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

66 DETERMINATIONS
(2) Determinations pertaining to series (śreḍhî-vyavahâra)
(i) SERIES IN ARITHMETIC PROGRESSION
(GEOMETRICAL INTERPRETATION)
Form of a series-figure (śreḍhî-kṣetra) :
79. As in the case of an earthen drinking glass
(śarâva) the width at the base is smaller and at the top
greater, so also is the case with a series-figure (śreḍhî-kṣetra).
The altitude (lambaka) of that (series-figure) is equal
to the number of terms (gaccha) of the (corresponding)
series.
The series-figure contemplated here is a plane figure resembling a
trapezium with equal flank sides
If a series be
a+(a+d)+(a+2d)+... to n terms,
then, according to the second part of the verse, the altitude of the corres-
ponding series-figure = n units, say n cubits.
80(i). The (partial) areas (phala) of the series-figure
for the successive cubits (kara) of the altitude form a series
which begins with the given âdi ('first term of the series')
and increases successively by the given caya ('common diffe-
rence of the series').
That is, the area of the series-figure for the first cubit of the altitude
= a, i.e., the first term of the series; the area of the series-figure for the
second cubit of the altitude = a+d, i.e., the second term of the series; the
area of the series-figure for the third cubit of the altitude = a+2d; and
so on.
Construction of a series-figure :
80(ii). I shall now describe the method for finding
the lengths of the base (i.e., lower side, bhû) and the face
(i.e., upper side, mukha) of the series-figure (corresponding
to the first term of the series).
81. The number of terms (pada), i.e., one, is the alti-
tude of the (corresponding) series-figure ; the first term of
Indological Truths