CHAPTER VI¶
On the Order and Construction of the Stylobate (Pedestal or Base-Pillar) of the Column, the Stereobate Foundation, the Ancient Roman Alphabet, and the Three Sets of Sixty Polyhedra Models Made by Pacioli alongside Leonardo da Vinci.
The stylobate (stilobata, which we call the pilastrello or basamento of the column, marked \(cdef\) in Plate 0213) is the rectangular pedestal that supports the column and its base.
Proportions and Mouldings of the Stylobate and Stereobate (Plate 0213, Plate 0185)
Width and Height of the Stylobate Die (:math:`cdef`):
The width \(ef = cd\) of the vertical die (shaft) of the stylobate must be exactly equal to the width of the plinth (:math:`hg`) of the column base standing upon it (\(1\frac{1}{2}\) column diameters), aligned plumb (a livello) so that the vertical lines \(ce\) and \(df\) carry the load directly without overhang or obliquity.
The height of the stylobate must be twice its width (\(2 : 1\) ratio, i.e., equal to two plinth lengths), so that it combines structural strength with visual grace, as seen in the Porta Speciosa (Plate 0185).
Universal Law of Square Projections (*Proiecture / Sportafore*):
Both the base (\(abcd\)) and the capital or cornice (cimasa, \(efmn\)) of the stylobate are adorned with stepped mouldings (plinth, tori, scotias, fillets).
In all these mouldings—and likewise in the architrave and cornice above the column—observe this universal rule: every projecting moulding (*sportafore / proiectura*) on the right and left must project outward by the exact amount of its own vertical height, so that its profile forms a square (respondino quadrate) even if there were 10,000 mouldings!
And the projection of the stylobate’s base (\(abcd\)) must be at least equal to (or slightly wider than, never narrower than) the projection of its upper cornice (\(efmn\)).
The Subterranean Foundation (*:term:`Steriobata <steriobata>`*):
Beneath the stylobate base \(ab\) must be laid a solid masonry foundation carried down underground to firm, level ground (fin al vivo piano a livello de bon muraro), equal in width at least to the full spread of the stylobate base \(ab\); this foundation is called the stereobate (steriobata) by the Ancients.
Nomenclature of the Seven Mouldings of the Stylobate Cornice: Counting downward from the top of the stylobate capital (\(efmn\)):
1st (highest): Acrotherio (ancient) / top fillet;
2nd: Cimatio (ancient) / Intaulato (modern);
3rd: Fastigio (fascia/corona);
4th: Echino (ancient) / Uovolo (modern egg-and-dart / ovolo);
5th: Baltheo or Trochilo (ancient) / Regolo (modern);
6th & 7th: Tenia (ancient) / Intaulatura (modern), resting immediately upon the die of the stylobate.
(And if you carve foliage, trophies, or animals upon the flat faces of the stylobate die \(cdef\), keep the relief within the plane so as not to weaken the vertical corner lines \(ce\) and \(df\).)
Inscriptions in the Ancient Roman Alphabet, Leonardo da Vinci in Milan (1496–1499), and the Three Sets of Sixty Material Polyhedra
Upon the flat die of the stylobate—as well as on friezes, pediments, and sepulchral monuments—it is customary to carve inscriptions and epitaphs in ancient Roman capital letters (lettere belle antiche con tutta proportione), which lend supreme beauty to the work. For this very reason I have placed in this volume (Appendix I: The Roman Geometric Alphabet, Folios 0139–0183) the exact geometric construction of the entire Ancient Alphabet with all its proportions, so that scribes and illuminators (scriptori e miniatori)—who are often so stingy in sharing their secrets—may see clearly that even without their pen and brush, the two mathematical lines, curved and straight (*:term:`circino <circino>` e libella*), bring all letters and all other things to perfection!
And this same truth shines forth in the perspective figures of all the regular and dependent bodies above in this book (Appendix II: Plates I–LIX), which were drawn by that most worthy painter, perspectivist, architect, and musician, endowed with every virtue, Leonardo da Vinci of Florence (Lionardo da Vinci Fiorentino), in the city of Milan when we were both in the service and stipend of the Most Excellent Duke Ludovico Maria Sforza Anglo in the years of our salvation 1496 to 1499—whence afterward, on account of diverse events in those parts [the French invasion of October 1499], we departed together and took up our dwelling together in Florence (donde poi da siemi per diversi successi in quelle parti ci partemmo e a Firenze pur insiemi trahemmo domicilio)!
And in Milan, with my own hands (de mie proprie mani), I constructed, colored, and adorned sixty material models (forme de dicti corpi materiali bellissime… numero 60) of those regular and dependent bodies for the said Duke; and I made another set of sixty in Milan for my patron Messer Galeazzo Sanseverino; and afterward in Florence I made a third set of sixty for our Lord the Perpetual Gonfaloniere Piero Soderini (Petro Soderino), which are presently kept in his palace [the Palazzo della Signoria / Palazzo Vecchio] in Florence!