user295: The quote below defines Vitarka-vicara as:

Ardency (atappa) + mindfulness (sati) => combines to make vitakka
Ardency (atappa) + alertness (sampajañña) => combines to make vicara


As Ajaan Lee, my teacher’s teacher, once noted, mindfulness combined with ardency turns into the concentration factor called vitakka, or directed thought, where you keep your thoughts consistently focused on one object, such as the breath. Alertness combined with ardency turns into another concentration factor: vicāra, or evaluation

Head & Heart Together, by Ṭhānissaro Bhikkhu, Chapter: Mindfulness Defined
No citation from the cannon have been given in this discussion.
What are the Tipitaka, commentary, sub commentary sources, including primary, secondary or tertiary source with citations, which defines Vitarka-vicara as such?
Are there other definitions of Vitarka-vicara from Tipitaka, commentaries, sub commentaries, including primary, secondary or tertiary source with citations?

user43: From Khuddaka Nikaya's The Questions of King Milinda (translation mine):

‘Venerable Nagasena, what is the characteristic mark of vitakka*?’ 
‘The characteristic mark of vitakka is "placing" (Appanā), Your Majesty.’  
‘Give me an example.’  
‘For example, Your Majesty, like a carpenter takes well-finished boards of wood and places (appeti) them in position.’    
Mil 3.3.13

*ideation, reasoning, putting forward ideas, postulating a premise


‘Venerable Nagasena, what is the characteristic mark of vicāra*?’
‘The characteristic mark of vicāra is pondering/mulling over (anumajjana), Your Majesty.’
‘Give me an example.’
‘For example, Your Majesty, if you strike on a copper vessel, it then rings for a while, it responds with a sound. Here, Your Majesty, the strike is a simile for vitakka and the reverberation is a simile for vicāra.’
Mil 3.3.14

*investigating a premise, considering an idea to weigh its implications

user16297: See SN 46.3
http://lucid24.org/sn/sn46/sn46-003/index.html

sati-sambojjhanga remembers Dhamma-teaching, then thinks (vitakka) about that Dharma.
Dhamma-vicaya-sambojjhnaga investigates that Dharma-teaching recollected by sati, by means of vicara (evaluation) paññāya (same word as the sampajano, what B. thanissaro translates as 'alertness'). 

ātāpi = ardency, is equivalent to the 3rd awakening factor vigor/viriya, also equivalent to 4 aspects of right effort.
So what Ajahn Lee is saying sounds idiosyncratic at first, but it is solidly based on EBT sutta.

295: <p>The quote below defines <a href="https://en.wikipedia.org/wiki/Vitarka-vicara" rel="nofollow noreferrer">Vitarka-vicara</a> as:</p>

<ul>
<li>Ardency (atappa) + mindfulness (sati) => combines to make vitakka</li>
<li>Ardency (atappa) + alertness (sampajañña) => combines to make vicara</li>
</ul>

<blockquote>
  <p>As Ajaan Lee, my teacher’s teacher, once noted, mindfulness combined with ardency turns into the concentration factor called vitakka, or directed thought, where you keep your thoughts consistently focused on one object, such as the breath. Alertness combined with ardency turns into another concentration factor: vicāra, or evaluation</p>
</blockquote>

<p>Head &amp; Heart Together, by Ṭhānissaro Bhikkhu, <a href="https://www.dhammatalks.org/books/Head&amp;HeartTogether/Section0009.html" rel="nofollow noreferrer">Chapter: Mindfulness Defined</a></p>

<p>No citation from the cannon have been given in this discussion.</p>

<p>What are the Tipitaka, commentary, sub commentary sources, including primary, secondary or tertiary source with citations, which defines <a href="https://en.wikipedia.org/wiki/Vitarka-vicara" rel="nofollow noreferrer">Vitarka-vicara</a> as such?</p>

<p>Are there other definitions of <a href="https://en.wikipedia.org/wiki/Vitarka-vicara" rel="nofollow noreferrer">Vitarka-vicara</a> from Tipitaka, commentaries, sub commentaries, including primary, secondary or tertiary source with citations?</p>
 43: <p>From Khuddaka Nikaya's The Questions of King Milinda (translation mine):</p>

<blockquote>
  <p>‘Venerable Nagasena, what is the characteristic mark of <code>vitakka*</code>?’ </p>
  
  <p>‘The characteristic mark of <code>vitakka</code> is "placing" (<code>Appanā</code>), Your Majesty.’  </p>
  
  <p>‘Give me an example.’  </p>
  
  <p>‘For example, Your Majesty, like a carpenter takes well-finished boards of wood and places (<code>appeti</code>) them in position.’    </p>
  
  <p><a href="https://suttacentral.net/mil3.3.13/en/tw_rhysdavids" rel="nofollow noreferrer">Mil 3.3.13</a></p>
</blockquote>

<p>*<sub>ideation, reasoning, putting forward ideas, postulating a premise</sub></p>

<hr>

<blockquote>
  <p>‘Venerable Nagasena, what is the characteristic mark of <code>vicāra*</code>?’</p>
  
  <p>‘The characteristic mark of <code>vicāra</code> is pondering/mulling over (<code>anumajjana</code>), Your Majesty.’</p>
  
  <p>‘Give me an example.’</p>
  
  <p>‘For example, Your Majesty, if you strike on a copper vessel, it then rings for a while, it responds with a sound. Here, Your Majesty, the strike is a simile for <code>vitakka</code> and the reverberation is a simile for <code>vicāra</code>.’</p>
  
  <p><a href="https://suttacentral.net/mil3.3.14/en/tw_rhysdavids" rel="nofollow noreferrer">Mil 3.3.14</a></p>
</blockquote>

<p>*<sub>investigating a premise, considering an idea to weigh its implications</sub></p>
 16297: <p>See SN 46.3
<a href="http://lucid24.org/sn/sn46/sn46-003/index.html" rel="noreferrer">http://lucid24.org/sn/sn46/sn46-003/index.html</a></p>

<ol>
<li>sati-sambojjhanga remembers Dhamma-teaching, then thinks (vitakka) about that Dharma.</li>
<li>Dhamma-vicaya-sambojjhnaga investigates that Dharma-teaching recollected by sati, by means of vicara (evaluation) paññāya (same word as the sampajano, what B. thanissaro translates as 'alertness'). </li>
</ol>

<p>ātāpi = ardency, is equivalent to the 3rd awakening factor vigor/viriya, also equivalent to 4 aspects of right effort.</p>

<p>So what Ajahn Lee is saying sounds idiosyncratic at first, but it is solidly based on EBT sutta.</p>
