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Domes built in the 16th, 17th, and 18th centuries relied primarily on empirical techniques and oral traditions rather than the architectural treatises of the time, but the study of dome structures changed radically due to developments in mathematics and the study of statics. Analytical approaches were developed and the ideal shape for a dome was debated, but these approaches were often considered too theoretical to be used in construction.
The Gothic ribbed vault was displaced with a combination of dome and barrel vaults in the Renaissance style throughout the sixteenth century. The use of lantern towers, or timburios, which hid dome profiles on the exterior declined in Italy as the use of windowed drums beneath domes increased, which introduced new structural difficulties. The spread of domes in this style outside of Italy began with central Europe, although there was often a stylistic delay of a century or two. Use of the oval dome spread quickly through Italy, Spain, France, and central Europe and would become characteristic of Counter-Reformation architecture in the Baroque style.
Multi-story spires with truncated bulbous cupolas supporting smaller cupolas or crowns were used at the top of important sixteenth-century spires, beginning in the Netherlands. Traditional Orthodox church domes were used in hundreds of Orthodox and Uniate wooden churches in the seventeenth and eighteenth centuries and Tatar wooden mosques in Poland were domed central plan structures with adjacent minarets. The fully developed onion dome was prominent in Prague by the middle of the sixteenth century and appeared widely on royal residences. Bulbous domes became popular in central and southern Germany and in Austria in the seventeenth and eighteenth centuries, and influenced those in Poland and Eastern Europe in the Baroque period. However, many bulbous domes in the larger cities of eastern Europe were replaced during the second half of the eighteenth century in favor of hemispherical or stilted cupolas in the French or Italian styles.
Only a few examples of domed churches from the 16th century survive from the Spanish colonization of Mexico. An anti-seismic technique for building called quincha was adapted from local Peruvian practice for domes and became universally adopted along the Peruvian coast. A similar lightweight technique was used in eastern Sicily after earthquakes struck in the seventeenth and eighteenth centuries.
Although never very popular in domestic settings, domes were used in a number of 18th century homes built in the Neoclassical style. In the United States, small cupolas were used to distinguish public buildings from private residences. After a domed design was chosen for the national capitol, several states added prominent domes to their assembly buildings.