Origins
The Roman solidus was a gold coin so reliable that its name became a word for dependability itself. Latin solidus meant 'firm, whole, undivided', from Proto-Indo-European *solh₂- ('whole'). When English borrowed it via French in the 14th century, the meaning was already rich: physically firm, morally dependable, intellectually complete.
The coin produced the most unexpected descendant. A soldier was originally one paid in solidi — a professional fighter whose service was purchased with hard currency. The word passed through Vulgar Latin soldārius and Old French soudier before arriving in English. Every soldier carries the memory of a Roman paymaster counting out gold.
Solder belongs to the same family. To solder is to make a joint solidus — firm and whole. The word entered English from Old French soudure, itself from Latin solidāre ('to make solid').
Figurative Development
Consolidate means 'to make solid together' — to merge separate things into one firm whole. Solidarity extends the metaphor to people: a group in solidarity stands as one undivided mass.
The mathematical sense arrived in the 16th century, when solid geometry distinguished three-dimensional shapes from flat ones. A solid figure is complete — it occupies space fully, not partially. Even in geometry, the Latin meaning of 'whole' persists.