Very interesting comments have been posted by Mr. Aravind Kolhatkar and Mr. H. N. Bhat. For the fear that they may not get noticed, I am reproducing them in this supplement.
(1) From Mr. Aravind Kolhatkar –
अनुद्यमेन तैलानि तिलेभ्यो नाप्तुमर्हति
This reminded me of something that I had forgotten over the last several decades.
विश्वनाथ in साहित्यदर्पण has cited तिल and तैल as an instance of लक्षणलक्षणा, whereby a derived word becomes generic to all similar words of that type. तैल is the extract of तिल, a word going back to times when that was the main oilseed in use. Later, more such oilseeds came into use but their extracts were also called तैल. Even mineral oil is called मिट्टीका तेल. Somewhat like all hydrogenated oils (वनस्पति तेल) being called as डालडा, that being the first one of its type.
(2) From Mr. Aravind Kolhatkar –
कर्मण्येवाधिकारस्ते मा फलेषु कदाचन कर्मण्येवाधिकारस्ते मा फलेषु कदाचन
In a lighter vein, this can also be translated as
“It is your duty to keep doing what you are meant to do. In the end you may not always get fruit as your reward, sometimes you may also have to settle with plain ‘channas’!
(3) From Mr. H. N. Bhat –
Aravindaji has rightly observed the specialization of meaning from the word तैल by expanding its scope. Strictly speaking, तैल means the oil derived from the word तिल = तिलानामिदम् (संबन्धि) – तैलम्। and extensively used in the generic sense of oil.
But what struck me was the plurality of तैल as it has no specific purpose to serve in the verse than filling in the metrical requirement. Here by the लक्षणलक्षणा – I would translate as the plurality of तिल by connotation by the plurality covers all other oil seeds like तिल and in this sense तैलानि would mean different kinds of oil. as in the usage “काकेभ्यो दधि रक्ष्यताम्” which implies all the birds or animals from which the curd is protected and not only crows.
I hope this would solve to certain extent the problem in the above reading. I got the same quoted in सुभाषित-रत्न-भण्डागार ascribed to शार्ङ्गधरपद्धति (४५४) without plurality with a different reading for the second half –
अनुद्यमेन कस्तैलं तिलेभ्यः प्राप्तुमर्हति?
as a rhetoric question.
And for the figure of speech, अलंकारः, it is a case of अर्थान्तरन्यास which is defined as followed:
8 A general proposition; उक्तिरर्थान्तरन्यासः स्यात् सामान्य-विशेषयोः Chandr.5.12. -9 (In Rhet.) A figure of speech thus defined by Mammaṭa:- प्रस्तुतस्य यदन्येन गुणसाम्यविवक्षया । ऐकात्म्यं बध्यते योगात्तत् सामान्यमिति स्मृतम् ॥ K. P.1. -1 A general statement or expression;
(4) From Mr. H. N. Bhat –
A very interesting and funny सुभाषित grasping the clue from the quoted verse कर्मण्येवाधिकारस्ते is found:
उद्योगः खलु कर्तव्यः फलं मार्जारवद् भवेत्।
जन्मप्रभृति गौर्नास्ति, पयः पिबति नित्यशः॥
The second half how the result will entail your effort like a cat. which (even though) is not a cow by birth, but drinks milk daily!
(5) From Mr. H. N. Bhat –
The translation would be precise for the quoted सुभाषित-
“The cat is not a cow (rather calf), but since birth it drinks milk daily.”