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We expose a few geometric techniques for determining intersections between lines and conic curves in a plane, and between planes and quadric surfaces in 3D projective space. We hope these techniques to be useful as elements for handling conics and quadrics in a Grassmann-Cayley algebra framework. In order to comply with this objective, we mostly derive our algorithms from ruler-only constructions, which possess an immediate translation in GrassmannCayley's formalism. At the basis of these constructions we use reference points which determine the conic or quadric. Besides intersections, we also address the determination of poles and polars, and we mention a possible application to the parameterization of portions of quadrics.

Belt, Brazil, associated with previous structural geology and geochronology studies, allow for a better understanding of Neoproterozoic events in this region. The Sanga da Cachoeira Complex and metasedimentary rocks of Arroio Marmeleiro Complex (U-Pb provenance age > 1.5 Ga) show 40 Ar/ 39 Ar spectra with no successful plateau age, attributed to the alteration or excess 40 Ar. Tonian (ca. 729 ± 9 Ma) 40 Ar/ 39 Ar hornblende age of metadiorites of the Cambaí Complex (U-Pb protolith age ca. 750 Ma) is interpreted to register the age of an early structure in this unit, where hornblende is a mineral of the composite banding fabric formed by remnants of original bedding, locally preserved, and added by metamorphic recrystallization. A cooling rate of at least 5 C/Ma is suggested for the Cambaí Complex, from its crystallization to its metamorphic event. The Cryogenian (<690 ± 8 Ma) 40 Ar/ 39 Ar hornblende and muscovite ages belonging to the Imbicuí Complex (protolith age ca. 869 Ma) whose ages are related to the late structure formed by a short and intense activity of the Cerro Branco Shear Zone, which experienced a rapid cooling of 12 C/Ma. The ages from the rocks belonging to such a diverse tectonic setting, including continental and intraoceanic island arc, oceanic crust low-K amphibolites and meta-harzburgites, and metasediments, presenting similar nature and fabric orientation, indicate that major tectonic-magmatic-metamorphic activity was responsible for the accretion of these lithotectonic units that gave rise to the São Gabriel Terrane in southern Brazil.