In 1682, Leibniz published an essay containing his solution to the classic problem of squaring the circle: the alternating converg-ing series that now bears his name. Yet his attempts to disseminate his quadrature results began seven years earlier and included four distinct approaches: the conventional (journal article), the grand (treatise), the impostrous (pseudepigraphia), and the extravagant (medals). This paper examines Leibniz’s various attempts to disseminate his series formula. By examining oft-ignored writings, as well as unpublished manuscripts, this paper answers (...) the question of how one of the greatest mathematicians sought to introduce his first great geometrical discovery to the world. (shrink)

● Any given placement (e.g. Sun in Taurus; Mars in Capricorn; Mercury in the third house) is necessarily common to tens of thousands of people. Saturn in the ninth house, for example, will not behave the same or produce the same effects in the twenty or one hundred charts in which we find it there. In each case Saturn will behave in accordance with the rest of the astrographic/chart composition (as if we stayed in the same hotel in different epochs (...) or different people contracted the same disease; our stay will be different each time, according to the epoch, and each person’s symptoms will too, be different, according to their individual biochemistry; not to mention that each chart or astrography, like each genetic code or sequence, is unrepeatable). Certainly, “no planet can produce, on its own, what only the combined or concerted action of all can” (BUSTAMANTE, 2023, SPICA magazine, pp. 93-111). Hence the synergistic nature of the interpretative exercise (i.e., the whole is greater than all its parts). The fundamental component of the mathematical expression of the interpretive exercise is: astrological triangulation, the functional denomination for what we know as synthesis (WEISS, 1946; LEO, 1983, HAND, 1981). In order to demonstrate its usefulness, as well as the convenience of its mathematical expression, we have chosen two individuals (JEFFREY DAHMER, STEVEN SPIELBERG) whose astrographies do not—according to the community—explain their lives. The rest of the astrographies correspond to those of serial killers JOHN WAYNE GACY, DAVID CARPENTER, and TED BUNDY. ● We explain, by means of algebraic notations, the synthesis and the functional values that make up the synthesis. ● We take the Moon and Neptune as relevant bodies for the purpose of diagnosing or studying endocrine or neurohormonal issues, and Mars, Pluto, and Saturn as relevant planets for the purpose of inferring violence or sinister behaviour, upon the case, and quadratures or oppositions—and conjunctions—between Venus and the Moon, the Moon and Neptune, and the Sun or Venus and Neptune or Uranus as indicators of neurohormonal disorders and/or sexual deviance (APA definition) . ● We consider quadratures (90º) or oppositions (180º)—and conjunctions—between Mercury or the Moon and Saturn, or between Mars or the Moon and Saturn, Uranus, Neptune, and/or Pluto as powerful indications of violence or mental disorders, upon the case. ● We have also regarded Sagittarius as a sign as expansive and abundant as its ruler, Jupiter, according to the best of its characterisations (or as an exceptionally swift and wild sign, according to other characterisations), and the fifth region of a natal chart as one closely related to fortune in a broad sense (material and immaterial). ● Because we advocate the idea that orbs should be predicated of the planet (size, speed), not the aspect itself, the gas giants (Jupiter, Saturn, Uranus, and Neptune) and the Sun have been granted up to 10º of orb (or 12º, in the case of broad influence ). We understand aspectual relationships as angular relationships held between two or more celestial bodies placed in signs with at least one property in common (according to our molecular theory of the ecliptic, compatible with the optical theory of the aspects from the Hellenistic tradition). (shrink)

We present a formal mechanical analysis using sweeping net methods to approximate surfacing singularities of saddle maps. By constructing densified sweeping subnets for individual vertices and integrating them, we create a comprehensive approximation of singularities. This approach utilizes geometric concepts, analytical methods, and theorems that demonstrate the robustness and stability of the nets under perturbations. Through detailed proofs and visualizations, we provide a new perspective on singularities and their approximations in analytic geometry.