पञ्चसिद्धान्तिका (आचार्य वराहमिहिर - सूर्य, रोमक, पौलिश, वासिष्ठ एवं पितामह सिद्धान्त)

70 PAÑCASIDDHĀNTIKĀ III.31
The rule is explained thus: The Moon moves in its own orbit, inclined to the ecliptic at an angle
equal to the maximum latitude. Hindu astronomy assumes this motion to be on the ecliptic itself
and gives the Moon's longitude, because there is only a maximum difference of 7'. Between the
ascending and the descending nodes the orbit is north of the ecliptic and therefore the latitude
measured on the great circle perpendicular to the ecliptic and passing through the Moon, is north.
Between the descending node and the ascending, the orbit is south and the latitude is south. The
distance between the node and the Moon, the latitude and the angle of inclination forming a spherical
triangle, we have : sin latitude = sin interval × sin maximum latitude. The maximum being small
and the latitude being generally less than this, sin latitude and sin maximum latitude are propor-
tional to the latitude and maximum latitude, and we have the formula, lat = max. lat × sin interval.
But the Paulīśa takes the latitude proportionate to the interval itself and gives the rule.
We have to consider here whether the author intends that the latitude is to be found in propor-
tion to the actual degrees of the interval or the sine of the interval in degrees. The triangle being
spherical, the correct thing would be to use the sine. But we have reason to think that the degrees
themselves are intended to be used in the proportion, for if the sine is to be used it must be men-
tioned. Also, this Siddhānta uses only the proportion by degrees in other places also, where propor-
tion by sines alone would be correct, as for e.g. in the solar eclipse, in correcting Rāhu and in
calculating valana, i.e. transformation of direction (see VI. 2-4, 8). Therefore the original Paulīśa
itself has instructed proportion by degrees, as being sufficiently accurate, which the author reiterates
here. But in computing the parallax (in time) in the case of the solar eclipse the sine is used either
by the Paulīśa itself, to avoid too much inaccuracy, or by the author VM to save the Siddhānta from
ridicule. As for TS they say that the author intends here proportion only by sine, that being the
proper thing to do.
Another thing should be mentioned here. In using proportion by degrees, the maximum error
will be in the neighbourhood of the nodes. With the maximum latitude 280', the latitude for 13°
interval would be 40½ minutes, which would be incompatible with the formula for eclipses (vide
VII. 5-6). Therefore it seems that the Siddhānta, though knowing that proportion by sine is the
correct thing for latitudes, gives proportion by degrees for the sake of ease of computation. Or by
taking liptāśatatrayeṇāśītim as the correct reading, which would make the maximum 380', the
incompatibility can be avoided. It may be argued that the error in the latitude would be great in the
neighbourhood of the maximum. But this is only erring one side while some others err on the
other. The mean maximum latitude is 309'. If some like Ptolemy give 240', which is less by 70',
what is wrong in taking that the Paulīśa gives 380', which is greater by the same amount?
Now for the readings: In the fourth foot of verse 30, mu is corrected into su because murāt is
meaningless. In the third foot of the 31st verse two syllables are wanting and nā is added for pur-
poses of syntax. For the same reason, śī-tama-nupā in the fourth foot is corrected into śī-tyā-nupā.
The correction of aśīti into saptati by TS here is unwarranted, because it is not known what it was
in the original Paulīśa. If this is done in conformity with the Saura, why not in conformity with the
Romaka, which gives 280', (see VIII. 11), and which is nearer to the Paulīśa?
Now follow six verses devoted to criticising the views of the Romaka, and an astronomer by name
Bhadraviṣṇu, the intention of the author being to create faith in his own work. (This was a custom
in those days, vide for instance the Brāhma-Sphuṭa-Siddhānta, Dūṣaṇādhyāya and the Vaṭeśvara
Siddhānta, Madhyamā-dhikāra, Chapter X). In several places of the text the readings are not clear
and we cannot be sure of what exactly the author intends to say, though the gist is clear, the matter