CHAPTER IX¶
On Lateral (Prismatic) Columns in Architecture, and on the Quadrature of the Circle.
Having spoken sufficiently for your needs concerning round columns, it seems fitting to say a brief word also concerning lateral (polygonal or prismatic) columns (colonne laterate, such as square, hexagonal, and octagonal piers and pilasters), so that their fabrication may not seem useless among the others—seeing that besides bearing weight in buildings, they lend the greatest beauty and variety to the sight!
Concerning these lateral columns, I need say no more than what I have already set forth for round columns above and for the regular and dependent bodies in Part I (Chapters LIX–LXI and LXIII), trusting in your keen intellects and in that foundation most necessary to every practitioner which you have diligently learned from me: the science of numbers and measures with the practice of their proportions.
By means of these, together with your two essential instruments—the compass (*:term:`circino <circino>`*) and the square/straightedge (*libella*), that is, the curved line and the straight line—you will always know how to proportion them, just as you see manifestly in the Ancient Roman Letters placed in this volume (Appendix I), every one of which is formed solely out of circles and squares (tondi e quadri) even if no pen or brush ever existed!
And although it is a common saying that it is difficult to proportion the circle to the square—since, as Aristotle and all the philosophers say of the quadrature of the circle (de quadratura circuli), sit scibilis et dabilis, quamvis nondum sit scita neque data (“it is knowable and grantable in nature, even though it is not yet known or given”)—perhaps today the man has already been born who will give it (forse in questo dì è nato chi la darà), just as I offer to show it palpably to anyone who would deny its possibility! For the rest, I refer you to what I wrote of these bodies in Part I.