“Archimedes to Dositheus greeting.

On a former occasion I sent you the investigations which I had up to that time completed, including the proofs, showing that any segment bounded by a straight line and a section of a right-angled cone [a parabola] is four-thirds of the triangle which has the same base with the segment and equal height. Since then certain theorems not hitherto demonstrated (ἀνελέγκτων) have occurred to me, and I have worked out the proofs of them. They are these: first, that the surface of any sphere is four times its greatest circle (τοῦ μεγίστου κύκλου); next, that the surface of any segment of a sphere is equal to a circle whose radius (ἡ ἐκ τοῦκέντρου) is equal to the straight line drawn from the vertex (κορυфή) of the segment to the circumference of the circle which is the base of the segment; and, further, that any cylinder having its base equal to the greatest circle of those in the sphere, and height equal to the diameter of the sphere, is itself [i.e. in content] half as large again as the sphere, and its surface also [including its bases] is half as large again as the surface of the sphere.

The cult of Hera is less manifold and less spiritual than many other Greek cults, but possesses great historic interest. It can be traced in most parts of ancient Greece, and had the strongest hold upon the sites of the oldest civilization, Argos, Mycenae, and Sparta; we can find no trace of its importation from without, no route along which it travelled into Greece; for in the islands, with the exception of Euboea and Samos where the legend connected the worship with Argos, it is nowhere prominent, nor does it appear to have had such vogue in Thessaly and along the northern shores as it had in Boeotia, Euboea, Attica, Sicyon, Corinth, and the Peloponnese19—93. We may regard the cult then as a primeval heritage of the Greek peoples, or at least of the Achaean and Ionic tribes; for its early and deep influence over these is attested by the antiquity and peculiar sanctity of the Argive and Samian worship. Whether it was alien to the Dorians in their primitive home, wherever that was, is impossible to decide; in the Peloponnese no doubt they found and adopted it, but they may have brought it with them to Cos and Crete, where we find traces of it. The Hera T∈λχινία of Rhodes, like the Spartan and Argive Hera, was probably pre-Dorian.

The study of the cults of Zeus is perhaps the most interesting chapter of the history of Greek religion, for it includes the two extremes of religious thought, the most primitive ideas side by side with the most advanced; and nearly all the departments of nature and human life were penetrated with this worship. Although the figures of Apollo, Athene, Dionysos, and Prometheus are of more importance in the history of external civilization and of the special arts of Greece, yet no character in Greek religion has such wealth of ethical content, or counts so much for the development of moral ideas, as the character of Zeus. At times he seems to overshadow the separate growths of polytheism; and at times in expressing the nature of Zeus the religious utterance became monotheistic.

The study of this as of the other Hellenic cults must consist in great part of an examination of the cult-titles, which must be carefully distinguished from mere poetical appellatives, and which on the whole are our most direct evidence of the ideas embodied in the state-religion. And the importance of the title in the worship was of the greatest; for public prayer and sacrifice were never made to God in the abstract, but to a particular divinity usually designated by some term that showed what sort of help the worshipper needed and expected; unless he addressed the deity by the right title, the help might be withheld; and a great part of the function of the oracles in Greece was to instruct the worshipper to what deity under what particular name he should pray.

The present work, however faulty and defective it may be in method or statement, need not be prefaced by any apology for the subject with which it deals. A compendious account of Greek cults, that should analyze and estimate the record left by Greek literature and monuments of the popular and public religion, has long been a desideratum in English and even to a certain extent in German scholarship. Until quite recent years the importance of Greek religion has been contemptuously ignored by English scholars. The cause of this neglect was perhaps the confusion of Greek mythology—that apparently bizarre and hopeless thing—with Greek religion; the effect of it is still apparent in nearly every edition of a Greek play that is put forth. Fortunately, this apathy concerning one of the most interesting parts of ancient life is now passing away; and since this book, the work of many years of broken labour, was begun, a new interest, stimulating to fruitful research, in Greek ritual and myth is being displayed in many quarters, especially at Cambridge.

The comparative study of religion has received signal aid from the science of anthropology, to which England has contributed so much; we have been supplied—not indeed with ‘a key to all the mythologies,’ but with one that unlocks many of the mysteries of myth and reveals some strange secrets of early life and thought.

The Hellenic ideal of the virgin-huntress, the goddess kindly to boys and maidens and to the living things of the wood, as it was perfected in the religious hymn and the Euripidean drama, was not fully embodied in Greek art until the age of Praxiteles and the great painters of Alexander's period. Yet the developed archaic art had done something for the expression of the Artemis-type, and had given it movement and life. The fragment of an Attic vase quoted above a shows a very striking representation of the divinity which we may date about 470 b. c. She is clad in Ionic chiton and mantle with a panther's skin over her shoulders, holding in her left hand the bow and raising in her right hand a flower towards her lips. The golden-coloured drapery and the white flesh suggest a cult-image of chryselephantine technique, and the figure may be a copy of the older image in the Brauronian temple on the Acropolis.

Of considerable importance also for character and style is the Pompeian statuette in the Museum of Naples (Pl. XXXII. b), representing Artemis striding forward, clad in a chiton with sleeves and a finely textured mantle, with a quiver at her back; the fingers are restored, but the one hand must have been holding a bow or torch, the other holding up the skirt of her dress; a diadem adorned with rosettes crowns her head, of which the hair has been given a golden tinge.