cover image: Journal of the Royal Asiatic Society of Bengal  1949 (Science)

Premium

20.500.12592/snsp7f

Journal of the Royal Asiatic Society of Bengal 1949 (Science)

1949

(3) One of the problems occupying the attention of Leibniz in 1693 was the integration of differential equations in series in particular that of the equation giving rise to the sine series: a2d2xIcly2-Fx = 0 which is in the notation of the present paper p2d2y/ds2+y = 0. The last-mentioned fact would appear to suggest that Leibniz's approach to the series was different from that of the Hindus. [...] The perpendiculars from the chosen point to the East-West line and the North-South line are termed respectively the bhujajya (y say) and the kotijyri (x say) through the point *; the distance of the foot of the former perpendicular from the East point (p — x = x say) is referred to as the aaram (meaning literally `arrow') of the chosen point. [...] The difference between the bhujäjytis through the extremities of the arc is called the bhujakhanclam of the gi8tacapain ; the difference between the kotijyas of the extremities and that between the scrams of the extremities are called kotikhamfam and garakhargam respectively. [...] The right-angled triangle whose hypotenuse is the radius through the mid-point of a giqctcdpam and sides are the bhujjyd and the kotijyd through the mid-point is similar to the right-angled triangle whose hypotenuse is the samastajyd of the 4i stacCipam and sides are the kotikhandam and the bhujakhandam of the ai stacCipam for the two triangles have their corresponding sides (in the order ment [...] difference between the istajyä and the ifacapant): y—s = 1 s) 2 l(n —1)/ 11+ (71 — 2)Y2 + + 11 1-11 (5)lira p n Next adding the equalities (2) we obtain LEMMA 3. The difference between the kotijyä of the mid-point Pi of the first cdpakhauclam and that of the mid-point P of the last cdpkhanclam is the sum of the pinclajyds (excluding the last) multiplied by the c5pakhaudasamastajy5 and
technology medicine science
Pages
46
Published in
India
SARF Document ID
sarf.120250
Segment Pages Author Actions
Cover
i-i unknown view
Frontmatter
ii-iv unknown view
The Sine and Cosine Power-Series in Hindu Mathematics
1-14 C.T. Rajagopal, A. Venkataraman view
Haemolysis by Bile Salts
15-24 A.C. Roy view
Ibn Al-Haitham on the Paraboloidal Focussing Mirror
25-40 H.J.J. Winter, W. ‘Arafat view
Backmatter
i-ii unknown view

Related Topics

All