THEODOSIUS, of Tripolis, a Greek geometer and astronomer, three of whose works were contained in the collection of lesser writings named 'O (tii/cpos aarpovo-p.ovp.evos (sc. TOVOS), or 'O p-iKpos aorpoVo/xos. Pappus of Alexandria, at the commencement of the sixth book of his %vvaymyrj, speaks of this collection, the study of which is indispensable to any one who would master the science of astronomy (rbv aejTpovop.oviJt.ivov roirov). These writings, which were highly esteemed in the school of Alexandria, were intermediate between the Elements of Euclid and the Almagest of Ptolemy, for the understanding of which, indeed, they formed an indispensable introduction. Of the life of Theodosius nothing is known. As to the time when he lived different opinions have been held, he being placed by some in the first century before and by others in the second century after the Christian era. The latter opinion is founded on an error of Suidas (s.v.), who on the one hand identifies the author of the three works referred to above with a sceptical philosopher of the same name who lived at the time of Trajan or later, and on the other hand distinguishes him from a native of Tripolis who wrote a poem on spring. It is now generally admitted that the subject of this article is the same as Theodosius the mathematician, who is mentioned by Strabo amongst the natives of Bithynia distinguished for their learning, and whose sons were also mathematicians, the same, too, as the inventor of a universal sun-dial (horologium irpbi irav K\Cp.a) of that name who is praised by Vitruvius (Be Architectura, ix. 9). His date, therefore, could not have been later than the 1st century B.C.; he may, however, have lived in the preceding cen-tury, inasmuch as the names mentioned by Strabo in the passage referred to above are, as far as we know, arranged chronologically, and Theodosius immediately follows Hip-parchus, who made astronomical observations between 161 and 126 B.C., and precedes Asclepiades the physician, who lived at Rome at the beginning of the 1st century B.C.
The statement that he was " of Tripolis " is made, not on the authority of Suidas, as has been erroneously said, but because he is so described in the title of his principal work. It is probable, therefore, that he was a native of Bithynia, and resided at Tripolis, where he wrote his work. Tripolis is generally taken to be the city of that name on the Phoenician coast, but it may have been a town of the same name in Lydia, on the Meander.
His chief workStpaipuca, in three bookstreats of the properties of the sphere and its sections, with the object of establishing the geometrical principles of spherical astronomy. This work, which is classical, is distinguished for the order and clearness of the exposition as well as for the rigour of its proofs, and has ever since formed the basis on which the subject of spherical geometry has been treated. It does not contain any trace of spherical trigono-metry, which, on the other hand, was the special subject of the work having the same title, and included in the same collection, of Menelaus of Alexandria, who lived at the end of the 1st century.
Montucla suspected that a great part of the three books of Theodosius must have been known before his time, and that he merely did with respect to this branch of geometry what Euclid had done with the elements, namely, he collected and incorporated in his work the different propositions found before his time by astronomers and geometers. This conjecture of Montucla has been confirmed by A. Nokk (Ucber die Sphdrik des Theodosius, Karls-ruhe, 1847), by Heiberg (Litterargeschichtliche Studien iiber Euklid, pp. 43 sq., Leipsic, 1882), and by Hultsch, from whose researches, and. especially owing to the publication by the last of the editio princeps of Autolycus, it is now quite certain that as early as the middle of the 4th century B.C. there existed a Greek text-book on Spherics which, in its essential contents, scarcely deviated from the three books of Theodosius. He must therefore he regarded as merely the editor, or at most the elaborator and expounder, of a doctrine which existed some centuries before him.
The Spherics of Theodosius was translated into Arabic at the beginning of the loth century, and from the Arabic into Latin in the 12th century by Plato of Tivoli (Tiburtinus). This translation was published in 1518 at Venice, but was found so faulty by J. Voegelinus that he published a new Latin version, together with additions from the Arabian commentators, Vienna, 1529, 4to; other Latin translations were published by P. Maurolycus, Messina, 1558, fol.; by C. Clavius, Rome, 158G, 4to; and by Barrow under the title, Tlieodosii Sphmrica, Methodo Nova Illustrata et Succincte Demonstrata, London, 1675, 4to. The Greek text was first published, and with it a Latin translation, by J. Peua, Paris, 1558, 4to; it has been edited since by Joseph Hunt, Oxford, 1707, and by E. Nizze, Berlin, 1852, but these two editions are founded on that of Pena. There is also a German translation by Nizze, Stralsund, 1826. His two editions are accompanied with valuable notes and an appendix containing additions from Voegelinus and others.
The two other works of Theodosius which have come down to us have not as yet been published in the original. The propositions, without demonstrations, in the work irepl rjixepuv Kai VVKTUV (On Days and Nights), in two books, were given by Dasypodius, in Greek and Latin, in his Sphm'icx Doctrime Propositiones, Strasburg, 1572, Svo. A Latin version of the complete work, with ancient scholia and figures, was given by Joseph Auria, Rome, 1591, 4to. Pappus has given a pretty full commentary on the first book of this work of Theodosius. His work irepi otK>)a-ea)^ (On Habitations) also was published by Auria, Rome, 158S. It gives an account of how, for every inhabitant of the earth from the equator.to the pole, the starry firmament presents itself in the course of a year. The proposi-tions in it were also given by Dasypodius in his work mentioned above.
This collection contained the following books:" Theodosii Tri-polita? Sphxricorum libri iii.; Euclidis Data, Optica, Catoptrica, ac Phxnomena; Theodosii Tripolitae De Habitationibus et JSfoctibus ac Diebus libri ii.; Autolyci Pitanas: De Sphtera Mota, et libri ii. De Ortu atque Occam Stellarum Inerrantium; Aristarchi Samii Be Magnitudinibus ac Distantiis Solis ac Lunx ; Hypsiclis Alexandrini 'Avtupopwbs sive De Ascensionibus ; Menelai Sphmricorum libri iii." Fabricius, Bibliotheca Orxca, ed. Harles, iv. p. 16.