Chandogya Upanisad -- mathematics and ritual

[Toke Lindegaard Knudsen]

Dear list-members,

I am doing research on the Sulbasutras of ancient India and I am
interested in the connection between ritual and mathematics in the
Vedic times (for example if mathematics has a ritual origin as
proposed by A. Seidenberg).  I came across one verse in the
Chandogya Upanisad (7.1.2)  which I found very interesting.  In the
verse Narada explains to Sanatkumara what he knows and has
studied and in the translation of Patrick Olivelle (Oxford) Narada
mentions two things, namely "mathematics" and "the science of
ritual."  There seems to be made a distinction here, i.e. that
mathematics has a status of a science separate from ritual and not
a tool used in ritual (for example geometry used for altar
constructions as indicated in the Sulbasutras).

However, I do not read sanskrit, nor do I have an edition of
Chandogya Upanisad with transliterated text.  Can anyone help me
with what exact words are used for "mathematics" and "the
science of ritual" in the above-mentioned verse?  I am interested in
knowing whether the word in the text indicates a branch of
mathematics (say, arithmetic or geometry) rather than
mathematics in general.

What is the dating of the Chandogya Upanisad?

Thank you very much.

Sincerely,
Toke Lindegaard Knudsen
tlk at math.ku.dk