user23342: In "The Longer Advice to Rāhula" the following appears:

Muditaṁ, rāhula, bhāvanaṁ bhāvehi.
Muditañhi te, rāhula, bhāvanaṁ bhāvayato yā arati sā pahīyissati.

Bhante Sujato translates this as

Meditate on rejoicing.
For when you meditate on rejoicing any discontent will be given up.

Thanissaro Bhikkhu:

“Develop the meditation of empathetic joy. For when you are developing the meditation of empathetic joy, resentment will be abandoned.

Bhikkhu Vagga:

"Rāhula, develop meditation on altruistic joy; for when you develop meditation on altruistic joy, any discontent will be abandoned.

Can somebody please explain which terms correspond to which here, and how the translation is carried out? Thank you

user10100: Arati is feeling boring, sad, annoying, mad, no-right, or envy when someone getting good resultant, something good or happiness, such as one feel boring when the opposite party win an election, or an ex-boyfriend feeling sad for an ex-girlfriend getting new partner.
Mudita is feeling happy, congratulation for someone getting good resultant, something good or happiness, such as one feel congratulation when the opposite party win an election, or an ex-boyfriend feeling happy for an ex-girlfriend getting new partner.

user254: Can somebody please explain which terms correspond to which here

"Muditaṁ"

rejoicing
empathetic joy
altruistic joy


"bhāvanaṁ bhāvehi"

Meditate on
Develop the meditation of
develop meditation on


"Muditañhi" and "bhāvanaṁ bhāvayato" (repeated as above)
arati

discontent
resentment


pahīyissati

given up
abandoned



how the translation is carried out?
I guess you're asking how translators learn to understand a new or "foreign" language?
I think people often have a teacher, when they're learning.
And when they learn, they learn:

Grammar
Vocabulary
Subject matter

... so they learn the meanings of words and also what the author is likely to be saying when they use those words.
I suppose you learn the "meaning" of a word by seeing it used in context and recognising it when you see it again. For example I think that "the meditation to develop metta" is called "metta bhavana" -- and I recognise "mudita" as being one of the four bhamaviharas (of which metta is another) -- and so together perhaps that helps me to understand or recognise what "Muditaṁ bhāvanaṁ bhāvehi" means (i.e. substituting mudita for metta).
Why is it that Aarti is translated as resentment in one case, but discontent in the others?
I think they ("resentment" and "discontent") are similar in meaning.
There are some essays about the brahmaviharas here: https://accesstoinsight.org/search_results.html?&q=brahmaviharas
One of those says,

These four attitudes are said to be excellent or sublime because they are the right or ideal way of conduct towards living beings (sattesu samma patipatti). They provide, in fact, the answer to all situations arising from social contact. They are the great removers of tension, the great peace-makers in social conflict, and the great healers of wounds suffered in the struggle of existence. They level social barriers, build harmonious communities, awaken slumbering magnanimity long forgotten, revive joy and hope long abandoned, and promote human brotherhood against the forces of egotism.
The Brahma-viharas are incompatible with a hating state of mind [...]

I think they're taught as being not only good-in-themselves but also as antidotes to "hating" (or hateful) states of mind, and more specifically four different remedies to four different types of hate.
I think mudita is the antidote to a type of hate that's called "envy" in English -- for example perhaps "he has all those nice things and is happy, I live in poverty and am sad, I deserve more than he does because I am virtuous and he's a cheat", and so on -- those are unhappy thoughts (which could be translated as both or either of the words "discontent" and "resentment").
And mudita tries to be happy because of someone else's success, for example -- "I'm happy that he's materially comfortable" ... or "I'm happy that other people praise him".

