BOOK REVIEWS-ISIS, 82: 4: 314 (1991) BOOK REVIEWS-ISIS, 82: 4: 314 (1991)

volume is that France did not always pro- vide the model for Latin American develop- ment in the sciences. An instructive exam- ple of this fact is Marcos Cueto, "Andean Biology in Peru: Scientific Styles on the Periphery," Isis, 1989, 80:640-658. We learn that for most of the present century the "center" for high-altitude physiological studies has been Peru, a "peripheral" re- gion. Cueto warns against the uncritical employment of the "periphery" concept because it "fails to capture the richness and complexity of the reception and recreation of Western science in noncore Western cultures" (p. 658). Similarly, a recent com- parative study of medical centers and pe- ripheries during the colonial period ques- tions the notion that replication of Old World motifs in the New World was either sought or achieved: Ronald L. Numbers, ed., Medicine in the New World: New Spain, New France, and New England (Tennessee, 1987).

ERIC HOWARD CHRISTIANSON

David Rapport Lachterman. The Ethics of Geometry: A Genealogy of Modernity. xx + 255 pp., figs., bibl., index. New York/ London: Routledge, 1989. $49.50, Can $59.50 (cloth); $17.95, Can $21.95 (paper). For those with the stamina to read it, this is a provocative book. Considered from the standpoint of the history of mathematics, it presents a pair of linked analyses of Eu- clid's Elements and Descartes's Geometry. Considered more broadly, this volume sketches the trajectory from antiquity to modernity in an account intended as a "critical counter-example" to postmodern- ist criticism.

David Lachterman begins with a simple question: "What is it to be a 'modern'?" (p. vii). Coming now, however, when "mo- dernity" is seen as the final episode of a completed epoch, this question implies an- other: Was modernity radically original, as it claimed to be, or was it merely the inev- itable successor of what had preceded it?

Reflecting on the word modern itself, Lachterman identifies the idea of "con- struction," the idea of the "mind as essen- tially the power of making" (p. 4), as the central element binding together the "constellation" of its meanings. In mathe- matics, he argues, specifically in the geo-

volume is that France did not always pro- vide the model for Latin American develop- ment in the sciences. An instructive exam- ple of this fact is Marcos Cueto, "Andean Biology in Peru: Scientific Styles on the Periphery," Isis, 1989, 80:640-658. We learn that for most of the present century the "center" for high-altitude physiological studies has been Peru, a "peripheral" re- gion. Cueto warns against the uncritical employment of the "periphery" concept because it "fails to capture the richness and complexity of the reception and recreation of Western science in noncore Western cultures" (p. 658). Similarly, a recent com- parative study of medical centers and pe- ripheries during the colonial period ques- tions the notion that replication of Old World motifs in the New World was either sought or achieved: Ronald L. Numbers, ed., Medicine in the New World: New Spain, New France, and New England (Tennessee, 1987).

ERIC HOWARD CHRISTIANSON

David Rapport Lachterman. The Ethics of Geometry: A Genealogy of Modernity. xx + 255 pp., figs., bibl., index. New York/ London: Routledge, 1989. $49.50, Can $59.50 (cloth); $17.95, Can $21.95 (paper). For those with the stamina to read it, this is a provocative book. Considered from the standpoint of the history of mathematics, it presents a pair of linked analyses of Eu- clid's Elements and Descartes's Geometry. Considered more broadly, this volume sketches the trajectory from antiquity to modernity in an account intended as a "critical counter-example" to postmodern- ist criticism.

David Lachterman begins with a simple question: "What is it to be a 'modern'?" (p. vii). Coming now, however, when "mo- dernity" is seen as the final episode of a completed epoch, this question implies an- other: Was modernity radically original, as it claimed to be, or was it merely the inev- itable successor of what had preceded it?

