Renaissance Geometricism

The Renaissance saw a revival of interest in many aspects of the Classical world of Ancient Greece and Rome – particularly in its philosophy, literature and architecture. An important aspect of this revival was a renewed interest in the philosophical ideas of Pythagoras and Plato. In fact Greek thought had proved capable of inspiring and reviving the intellectual life and arts of Western Europe for centuries, despite the fragility of its influence during the turbulence of the Early Middle Ages. But the Renaissance, with its reaction against the narrow medieval scholasticism, saw a much broader interest in Platonism in particular.

One of the most important aspects of this stream of thought was its engagement with mathematics and with Geometry in particular. Part of its great originality lay in the belief that Nature could be best understood through the abstract medium of number and measurement – an intuition that of course laid the foundation of Science. But these principles, which led it to give a high value to ideal formulations of numbers, proportions and geometric form, also exerted a strong aesthetic appeal. It was this aspect of Platonism that became a source of inspiration to artists from the very beginning of the Renaissance – in particular, the Pythagorean notions of ratio and harmonic relations as underlying, but at the same time existing above and beyond, the mundane world.

This revived interest in geometry was associated with another field of enquiry, one that had been developed during the Islamic tenure of Classical Greek knowledge, that of Perspectiva, that is to say, of the science of Optics and the mechanics of human perception. Discoveries in this area were of equal interest to scientist and artists alike – in fact the problems of creating a convincing representation of three dimensions onto a two-dimensional surface exerted a particular and sustained fascination throughout the Renaissance. This preoccupation reflected the abiding spirit of the time, common to both the arts and sciences, which might be characterised as a drive to explore and grasp reality.

This fascination with the aesthetic aspects of Geometry culminated, one might say, in the art of an obscure group of German artist/craftman in the mid-16th century (Wenzel Jamnitzer, Lorenz Stoer, Johannes Lencker and Peter Halt), samples of whose work is presented below. This period, in mid-16th century Germany, saw the publication of a handful of books that presented a range of intriguing geometric drawings that were unlike anything that had ever appeared before, or have been seen since. The initial response to this early Geometricism is surely that of their strangely modern quality…

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The title-page of Lorenz Stoer’s folio of watercolours Geometria et Perpectiva: Corpus Regulata et Irregulata; c.1575 - 1600

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A page from Lorenz Stoer’s folio of watercolours Geometria et Perpectiva: Corpus Regulata et Irregulata; c. 1575 - 1600

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A page from Lorenz Stoer’s folio of watercolours Geometria et Perpectiva: Corpus Regulata et Irregulata; c. 1575 - 1600

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A page from Lorenz Stoer’s folio of watercolours Geometria et Perpectiva: Corpus Regulata et Irregulata; c. 1575 - 1600

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The Platonic solids and their associated Elements. Woodcut tile-page for Geometria et Perpectiva, Lorenz Stoer; c. 1575 -1600

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Page 4 from Lorenz Stoer’s woodcut volume Geometria et Perpectiva; Nuremberg, 1571

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Page 7 from Lorenz Stoer’s woodcut volume Geometria et Perpectiva; Nuremberg, 1571

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Page from Wentzel Jamnitzer’s Perspectiva Corporum Regularium; Nuremberg, 1568

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Page from Wentzel Jamnitzer’s Perspectiva Corporum Regularium; Nuremberg, 1568

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Page from Wentzel Jamnitzer’s Perspectiva Corporum Regularium; Nuremberg, 1568

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Page from Wentzel Jamnitzer’s Perspectiva Corporum Regularium; Nuremberg, 1568

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Page from Wentzel Jamnitzer’s Perspectiva Corporum Regularium; Nuremberg, 1568

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Page from Wentzel Jamnitzer’s Perspectiva Corporum Regularium; Nuremberg, 1568

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Page from Johannes Lencker’s Perspectiva Literaria; Nuremberg 1567

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Page from Johannes Lencker’s Perspectiva Literaria; Nuremberg 1567

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The Mazzocchio motif, drawing by Paolo Uccello (mid-15th century)

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The Mazzocchio motif, drawing by Leonardoda Vinci (early 16th century)

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The Mazzocchio motif, engraving by Wentzel Jamnitzer (mid 16th century)

