The Questio de aqua et terra is a cosmological treatise traditionally attributed to Dante Alighieri. However, the authenticity of this text is controversial, due to discrepancies with Dante's established works and to the absence of contemporary references. This study investigates the authenticity of the Questio via computational authorship verification (AV), a class of techniques which combine supervised machine learning and stylometry. We build a family of AV systems and assemble a corpus of 330 13th- and 14th-century Latin texts, which we use to comparatively evaluate the AV systems through leave-one-out cross-validation. Our best-performing system achieves high verification accuracy (F1=0.970) despite the heterogeneity of the corpus in terms of textual genre. The key contribution to the accuracy of this system is shown to come from Distributional Random Oversampling (DRO), a technique specially tailored to text classification which is here used for the first time in AV. The application of the AV system to the Questio returns a highly confident prediction concerning its authenticity. These findings contribute to the debate on the authorship of the Questio, and highlight DRO's potential in the application of AV to cultural heritage.