Theodosii sphaericorum elementorum libri III ex traditione Maurolyci, Messanensis Mathematici. Menelai sphaericorum lib III. Ex traditione ejusdem. Maurolyci sphaericorum lib II. Autolyci de sphaera, quae movetur Liber. Theodosii de habitationibus. Euclidis phaenomena. Brevissime demonstrata. Demonstratio et praxis, trium tabellarum scilicet Sinus recti, Foecundae et Beneficae ad Sphaeralia triangula pertinentium. Compendium mathematicae mira brevitate ex clarissimis Authoribus. Maurolyci de Sphaera sermo

First edition, 'excessively rare' (Sotheran), of Maurolico's Latin translations of works on 'sphaerics' by four ancient Greek writers, Autolycus, Menelaus, Euclid and Theodosius, those of the first two authors constituting the first printed editions. Maurolico, one of the most original mathematicians of the 16th century, appended his own original propositions on sphaerics, probably based on astronomical observations made from 1548 to 1550 in Sicily, as well as a number of trigonometrical tables, including the first printed tables of secants. Sphaerics, the geometry of the sphere, was regarded by the ancient Greeks as a branch of astronomy rather than of geometry. The order in which the works are presented by Maurolico is pedagogical rather than historical. He begins with the Sphaerica of Theodosius of Bithynia (ca. 160 BC - ca. 100 BC), a mathematician and astronomer who lived in Tripoli on the Fenicia coast who is thought to be a younger contemporary of Hipparchus, the inventor of trigonometry (although no work by Hipparchus on this subject has survived). Arranged in three books, the Sphaerica discusses the properties of circular arcs lying on the surface of a sphere, notably great circles. Maurolico's version is based on a Latin manuscript of Plato of Tivoli (in turn prepared on the basis of an Arabic translation). The Sphaerica first appeared in the compendium Sphaera published at Venice in 1518; the first separate Latin edition at Vienna in 1529; and the editio princeps of the Greek text at Paris in the same year as the present work. Maurolico also includes later in the present volume his translation of Theodosius's De Habitationibus, which treats the phenomena caused by the rotation of the earth, particularly what parts of the heavens are visible from different geographical locations. Maurolico next presents his translation of the Sphaericorum of Menelaus of Alexandria (fl. 100 AD). "Menelaus' major contribution to the rising science of trigonometry was contained in his Sphaerica, in three books. It is this work which entitles him to be regarded as the founder of spherical trigonometry and the first to have disengaged trigonometry from spherics and astronomy and made it a separate science" (DSB). The book introduces the concept of spherical triangle (a figure formed by three great circle arcs, which he named 'trilaterals') and proves Menelaus's theorem on the ratios of the lengths of the segments in which the sides of a triangle are divided by a straight line that intersects them all (and its analogue for spherical triangles). The work has not survived in the original Greek, and Maurolico's translation, the first printing of the text in any form, was at first thought to have been based on an Arabic manuscript, but is now believed to derive from a Latin translation by Gerard of Cremona (d. 1187). Maurolico's translation of Menelaus is followed by his own work Sphaericorum, in two books. This is a continuation and completion of the Sphaericorum of Menelaus, and is "among the most interesting books on the subject published between the sixteenth and seventeenth centuries", according to the National Edition of the works of Maurolico (currently in preparation). Maurolico informs us that his sources for this work, apart from Theodosius, Menelaus and Ptolemy's Almagest, are the treatises of Thabit ibn Qurra, Geber, Peurbach and Regiomontanus. Maurolico also includes later in the present volume a second work of his own composition entitled De Sphaera sermo, which contains a series of theoretical and practical considerations in relation to astronomy on the sphere ('inter Sicut planas circulum, ita inter solidas figuras Sphaeram maximae excellentiae them multis plane rationibus constat'). The next work in the volume is Maurolico's translation of De sphaera quae movetur by Autolycus of Pitane (fl. 300 BC), which is believed to be the oldest mathematical treatise from ancient Greece that is completely preserved (all earlier Greek math.…