Sabine Rommevaux: Clavius: Une clé pour Euclide au XVIe siècle. (Mathesis.),Clavius: Une clé pour Euclide au XVIe siècle. (Mathesis.) by Sabine RommevauxReview by: rev. by Jens HøyrupIsis, Vol. 98, No. 3 (September 2007), pp. 621-622Published by: The University of Chicago Press on behalf of The History of Science SocietyStable URL: http://www.jstor.org/stable/10.1086/524238 .

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BOOK REVIEWS—ISIS, 98 : 3 (2007) 621

ment, is placed by theAnatomyin the larger pat-terns of universal madness he diagnoses as amoral philosopher. But Gowland also notes animportant tension in theAnatomyhere: Burtonat times portrays himself as a Stoic sage, re-moved from the madness of the world and ableto laugh contemptuously, yet his philosophicalconsolations for melancholy are themselvesrather disconsolate. Burton betrays an emotionalsuffering appropriate to one engaged with butdisappointed by the realities of the world; theAnatomydisplays an Augustinian orientation to-ward emotional suffering, signaling that melan-choly is the result not of a failure to attain theinvulnerable wisdom of the sage but of the Fall.Those interested in how Burton can be placed

in the long history of the idea of melancholy willfind this theme compressed, but Gowland’slarger point here is surely right: Burton was notdeveloping a position on the idea of melancholyas much as intervening in a fashion intended toquestion the notion that melancholy could beusefully theorized at all. Importantly, Gowlanddoes note that Burton continually emphasizedthe interaction of the physiological and the psy-chological in ways that considerably expandedthe horizon of treatment toward moral-philo-sophical ideas and aims, even where he wasworking within the conventional terms of medi-cal analysis. The suggestion that the medicaltopic and structure of theAnatomyserved as bothplatform and mask for religious criticism is aninteresting one, but Gowland does not explorethe background issues surrounding how the ju-risdictional competencies of medicine and divin-ity were coordinated or contested in the activityof healing in the seventeenth century, whichwould help in assessing the significance of thismove. In any case, those interested in the Re-naissance history of medicine and its allied sci-ences will benefit from Gowland’s intelligentand far-ranging discussion of the intellectual andpolitical “worlds” to which theAnatomywas ad-dressed; and Burton scholars will be much in-debted to Gowland’s thorough and insightfulanalysis of the text and its many references. Fi-nally, for the many who are curious about thiscelebrated but labyrinthine text, here is an illu-minating and engaging guide.

JEREMY SCHMIDT

Sabine Rommevaux.Clavius: Une cle´ pour Eu-clide au XVIe sie`cle. (Mathesis.) 313 pp., figs.,apps., bibl., indexes. Paris: Librairie Philoso-phique J. Vrin, 2005.€30 (paper).

From the later sixteenth century onward, Jesuitswere for generations the mathematics teachers ofmuch of the elite of Catholic Europe; the teacherof these teachers was Christoph Clavius (1538–1612), first as professor of mathematics at theCollegio Romano, later through his writings. Ar-guably the most important of these is his editionof theElements,with ample commentary and ex-tensions. This work has now been admirably an-alyzed by Sabine Rommevaux.The analysis con-stitutes the first part of the volume (pp. 13–113).A second part (pp. 115–276) contains a very pre-cise yet very smooth French translation of thedefinitions of book 5, including the several ex-tensive independent treatises (on arithmetical,geometrical, and harmonic proportions) thatClavius includes along with his commentaryproper. Four appendixes list the different edi-tions of Clavius’sElements;confront the (Latin)formulations of the definitions of book 5 as of-fered by Campanus, Zamberti, Commandino,and Clavius; translate Clavius’s version of thepostulates and axioms of books 1, 5, and 7; andtranslate Clavius’s treatment of the similarity ofcircular segments from book 3 (this serves, to-gether with the definitions of book 5, as substan-tiation of the analysis). The book is unusual fora French publication in that it contains not onlya name but also a subject index.Rommevaux shows, first, that Clavius’s ver-

sion is wrongly (though often) characterized as“a redaction”: in contrast to Campanus, Claviusdoes not change the Euclidean text much; as arule his commentaries and addenda are keptapart as scholia. These, on the other hand, some-times go well beyond Euclid. In Rommevaux’swords, Clavius produces “a manual containingeverything which is useful for a mathemati-cian—concerning the geometry of plane andsolid figures, the theory of proportions, and thetheory of numbers—for understanding the trea-tises of ancient and modern mathematicians, butalso texts on natural philosophy” (p. 58). In otherwords, Clavius created a set ofelementsof math-ematics as mathematics had come to lookforhim.The pedagogical aim of Clavius’s endeavor

stands out clearly. When treating of the variousproportionalities, he takes care not only to pro-duce examples that avoid the intricacies of frac-tions and surds, when these are superfluous, butalso to show how such examples can be con-structed; clearly, his book is meant for futureteachers. In her conclusion, Rommevaux airs asuspicion that it may on the other hand have beentoo extensive and rich to have been entirelysuited as a teaching manual, at least for the first

