French mathematician Michel Chasles (1793–1880), a staunch defender of pure geometrical methods, is now mostly remembered as the author of the
Aperçu historique
(1837). In this book, he retraced the ...history of geometry in order to expound epistemological theses on what constitutes a virtuous practice of geometry. Amongst these stands out the assertion that the values of generality and simplicity in mathematics are intimately connected. In this paper, we flesh out this claim by analysing Chasles’s geometrical solutions to the century-old problem of the attraction of the ellipsoids. We show how these solutions echo Chasles’s evaluation of the relative strengths of geometrical and analytical methods, and how they embody a set of normative rules for the geometer’s practice whose observance Chasles deemed necessary and sufficient for the development of general methods and theories.
To assess the additional value of adrenal venous sampling (AVS) to diagnose primary aldosteronism sub-types in patients who have a unilateral nodule detected by computed tomography (CT scan) and who ...should undergo an adrenalectomy.
A retrospective study to assess consecutive patients with primary aldosteronism undergoing an adrenal CT scan and AVS. Criterion for selective cannulation was an equal or higher cortisol level in the adrenal vein compared to the inferior vena cava. An adrenal-vein aldosterone-to-cortisol ratio of at least two times higher than the other side defined lateralization of aldosterone production.
Sixty-seven patients (mean age 52 years, 39 men) underwent a CT scan and AVS. In nine patients (13%), cannulation of the right adrenal vein led to a technical failure. Both procedures led to diagnosis of 29 patients with adenoma-producing aldosterone (APA; 50%), 23 bilateral adrenal hyperplasias (40%), and six unilateral adrenal hyperplasias (10%). Of the 45 patients with a nodule detected by CT, subsequent AVS showed bilateral secretion in 16 patients (36%). Compared to the strategy of coupling CT scans with AVS to diagnosis APA, a CT scan alone had an accuracy of 72.4% (P < 0.001). Among patients with a macronodule detected by CT, 13 (37%) had bilateral secretion as assessed by AVS. The patients with a macronodule detected by CT alone had the same risk of a discrepancy as those with a small nodule (P = 0.99).
AVS is essential to diagnose the unilateral hypersecretion of aldosterone, even in patients in whom a unilateral macronodule is detected by CT, to avoid unnecessary surgery.
Of Euclid’s lost manuscripts, few have elicited as much scholarly attention as the Porisms, of which a couple of brief summaries by late-Antiquity commentators are extant. Despite the lack of textual ...sources, attempts at restoring the content of this absent volume became numerous in early-modern Europe, following the diffusion of ancient mathematical manuscripts preserved in the Arabic world. Later, one similar attempt was that of French geometer Michel Chasles (1793–1880). This paper investigates the historiographical tenets and practices involved in Chasles’ restoration of the porisms, as well as the philosophical and mathematical claims tentatively buttressed therewith. Echoes of the Quarrel of the Ancients and the Moderns, and of a long-standing debate on the authority and usefulness of the past, are shown to have decisively shaped Chasles’ enterprise—and, with it, his integration of mathematical and historical research.
This essay explores the research practice of French geometer Michel Chasles (1793–1880), from his 1837 Aperçu historique up to the preparation of his courses on ‘higher geometry’ between 1846 and ...1852. It argues that this scientific pursuit was jointly carried out on a historiographical and a mathematical terrain. Epistemic techniques such as the archival search for and comparison of manuscripts, the deconstructive historiography of past geometrical methods, and the epistemologically motivated periodization of the history of mathematics are shown to have played a crucial role in the shaping of Chasles's own theories. In particular, we present Chasles's approach to the ‘material history’ of algebraic symbolism and argue that it motivated and informed his subsequent invention of a novel notational technology for the writing of geometrical proofs and propositions. In return, this technology allowed Chasles to carry out a programme for the modernization of geometry in keeping with epistemic requirements he had also delineated via a form of historical writing.
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