Well, they didn't. During the industrial revolution, it was largely trial and error, causing great catastrophes.

Bridges are an interesting example: In the nineteenth century with the expansion of the railroad, iron replaced timber in bridge building as wood was unable to hold the load of trains. At that time, engineers knew how to build stone and wooden bridges - due to the accumulated knowledge during the centuries- but iron was a new material (technology). These iron brides collapsed in numbers that are still discussed today causing the death of thousands of people. Due to the great number of collapses of iron railway bridges, in 1847 Queen Victoria appointed a commission to look into the use of iron in bridges charging its members to

"endeavor to ascertain such principles and form such rules as may enable the Engineer and Mechanic, in their respective spheres, to apply the Metal with confidence, and shall illustrate by theory and experiment the action which takes place under varying circumstances in Iron Railway Bridges which have been constructed"

Even that commission, whose report was published in 1849, promulgated a misguided idea about the fatigue of metals, theorizing that "crystallization" occurred under vibratory action, and this misconception was to persist well into the 20th century (Petroski, 1992).

Notable examples are the Tay bridge collapse in 1879 and the Quebec bridge failure in 1907. After the collapse of the 157-foot long truss bridge at Ashtabula, Ohio in 1876, which killed almost a hundred people, prompted Harper's Weekly to ask "Is there no method of making iron bridges of assured safety?". Of course, this question sounds ridiculous today.

All the above is from Henry Petroski's excellent book "To engineer is Human. The Role of Failure in Successful Design", 1992 which provides great examples of how failures guide the technological progress.