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622 BOOK REVIEWS—ISIS, 98 : 3 (2007)

years. Clavius’s detailed discussion of all pos-sible cases, together with “the overweight dem-onstrations and length of the commentaries,”“often make the reading fastidious”—but this iscounterbalanced by his “care for transparency,coherence, systematicity, and well-structureddiscourse” (p. 112).Rommevaux repeatedly confronts Cam-

panus’s approach with that of his medieval pre-decessors, to whom he owes much but whom healso criticizes. Going beyond the task Romme-vaux has set herself, but using her material, onemay notice that Clavius was in general harmonywith his times. Campanus made a genuine re-daction, and Rommevaux points out that he hadgood reasons for doing so—namely, that thewidespread version of his times (“Adelard II”/Robert of Chester) was often rather a suggestionof Euclid than Euclid himself; but since Cam-panus appears also to have used the very preciseGreco-Latin translation, this reason was not co-ercive—Campanus made a redaction becausethat was what his times needed. The Euclid thatwas widespread when Clavius wrote was thecombination Zamberti-Campanus (Paris, 1516;Basel, 1537, 1546, 1558). Zamberti had human-istic legitimacy; Campanus was useful. Clavius,keeping his own interventions in scholia, pro-duced a text that was both philologically legiti-mate and useful for students of mathematics.Further, his rejection of Oresme’s notion of ad-dition and multiplication of ratios (book 5, com-mentary to definition 10) because of its counter-intuitive implications sounds much like JuanVives’s refutation of the sophisticated logic ofthe fourteenth century as not dealing with thelogic of ordinary discourse.

JENSHøYRUP

Victoria Sweet.Rooted in the Earth, Rooted inthe Sky: Hildegard of Bingen and PremodernMedicine.(Studies in Medieval History and Cul-ture.) xvi � 326 pp., illus., bibl., index. NewYork/London: Routledge, 2006. $75 (cloth).

This book is a thought-provoking introductionto the medical worldview of the German abbess,visionary, and writer Hildegard of Bingen(1098–1179). Its thesis is that Hildegard’sCau-sae et curae(Causes and Cures) is both uniqueas a record of a medieval individual’s medicalpractice and at the same time a valuable sourcefor understanding premodern European medi-cine globally. In particular, Victoria Sweet ar-gues that the ways in which Hildegard handlesconcepts such as “humor” and “element” point

beyond learned notions to embrace an agricul-tural society’s comprehension of how the mate-rial earth, air, water, and fire surrounding usshape life. It was this quotidian frame of refer-ence that endowed humoral theory with suchlongevity.In Sweet’s view,Causae et curaebegan as a

reference manual for the nun-infirmarian ofHildegard’s new convent at Rupertsberg, a prop-osition that rests on the admittedly speculativepremise that Hildegard herself trained as an in-firmarian. The sections ofCausae et curaecon-taining directives for remedies (books 3–5) werelater supplemented by books 1 and 2, whichpresent the cosmological and physiologicalfoundations of health and illness. Sweet thus in-verts the argument presented by Laurence Mou-linier in her critical edition ofCausae et curae—namely, that books 3–5 were extracted fromHildegard’sPhysicaby a later hand. Sweet’s aimis to establish the practical credentials ofCausaeet curaeby vindicating the authenticity and pre-eminence of the sections devoted to remedies.But the unintended consequence is to isolateCausae et curaefrom the rest of Hildegard’s cor-pus. This isolation is reinforced by Sweet’s skep-ticism about connecting practical medicine to re-ligious approaches to healing. ThusRooted inthe Earth, Rooted in the Skybypasses both theevidence of Moulinier’s apparatus fontium,which exposes the links betweenCausae etcurae, Physica,and Hildegard’s visionary writ-ings, and recent scholarship on medieval monas-ticism’s nondualistic approach to medicine—forexample, by Frederick Paxton andWimVerbaal.The core of Sweet’s study, particularly her

analysis of the structure and underlying world-view ofCausae et curae,is fresh and persuasive.She peels back the layers of Hildegard’s appar-ently digressive prose to reveal a backbone ofcoherently articulated ideas and to bring to thefore her distinctive way with medical words. Forexample, “humor” denotes not only a primalcomponent substance of the body (an idea de-rived from ancient texts) but also the tangiblemoisture found in both plants and humans.Chapter 5, “The Green Humor,” is especially il-luminating. Here Sweet explains Hildegard’ssignature concept ofviriditas (“greenness”), aterm used sparingly inCausae et curaebut fre-quently in the visionary writings as an image ofhuman physical and spiritual vitality. Sweet ob-jects that the conventional definition of “viridi-tas” as “life force” merely substitutes one meta-phor for another. The Church Fathers whomHildegard read, after all, understoodviriditas assomething specific—namely, the kind of soul

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