**Abstract**

The role of geometry and arithmetic in ancient building is common knowledge, but it has seldom been proved by measured drawing. This chapter looks for the remote origins of design criteria and ancient canons, and their application in representative antique and medieval architecture. Architectural design had to reflect the universal cosmic Order and Harmony and the ancient and medieval architectdesigner had to rely on the same intangible instruments, i.e. the geometry and the arithmetic's, created by the Divine Geometer. The geometry of forms and the numbers of quantities and dimensions served as a mayor instrument for developing coherent modulation in the design and the structure of the building and his environment. They also served as a symbol and an allegorical sign to convey intangible messages from the commissioner. Metric analysis reveals this evident design practices and their probable semantic content. This is illustrated in the analysis of six cases: the Cheops pyramid at Memphis, the Pantheon at Rome, the Charlemagne's Palace Chapel at Aachen, the Our Lady's Cathedral at Chartres, the S. Francis Basilica at Assisi and the Castel del Monte at Andria. This historic examples should inspire modern creative design and modern sustainable construction.

**Keywords:** metric analysis, modulation, medieval design, design arithmetic and geometry, design history, ad quadratum, proportion, golden mean, sustainable construction, Cheops pyramid, Pantheon Rome, Carolingian Chapel Aachen, cathedral at Chartres, S. Francis Basilica, Castel del Monte Andria
