The characteristic structural forms of large Renaissance churches-domes, drums, pendentives, and barrel vaults-were the products of innovation in theory and practice during the later fifteenth century in Italy that culminated in Bramante's projects for the new Saint Peter's. Significant ideas were contributed by Leon Battista Alberti, Francesco di Giorgio, and Leonardo da Vinci. Francesco di Giorgio's geometrical methods of design for churches as described in his second treatise incorporate a procedure for calculating the thickness of walls bearing vaults. Francesco di Giorgio tested the procedure in his own churches, and it was later used by Bramante.

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