לא ס"ד דכתיב (דברים א, ד) אחרי הכותו את סיחון וכי נח נפשיה דאהרן אכתי הוה סיחון קיים דכתיב
so here, [I may say that the occurrence of] the expression 'fortieth year' in the two contexts provides us with a gezerah shawah, [showing that] just as in the one case<span class="x" onmousemove="('comment',' The death of Aaron.');"><sup>19</sup></span> [the date is reckoned] from the Exodus, so in the other case<span class="x" onmousemove="('comment',' The address of Moses.');"><sup>20</sup></span> also. But how do you know that [in respect of these two incidents] that of Ab was prior? Perhaps that of Shebat was prior?<span class="x" onmousemove="('comment',' I.e., the address of Moses was prior to the death of Aaron, the fortieth year having commenced with the Tishri preceding Moses' address.');"><sup>21</sup></span> - Do not imagine such a thing. For it is written [in connection with the latter], 'After he had smitten Sihon';<span class="x" onmousemove="('comment',' Deut. I, 4.');"><sup>22</sup></span> and when Aaron died Sihon was still alive, as it is written
Rashi on Rosh Hashanah
The [variant text] "What does this teach us?" is in error rather the text is "this teaches us that Nissan is the New Year for Kings..."
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Rashi on Rosh Hashanah
Where they appointed him - the princes met and concluded that he should be appointed
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Rashi on Rosh Hashanah
For both of them - Someone who writes a document in the Adar after the first's ascension can write either in year x of the dead king or can write in the first year of the new king
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Rashi on Rosh Hashanah
He died in Nissan and a successor took over in Nissan [of that same year] - and it is the law that if he ascended in any month that until the coming Nissan can use both the count of the dead king and that of the new one.
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Rashi on Rosh Hashanah
and the second year to the second king - He who writes "from x's ascension" does not count the second year to the dead king because this year was not his and the first isn't counted to the second [king] because he hadn't ascended then rather the second is counted as the second [king's] first year.
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Rashi on Rosh Hashanah
You might think you couldn't count 2 kings for one year - [your initial thought might be] that since the king didn't reign for long the entire year should be accredited to the first dead king.