Reflecting on the word modern itself, Lachterman identifies the idea of "con- struction," the idea of the "mind as essen- tially the power of making" (p. 4), as the central element binding together the "constellation" of its meanings. In mathe- matics, he argues, specifically in the geo-

metrical construction of equations, modern thinkers from Descartes through Kant found the defining example of the mind cre- ating what it knew. Lachterman thus re- duces the radical originality of modern thought to the fundamental novelty of con- struction in modern mathematics, and this latter claim is what he wants to demon- strate.

In Lachterman's presentation Euclid and Descartes possess iconic status. Each is emblematic of a "mathematical ethos," the one ancient, the other modern. He uses this term in the Aristotelian sense of ta ethe, and what he means are the "disparate ways (mores) and styles in which the Euclidean and the Cartesian geometer do geometry, comport themselves as mathematicians both toward their students and toward the very nature of those learnable things (ta mathemata) from which their disciplined deeds take their name" (p. xi). The presup- position here is that mathematics is never the entirely private pursuit of its practition- ers. Ideas about teaching and learning are necessarily woven into its fabric. As a re- sult, mathematics is always acted out in a context determined by two roles (teacher and student or master and apprentice), whether or not each is actually filled at the moment.

The dispositions governing each mathe- matical ethos are not themselves mathe- matical. The situation is the most stark in the case of Euclid's Elements. There, math- ematical technique is presented as having been reined in, with varying success, by Euclid's tacit acceptance of overarching ontological and pedagogical commitments. As an interpretative tool this scheme sug- gests a dynamic of tensions in the text, aris- ing from a dialectic of agendas in the sur- rounding world. For example, Lachterman depicts Euclid in book 5 as having fash- ioned a theory of proportion that accommo- dates the fact of incommensurability while vindicating a pretheoretical experience of the subject.

Might it be, Lachterman asks, "that the horizon of ancient ontology, as articulated in Plato and Aristotle, is the artfulness of teaching what can be learned and learning what can be taught ... rather than the craft of letting what has been fashioned come to stand on its own?" (p. 114). For Plato and Aristotle this seems exactly right. How much Euclid's practice was circumscribed by the same horizon is a profoundly inter-

metrical construction of equations, modern thinkers from Descartes through Kant found the defining example of the mind cre- ating what it knew. Lachterman thus re- duces the radical originality of modern thought to the fundamental novelty of con- struction in modern mathematics, and this latter claim is what he wants to demon- strate.

In Lachterman's presentation Euclid and Descartes possess iconic status. Each is emblematic of a "mathematical ethos," the one ancient, the other modern. He uses this term in the Aristotelian sense of ta ethe, and what he means are the "disparate ways (mores) and styles in which the Euclidean and the Cartesian geometer do geometry, comport themselves as mathematicians both toward their students and toward the very nature of those learnable things (ta mathemata) from which their disciplined deeds take their name" (p. xi). The presup- position here is that mathematics is never the entirely private pursuit of its practition- ers. Ideas about teaching and learning are necessarily woven into its fabric. As a re- sult, mathematics is always acted out in a context determined by two roles (teacher and student or master and apprentice), whether or not each is actually filled at the moment.

The dispositions governing each mathe- matical ethos are not themselves mathe- matical. The situation is the most stark in the case of Euclid's Elements. There, math- ematical technique is presented as having been reined in, with varying success, by Euclid's tacit acceptance of overarching ontological and pedagogical commitments. As an interpretative tool this scheme sug- gests a dynamic of tensions in the text, aris- ing from a dialectic of agendas in the sur- rounding world. For example, Lachterman depicts Euclid in book 5 as having fash- ioned a theory of proportion that accommo- dates the fact of incommensurability while vindicating a pretheoretical experience of the subject.

Might it be, Lachterman asks, "that the horizon of ancient ontology, as articulated in Plato and Aristotle, is the artfulness of teaching what can be learned and learning what can be taught ... rather than the craft of letting what has been fashioned come to stand on its own?" (p. 114). For Plato and Aristotle this seems exactly right. How much Euclid's practice was circumscribed by the same horizon is a profoundly inter-

713 713