23342: <p>In &quot;The Longer Advice to Rāhula&quot; the following appears:</p>
<blockquote>
<p>Muditaṁ, rāhula, bhāvanaṁ bhāvehi.
Muditañhi te, rāhula, bhāvanaṁ bhāvayato yā arati sā pahīyissati.</p>
</blockquote>
<p>Bhante Sujato translates this as</p>
<blockquote>
<p>Meditate on rejoicing.
For when you meditate on rejoicing any discontent will be given up.</p>
</blockquote>
<p>Thanissaro Bhikkhu:</p>
<blockquote>
<p>“Develop the meditation of empathetic joy. For when you are developing the meditation of empathetic joy, resentment will be abandoned.</p>
</blockquote>
<p>Bhikkhu Vagga:</p>
<blockquote>
<p>&quot;Rāhula, develop meditation on altruistic joy; for when you develop meditation on altruistic joy, any discontent will be abandoned.</p>
</blockquote>
<p>Can somebody please explain which terms correspond to which here, and how the translation is carried out? Thank you</p>
 10100: <p><strong>Arati</strong> is feeling boring, sad, annoying, mad, no-right, or envy when someone getting good resultant, something good or happiness, such as <strong>one feel boring when the opposite party win an election</strong>, or an ex-boyfriend feeling sad for an ex-girlfriend getting new partner.</p>
<p><strong>Mudita</strong> is feeling happy, congratulation for someone getting good resultant, something good or happiness, <strong>such as one feel congratulation when the opposite party win an election</strong>, or an ex-boyfriend feeling happy for an ex-girlfriend getting new partner.</p>
 254: <p><strong>Can somebody please explain which terms correspond to which here</strong></p>
<ul>
<li>&quot;Muditaṁ&quot;
<ul>
<li>rejoicing</li>
<li>empathetic joy</li>
<li>altruistic joy</li>
</ul>
</li>
<li>&quot;bhāvanaṁ bhāvehi&quot;
<ul>
<li>Meditate on</li>
<li>Develop the meditation of</li>
<li>develop meditation on</li>
</ul>
</li>
<li>&quot;Muditañhi&quot; and &quot;bhāvanaṁ bhāvayato&quot; (repeated as above)</li>
<li>arati
<ul>
<li>discontent</li>
<li>resentment</li>
</ul>
</li>
<li>pahīyissati
<ul>
<li>given up</li>
<li>abandoned</li>
</ul>
</li>
</ul>
<p><strong>how the translation is carried out?</strong></p>
<p>I guess you're asking how translators learn to understand a new or &quot;foreign&quot; language?</p>
<p>I think people often have a teacher, when they're learning.</p>
<p>And when they learn, they learn:</p>
<ul>
<li>Grammar</li>
<li>Vocabulary</li>
<li>Subject matter</li>
</ul>
<p>... so they learn the meanings of words and also what the author is likely to be saying when they use those words.</p>
<p>I suppose you learn the &quot;meaning&quot; of a word by seeing it used in context and recognising it when you see it again. For example I think that &quot;the meditation to develop <em>metta</em>&quot; is called &quot;<em><a href="https://www.google.com/search?q=metta+bhavana" rel="nofollow noreferrer">metta bhavana</a></em>&quot; -- and I recognise &quot;mudita&quot; as being one of the four <em>bhamaviharas</em> (of which <em>metta</em> is another) -- and so together perhaps that helps me to understand or recognise what &quot;Muditaṁ bhāvanaṁ bhāvehi&quot; means (i.e. substituting mudita for metta).</p>
<p><strong>Why is it that Aarti is translated as resentment in one case, but discontent in the others?</strong></p>
<p>I think they (&quot;resentment&quot; and &quot;discontent&quot;) are similar in meaning.</p>
<p>There are some essays about the brahmaviharas here: <a href="https://accesstoinsight.org/search_results.html?&amp;q=brahmaviharas" rel="nofollow noreferrer">https://accesstoinsight.org/search_results.html?&amp;q=brahmaviharas</a></p>
<p>One of those says,</p>
<blockquote>
<p>These four attitudes are said to be excellent or sublime because they are the right or ideal way of conduct towards living beings (sattesu samma patipatti). They provide, in fact, the answer to all situations arising from social contact. They are the great removers of tension, the great peace-makers in social conflict, and the great healers of wounds suffered in the struggle of existence. They level social barriers, build harmonious communities, awaken slumbering magnanimity long forgotten, revive joy and hope long abandoned, and promote human brotherhood against the forces of egotism.</p>
<p>The Brahma-viharas are incompatible with a hating state of mind [...]</p>
</blockquote>
<p>I think they're taught as being not only good-in-themselves but also as antidotes to &quot;hating&quot; (or hateful) states of mind, and more specifically four different remedies to four different types of hate.</p>
<p>I think mudita is the antidote to a type of hate that's called &quot;envy&quot; in English -- for example perhaps &quot;he has all those nice things and is happy, I live in poverty and am sad, I deserve more than he does because I am virtuous and he's a cheat&quot;, and so on -- those are unhappy thoughts (which could be translated as both or either of the words &quot;discontent&quot; and &quot;resentment&quot;).</p>
<p>And mudita tries to be happy because of someone else's success, for example -- &quot;I'm happy that he's materially comfortable&quot; ... or &quot;I'm happy that other people praise him&quot;.</p>