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The Mazzocchio motif, engraving by Peter Halt (early 17th century)

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Section of floor mosaic from the Basilica di San Marco, Venice (showing a small stellated dodecahedron); Paolo Uccello (1397 – 1475)

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Geometric/perspective figure, attributed to Martino da Udine (1470 – 1548)

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Geometric/perspective figure, attributed to Martino da Udine (1470 – 1548)

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Skeletised polyhedron, woodcut from drawing by Leonardo da Pisa for Luca Pacioli’s De Divina Proportione 1509

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Skeletised polyhedron, woodcut from drawing by Leonardo da Pisa for Luca Pacioli’s De Divina Proportione 1509

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Geometric diagrams, drawn by Leonardo da Pisa for Luca Pacioli’s De Divina Proportione 1509

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Geometric diagrams, drawn by Leonardo da Pisa for Luca Pacioli’s De Divina Proportione 1509

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Geometric diagrams, drawn by Leonardo da Pisa for Luca Pacioli’s De Divina Proportione 1509

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Geometric diagrams, drawn by Leonardo da Pisa for Luca Pacioli’s De Divina Proportione 1509

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Geometric diagrams from the sketchbooks of Albrecht Dürer

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Geometric diagrams from the sketchbooks of Albrecht Dürer

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Geometric diagrams from the sketchbooks of Albrecht Dürer

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Geometric diagrams from the sketchbooks of Albrecht Dürer

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Johannes Kepler’s Platonically-inspired model of the planetary orbits; from his Mysterium Cosmographicum, 1596

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Regular three-dimensional arrangements; from Johannes Kepler’s Harmonices Mundi, 1619

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Plato’s ‘five basic solids’, with their associated Elements of Eath, Air Fire and Water; from Johannes Kepler’s Harmonices Mundi, 1619

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Johannes Kepler’s further investigations into plane and polyhedral geometry; from his Harmonices Mundi, 1619

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The frontispiece of Petrus’ Apianus Instrument Buch; the first printed treatise on Astronomy and Surveying, 1533

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Turned ivory ornaments featuring polyhedra; from the Court at Dresden, 17th century

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Page from La Pratica di Prospettiva, Lorenzo Sirigatti, Venice, 1596

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Page from La Pratica di Prospettiva, Lorenzo Sirigatti, Venice, 1596

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Intarsia (wooden inlay) panel by Fra Giovanni of Verona: from the monastery of Monte Olivetto, near Siena, c. 1503-06)

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Intarsia (wooden inlay) panel by Fra Giovanni of Verona: from the Church of Santa Maria in Organo, Verona, c.1494 - 1499

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Intarsia (wooden inlay) panel by Fra Giovanni of Verona: from the monastery of Monte Olivetto, near Siena, c. 1503-06).

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Intarsia (wooden inlay) panel by Fra Giovanni of Verona: from the Church of Santa Maria in Organo, Verona, c.1494 - 1499

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Leaf from an Intarsia (wooden inlay) cabinet; early 17th century, Frankfurt

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Arcane Renaissance geometry: Polyhedral model on the tomb of Sir Anthony Ashley, in a parish Church near Salisbury, England

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Arcane Renaissance geometry: A mystical diagram by the Rosicrucian Abraham von Franckenberg; 1639

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Arcane Renaissance geometry: Woodcut of magical/mystical figure by Giordano Bruno; 1588

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Arcane Renaissance geometry: Woodcuts of magical/mystical figures by Giordano Bruno; 1588

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Proto-Cubism in the mid-15th century: detail of Jerusalem in Piero della Francesco’s The Recovery of the True Cross (c.1450)

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The geometrically-inspired Hortus Palatinus at Heidelberg Castle; 1618

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Baroque geometricism: from the perspective studies of Vredeman de Vries. 1.

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Baroque geometricism: from the perspective studies of Vredeman de Vries. 2.

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Baroque geometricism: from the perspective studies of Vredeman de Vries. 3.

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Study of proto-Cubist figures; woodcut by Erhard Schön, from his Underweissung der Proportion, Nuremberg, 1530. 1.

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Study of proto-Cubist figures; woodcut by Erhard Schön, from his Underweissung der Proportion, Nuremberg, 1530. 2.