They don't make furniture like they used to...

[JohnD]

I reckon the carving on my dining chairs certainly looks hand done though..

That's what they wanted you to think! I have something similar.

Your goat legs look to me like they were machined out of a block.

 

[gregers]

get your self some poly glue,follow instructions and using masking tape to support any breakages while the glue sets.
on the legs could it not be possible to drill out for a small dowel so this supports it.

 

[matz]

the chair - glue up with resin W (white woodworking glue) and cramp using blocks as mentioned earlier so joint goes together perfectly with no steps. When glue dry, counterbore with forstener bit and screw the joint together across the breakage line to add extra strength then plug holes with matching wood and finish off. This is a tricky repair and you only have one chance to get it right when gluing - gluing up accurately is paramount or the joint will break again and an effective repair then will be near impossible. Even when glued, there will be a weakness so keep it as a reserve chair and not one for normal useage..

The chest - remove the broken away leg and reglue all the loose/ broken bits to the leg itself then glue the leg to the underside of the chest. When glue set, add glueblocks to reinforce the leg to the base.