पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

86 DETERMINATIONS
(3) Determinations pertaining to plane figures
(Kṣetra-vyavahāra)
(i) INTRODUCTION
Fundamental property of rectilinear figures :
108. (In rectilinear figures) the sum of all sides except
one, is neither equal to nor less than the side excepted,
because a curved path is neither less than nor equal to the
straight path.
What the author means here to say is that a rectilinear figure, such
as a quadrilateral or a triangle, is possible only when each of its sides is
less than the sum of the remaining sides.
Nārāyaṇa has made this statement more clearly :
“When in a rectilinear figure, the sum of the other sides is less than
or equal to the greatest side, it is impossible.”¹
Āryabhaṭa II states the same condition as follows :
“When (in a rectilinear figure) each side is less than half the sum
of all the sides, it is possible ; when (on the other hand) half the sum of
all the sides is less than (or equal to) any one of the sides, it is im-
possible.”²
Condition for the existence of ‘the perpendiculars dropped
from the vertices to the base’ and ‘the segments into which
the base is divided by them’ in the case of a quadrilateral :
109. Only in those (quadrilateral) figures in which the
square of base minus face exceeds the product of the difference
and sum of the flank sides, do ‘the perpendiculars dropped
from the vertices to the base’ (lamba) and ‘the segments into
which the base is divided by them’ (abadhā) exist.
Nārāyaṇa has criticised this rule.³ His criticism, however, is not
well-grounded as it is based on an impossible quadrilateral.

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¹ GK, II, p. 48, lines 8-11. So also says Bhāskara II. See L (ASS),
pp. 151-152, vs. 163.
² MSi, xv. 64.
³ GK, II, p. 49.