I assume you're just consulting the L scale and, in effect, contriving to use the rest of the slide rule as a clumsy caliper for adding L scale lengths. This is not, strictly speaking, "adding" with a slide rule. You could do that crude operation with any measuring stick.I knew what you were doing. I can also "add" with a yardstick. But I wouldn't claim that a yardstick is an adding machine and then get into a debate about it. I truly hope that at least some of your victories in life are more glorious than this one.
This is no more contrived than the "explanation" of how a complex thing such as an eye could evolve through random mutations, except that I can actually demonstrate the addition.
Colorful words also do not belie the actuality of adding two numbers with the same precision as "multiplying" on the same device. The multiplication is nothing but adding lengths calibrated to Logs. I merely use the Log scale to add numbers. A slide rule adds.