Episodes in the Mathematics of Medieval Islam by J. L. Berggren

Author:J. L. Berggren
Language: eng
Format: epub
Publisher: Springer New York, New York, NY

Finally, Thābit shows the correspondences between the geometric solution given and the algebraic solution. BH = BW ↔

half the number of roots,

Square on BW ↔

square of the above,

Rectangle on HA · AB ↔

numbers,

Square on AW ↔

sum of the two preceding,

AW ↔

square root of the sum,

AW – BW = AB ↔

the square root less half the number of roots.

He adds (p/2)2 to each side to obtain

With his geometrical interpretation of all terms as areas he is able to apply Euclid II,6 to the left-hand side to obtain

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