LM 56 temperature trip point resistor selection
It's not explicitly stated, but a quick glance over the datasheet suggests that there the value of \$T\$ should be in specified in Celsius degrees for the equations. This is modestly confirmed by the sparse examples given and by another odd detail -- that the value of \$395\:\text{mV}\$ divided by their rate just happens to land on a convenient numeric intersection of Celsius and Fahrenheit temperature scales. That's settled.

All they want you to do is calculate \$V_{\text{T}_1}\$ and \$V_{\text{T}_2}\$ using their convenient formula, \$V\left(T\right)=395\:\text{mV}+T\cdot 6.2\:\frac{\text{mV}}{^\circ\text{C}}\$. You do this twice, once for each of your temperatures. You have two. So you make up two voltage values from them using that formula. This gives you \$V_{\text{T}_1}=V\left(2\:^\circ\text{C}\right)\$ and \$V_{\text{T}_2}=V\left(40\:^\circ\text{C}\right)\$.

With that in hand, you follow their step by step process of computing first \$R_1\$, then \$R_2\$, and then finally \$R_3\$.

$$\begin{align*}
V_{\text{T}_1} &amp;= 395\:\text{mV}+2\:^\circ\text{C}\cdot 6.2\:\frac{\text{mV}}{^\circ\text{C}}=407.4\:\text{mV}\\\\
V_{\text{T}_2} &amp;=395\:\text{mV}+40\:^\circ\text{C}\cdot 6.2\:\frac{\text{mV}}{^\circ\text{C}}=643\:\text{mV}\\\\
R_1 &amp;= V_{\text{T}_1}\:\frac{27\:\text{k}\Omega}{1.25\:\text{V}}\approx 8.8\:\text{k}\Omega\\\\
R_2&amp;=V_{\text{T}_2}\:\frac{27\:\text{k}\Omega}{1.25\:\text{V}}-R_1\approx 5.09\:\text{k}\Omega\\\\
R_3&amp;=27\:\text{k}\Omega-R_1-R_2\approx 13.1\:\text{k}\Omega
\end{align*}$$

It's boiler-plate.

The datasheet also goes into other discussions about offset, sensor, and output errors. But that's a different topic.



If you decide on specific resistor values for \$R_1\$ and \$R_2\$ and want to still hold to the idea that \$R_3=27\:\text{k}\Omega-R_1-R_2\$, then you can work out the final temperatures for those choices as:

$$\begin{align*}
T_1 &amp;= \frac{R_1\cdot 1.25\:\text{V}-27\:\text{k}\Omega\cdot 395\:\text{mV}}{6.2\:\frac{\text{mV}}{^\circ\text{C}}\cdot 27\:\text{k}\Omega}\\\\
T_2 &amp;=\frac{\left(R_1+R_2\right)\cdot 1.25\:\text{V}-27\:\text{k}\Omega\cdot 395\:\text{mV}}{6.2\:\frac{\text{mV}}{^\circ\text{C}}\cdot 27\:\text{k}\Omega}
\end{align*}$$

You can then decide if that is close enough for your purposes, given standard resistor values near the calculated ones.