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

PLANE FIGURES 87
Enumeration of primary plane figures :
110–111. The rectangular quadrilateral, the equilateral
quadrilateral, the equi-bilateral quadrilateral, the equi-trila-
teral quadrilateral, the inequilateral quadrilateral, the equi-
lateral triangle, the scalene triangle, the isosceles triangle, the
circle, and the segment of a circle—these are the ten (primary)
plane figures ; the areas of these (figures) should be determined
by applying their own rules. And by considering (the shape
in terms of ) these (figures) should be obtained the areas of
other figures, such as (those of the shape of ) an elephant's
tusk, a felloe, etc.
Nârâyaṇa, too, like Śrīdhara takes the primary plane figures to be 10
in number. But his list of primary plane figures differs from that of
Śrīdhara in so far as "the segment of a circle" has been replaced by him
by "the conch-figure."
Mahâvîra gives the following list of 16 primary plane figures : .
(1-3) Three varieties of triangles, equilateral, isosceles, and scalene ;
(4-8) Five varieties of quadrilaterals, equilateral, equidichastic (dvi-dvi-
sama), equibilateral, equitrilateral, and inequilateral ;
(9-16) Eight varieties of curvilinear figures, a circle, a semi-circle, an
ellipse, a conchiform area, a concave circle, a convex circle, an
outlying annulus, and an in-lying annulus.
Mahâvîra’s classification of quadrilaterals deserves special attention,
as it differs from that of Śrīdhara. Śrīdhara’s commentator has referred
to this classification, and has tried to justify Śrīdhara’s classification.
On a formula for the area of a triangle or a quadrilateral :
112–114. (It is said that) the product of half the sums
of the sides and counter sides (i.e., the product of half the
sum of the base and face and half the sum of the flank sides)
of a triangle or a quadrilateral, gives the gross value of the
area.¹ But this result is true only for those figures in which the
difference between the altitude and the flank sides is small.
In the case of other figures the above result is far removed from
¹ Reference is evidently to BrSpSi, xii. 21(i) where this rule is given.
This rules occurs also in GSS, vii. 7(i), MSi, xv. 66. and GK, II, p. 3, vs. 8.