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

SERIES IN ARITHMETIC PROGRESSION 67
the series (mukha) as diminished by half the common diffe-
rence of the series is the base (dharā) ; and that (base) in-
creased by the common difference of the series is the face
(vaktra). All these should be shown by means of threads.
That is,
base = a − d/2,
and face = (a − d/2) + d, i.e., a + d/2.
82. (Two) threads should then be stretched out, one
on either side, joining the extremities of those base and face :
these are the flank sides (bāhu) of the series-figure.
When the base is negative, these threads should be
stretched out crosswise.
Thus the series-figure will be of one of the following two forms :
(i) (ii)
[चित्र १: समलम्ब चतुर्भुज (Trapezoid) — ऊपर 'face', नीचे 'base', बाएँ व दाएँ 'flank side', मध्य में लम्ब 'altitude']
[चित्र २: परस्पर सम्मुख दो त्रिभुज (Crossed/Hourglass) — ऊपर 'face', नीचे 'base', मध्य में लम्ब 'altitude']
Forms (ii) corresponds to the negative base.
83. (When the base is negative the series-figure reduces
to two triangles situated one over the other.) In the upper
triangle, the altitude is equal to the face as divided by
face minus base ; and that subtracted from one gives the
altitude in the lower triangle.
That is,
(i) altitude of the upper triangle = face / (face − base), i.e., (2a + d) / 2d,
(ii) altitude of the lower triangle = 1 − face / (face − base), i.e., (d − 2a) / 2d.
Indological Truths