The simple analog computer is essentially a comparator circuit where balancing the circuit gives you an approximate answer to several mathematical functions. It functions similar to a slide rule. I don't know what the earliest version of this is, but they were common in the late 50s and early 60s as kits.
The ones I am aware of:
- 1958 - Mr. Math in June issue of Radio Electronics (https://worldradiohistory.com/Archive-Radio-Electronics/50s/1958/Radio-Electronics-1958-06.pdf)
- 1959 - Calculo Analog Computer Kit (http://www.ccapitalia.net/descarga/docs/1959-calculo-analog-computer.pdf)
- 1960 - Edmund Analog Computer (https://computarium.lcd.lu/photos/albums/EDMUND_ANALOG_COMPUTER/album/index.html)
- 1961 - General Electric Project 4 Computer (EF-140) (http://www.ccapitalia.net/descarga/docs/1961-general-electric-EF-140.pdf)
- 1962 - American Basic Science Club Analog Computer (https://t-lcarchive.org/american-basic-science-club-analog-computer/)
- 196? - Mac-1 Mini Analog Computer (http://www.vintage-icl-computers.com/icl48d)
- 1966 - Pot Computer in January issue of Electronics Illustrated (https://worldradiohistory.com/Archive-Electronics-Illustrated/Electronics-Illustrated-1966-01.pdf)
- 1969 - Science Fair Electronic Computer Kit (https://www.computerhistory.org/collections/catalog/X744.86A)
- 2008 - Calculatoria (http://www.nicolamarras.it/calcolatoria/calcolatrice_analogica_en.html)
In December of 1961, the Edmund Analog Computer and G.E. EF-140 were described in an overview of this type of circuit in an article in Popular Electronics (https://worldradiohistory.com/Archive-Poptronics/60s/61/Pop-1961-12.pdf).
More recently, similar instructions were given to explore this circuit as a school activity in https://schoolbag.info/science/laboratory/8.html. It was also recreated here: http://www.arthropodsystems.com/AnalogComputer/AnalogComputer1.html. The circuit was also implemented with high-precision potentiometers in 2008 as listed above.
I would be very interested in any other versions of this or more information about these. Specifically, more information about the Mac-1 and copies of the manual for the Edmund Analog Computer and the Science Fair one. Here's a summarized version of the Edmund manual in Czech (I think): http://dexovo.cz/analogove-vypocetnictvi-edmund-cast-i.php.