The studies of Bonaventura Cavalieri’s indivisibles by Giusti, Andersen, Mancosu and others provide a comprehensive picture of Cavalieri’s mathematics, as well as of the mathematical objections to it as formulated by Paul Guldin and other critics. Issues that have been studied in less detail concern the theological underpinnings of the contemporary debate over indivisibles, its historical roots, the geopolitical situation at the time, and its relation to the ultimate suppression of Cavalieri’s religious order. We analyze sources from the seventeenth through twenty-first centuries to investigate this relationship.

Between 1621 and 1626, the soldier-historian Philip O’Sullivan Beare authored treatises to motivate Catholic powers toward greater intervention in Ireland, and to defend his country’s honor more generally. Moving beyond political theology, the author’s unfinished manuscript Zoilomastix incorporated natural history and astronomy. The current article draws attention to a previously overlooked fragment wherein the Irishman considered contemporary debates on the structure of the heavens. It first considers the material history of the fragment, before exploring the influence of continental pedagogic and military networks upon the author. The paper then presents evidence of O’Sullivan Beare’s adherence to Thomist, Bellarminian cosmology, and of his disagreement with Clavius and Galileo, via Jacques du Chevreul’s 1623 commentary on Sacrobosco’s Sphere. Contrasting the fragment’s contents with the cosmogony published in the author’s Patritiana decas (1629), it demonstrates that these exegetic readings were part of the author’s wider strategy for “making truth” amidst shifting political, confessional, and cosmological paradigms.

In the last decades, the notion of “economy” has gained a central importance in accounts of early modern experimental culture. Historians of economic science have primarily focused on the repurposing and recycling of materials, namely on thrift as a virtue of the skilled experimenter. In this paper, I propose to consider economy as a quality enacted by technology. As a matter of fact, technology could actualize the principles of economy in its performance, and its “degree of economy” could be measured. I argue that one of the key parameters used to quantify economy was the temporal performance of technology. To ground my view of “time thrift,” I analyze unpublished documents relating to eighteenth-century inventions based on the action of fire (cooking, lighting), scientific reports written by scientists on such inventions, as well as expert assessments on manufacturing activities also connected with the management of heat (distillation).

This article considers the doctrine of energetical vitalism as proposed by the early twentieth-century philosopher, Eugenio Rignano. Rignano’s energetical vitalism aimed to present a comprehensive biological theory, addressing distinct phenomena of purposiveness—or what are called teleological phenomena—exclusive to the organic domain. His doctrine pivoted on two key hypotheses. The first, the hypothesis of vital energy, posited that life’s distinctiveness emanates from a unique energy form he termed “vital (or nervous) energy.” Rignano believed that while this form of energy shares attributes with conventional energy forms and adheres to basic laws of energetics, its manifestations are exclusively organic, dictating specific purposive phenomena. The second hypothesis, termed “centroepigenetic,” asserted that vital energies primarily accumulate in the chromosomes within nuclei but can be transferred through intercellular bridges connecting germinal and somatic nuclei. Rignano’s energetical vitalism synthesized ideas from three significant scientific trends of his era: the energetics, neo-Lamarckian, and mnemic movements. In closing, this article critiques Rignano’s energetical vitalism with two primary assertions. First, while empirical support for the vital energy hypothesis remains elusive, vitalism’s historical significance is arguably more profound than contemporary physicalists recognize, and it remains logically defensible to propose vitalistic hypotheses, irrespective of physicalist metaphysical constraints. Second, Rignano’s centroepigenetic hypothesis can be seen as prescient in light of recent molecular genetic discoveries. These two points are informed by Hasok Chang’s perspectives on “outdated” scientific theories.