Why is binary search called binary search?
I tried to look up the Mauchly reference cited by Knuth but my library seems to have misplaced their copy. 

In the meantime, consider the following early-ish citations for "binary search":


Halpern, Mark. "Variable-width tables with binary-search facility." Communications of the ACM 1.2 (1958): 1-4.


  The family of subroutines described in this report was designed to create, search and maintain tables which are to contain entries of different lengths, and yet be amenable to search by partition, or “binary” search. 

Nagler, H. "An estimation of the relative efficiency of two internal sorting methods." Communications of the ACM 3.11 (1960): 618-620.


  This report concerns the IBM 705, models I and II. It is a study of the machine time required by two internal sorting methods, the conventional two-way merge, and a form of the binary search, which is due to D. Mordy, of the IBM Corporation.

Petersen, T. L. RE-ENTRY VEHICLE SYNTHESIS PROGRAM. No. STL/TR-60-0000-09103 (pdf link). TRW SPACE TECHNOLOGY LABS LOS ANGELES CA, 1960.


  The value of ${V_0}^*$ for which $g({V_0}^*) = 0$ must now be found. It is easily seen that $g(0) = K_3 - 1$ and $g(K_1) = -1$, so that the required value of  ${V_0}^*$ lies between 0 and $K_1$ if $K_3&gt;1$. A binary search is conducted for the root of $g({V_0}^*)$; the ${V_0}^*$ selected is that for which the absolute value of the difference between consecutive values of ${V_0}^*$ is less than $0.01$.



I'll note how the first 1958 citation uses quotation marks around "binary" but by the third citation in 1960, a binary search is mentioned without any further description or explanation. The allusion to "search by partition" would tend to suggest that explanation 2) is closer, but further verification is required.