Very nice hand drill-press,
looks like the 1st one, the cranks turn the drill & feeds the drill? how do you control the feed?
2nd Drill-press looks like you flip the feed bar into the gears?
Not exactly a drill press. These were used primarily to drill holes in building timber frame buildings -- post and beam construction. The holes received the wooden pegs that held it all together. Drill presses and beam drills are older than this tool (Diderot illustrated those in his 1750 encyclopedia.)
These are portable. Drill one hole in a beam or post, pick it up and move it to the next place you need a hole. Both those pictured have a geared bar for raising or lowering the drill apparatus, but these are not feed bars. There's a catch on the top wooden bar to hold the drill apparatus in the up position. Feed is primarily controlled by the lead screw on the auger bit.
You place the contraption on the beam so that the bit is in the correct position for the hole to be bored. Then you sit on the long area in the front, release the bit from the catch, and work the handles like a bicycle crank. When the hole is done, you shift the gears so that they engage the "feed" bar and retract the drill.
The first one drills a hole at a fixed 90 degree angle. The second can adjust to drill at angles (note the hemispherical tracks attached to the base, and the wing-nuts that hold the drill frame in place.
The first timber framer to use one of these instead of the traditional T-handle auger must have felt like he "done died and gone to heaven."