Some remarks on the meaning of equality in Diophantos’s Arithmetica

Diophantos in Arithmetica, without having defined previously any concept of “equality” or “equation,” employs a concept of the unknown number as a tool for solving problems and finds its value from an equality ad hoc created. In this paper we analyze Diophantos’s practices in the creation and simplification of such equalities, aiming to adduce more evidence on certain issues arising in recent historical research on the meaning of the “equation” in Diophantos’s work.     

Chemometrically Assisted Optimization of Pregabalin Fluorescent Derivatization Reaction with a Novel Xanthone Analogue and Validation of the Method for the Determination of Pregabalin in Bulk via a Plate Reader

Quantitation of chromophore-free analytes is always a challenge. To this purpose, derivatization of the analyte constitutes a common strategy, leading to a product with a strong signal. In the current study, a novel xanthone analogue was utilized for the first time for the derivatization of pregabalin, a model analyte with a primary amine moiety that lacks a chromophore. The fact that only the xanthene-based derivative, formed after the derivatization reaction fluoresces, enables avoiding its chromatographic separation from the reagent and thus reducing the analysis time of a series of samples in 1–2 min via a plate reader. The reaction conditions were optimized via a central composite design (CCD), with fluorescence signal as the measure of the yield. The following factors that affect the derivatization reaction were chosen: (a) temperature, (b) reaction time, and (c) triethylamine solution volume used to drive the reaction to completion. After the identification of the optimal conditions, the method was validated according to ICH guidelines, using a fluorescence plate reader for signal measurement (λ_ex = 540, λ_em = 615 nm). Finally, the newly developed high-throughput method was applied to the determination of drug content in pregabalin bulk.