Measured Words extends the boundaries of the field that studies the interaction between art and sciences by foregrounding the importance of the verbal and graphic dimensions that shaped the thought of Renaissance mathematical humanists. Building on Paul Lawrence Rose's foundational work, Arielle Saiber studies four moments of close interaction between the mathematico-scientific and the verbal-graphic spheres.
The first case study considers Leon Battista Alberti's De Componendis Cifris (1466), a text best known for its often-cited opening lines, in which Alberti praises the invention of movable-type printing. And although his contemporaries did not adopt his method of creating cyphers through a double alphabet-wheel system (which Saiber explains and schematizes with clarity), the significance of this twenty-five-page manuscript goes beyond its primacy as the first treatise on coding—less articulated precedents include Hildegard von Bingen's Lingua Ignota and the early fifteenth-century Voynich manuscript (Beinecke Library MS 408). As Saiber's analysis indicates, De Componendis Cifris is the product of a mind proficient in analytic processes that break down complex information into its building blocks, that identify patterns and proportions, and that create new metered compositions; skills that Alberti honed through his lifelong studies of languages and mathematics.
Measured Words’s second and longest chapter studies Luca Pacioli's Degno alphabeto Anticho—published in De Divina Proportione (1509)—because his “letterforms are connected to the geometry he used to compute the proportions of things ‘divine’” (49). Saiber begins her inquiry by considering the thirty-some capitals appearing in the 1495 double portrait picturing the mathematician with—likely—the Duke of Urbino, reproduced on the dust jacket. Even without a systematic examination of the individual letterforms—an unfortunate omission because the differences, including the B’s upper lobe, the C’s aperture, the P’s stem-to-bowl proportion, the R’s leg, and the S’s spine stress, suggest evolution in the letterforms’ graphics—Saiber has a compelling case for the close resemblance between the 1495 painted and the 1509 printed capitals; this proves Pacioli's long-standing interest in letterforms and confirms that he “dictated” every detail of this painting. Saibers prefaces the discussion of the 1509 letters by noting that the divine proportion is a “condimento” (64), a sort of beauty sauce rather than the essence of letterforms (and architectural proportions). Pacioli's letters embody a special ratio in their height-to-stem thickness, 9:1, which sets them apart from those designed by his contemporaries, including Alberti and Felice Feliciano. More importantly, Pacioli's letterforms follow not from epigraphic but from mathematical studies, and particularly from his belief in the foundational role of the circle and the square.
Chapter 3 weaves the story of the twenty-five-line poem that Niccolò Tartaglia composed in 1539 to present his solution of the cubic equation to Girolamo Cardano, who, in return, gave Tartaglia access to his patronage connections. This witty and elegant composition in terza rima was Tartaglia's “calculated act of revealing while concealing, and concealing while revealing” (109). Unfortunately, he miscalculated Cardano's ability to untangle the poem and uncover the cubic equation's general solution, a pivotal advancement in algebra. Though crediting the discovery to Tartaglia, whose fame now rests with the title-page woodcut of his 1537 Nova Scientia, presenting Euclid as gatekeeper to all learning (analyzed by Saiber, 127–34), in 1545 Cardano published the solution to the equation in his Ars Magna.
In the last chapter, Saiber brings back to life Giambattista Della Porta's Elementorum Curvilineorum Libri Tres, a treatise on curves first published in 1601 and then revised and reissued in 1610 under the auspices of the Lincei, sporting Federico Cesi as dedicatee. Despite the prestigious association, Della Porta's only mathematical tract fell immediately into oblivion. While its subject was irrelevant to contemporary mathematical discussions, its eccentric language and tone capture and epitomize early Baroque Neapolitan culture: “with its neologisms, its repeated figures, its incremental building of more and more complex curves … Della Porta blurs the lines between pure mathematics, art, and artifice” (141).
Together with her lively writing style, Saiber's erudition, based on close reading of primary sources and a remarkable command of secondary literatures, make Measured Words a pleasure to read. Scholars will return to this book for research leads and for chapters to assign to their graduate and undergraduate students.
