Tripping through dance history with de Mille; America Dances, by Agnes de Mille. New York: Macmillan Publishing Compan. $24. 95.

As early as the beginnings of theater in America, dancing had a place on the stage. Before that, dancing masters taught the early settlers their manners and the dances from England and France, often incurring the wrath of self-righteous ministers, such as stern Increase Mather. Predating the coming of the white man , native Americans performed dances to call down rain from the heavens, ensure victories over enemies, and mark the cycle of the seasons. Mixed into this rich melange were the rhythms and dances brought from Africa by the black slaves.

In her new book, "America Dances," Agnes de Mille celebrates the amazing transition of borrowed material into a uniquely American art form that is the culmination of the history of dance in America. There is no better person to speak on the subject, who could bring greater vision or eloquence, than de Mille , a substantial creator of dance for the past five decades.

As a child she was inspired by a performance by Anna Pavlova. De Mille spent a long apprenticeship in the United States and England before success and recognition for "Rodeo" (1942) and "Oklahoma!" (1943). Her work on Broadway and her ballets have assured her a position of importance in defining the character of American dance.

"America Dances" began as a lecture commissioned for Harvard University's summer dance program, then expanded with live dancers into a pageant with the Joffrey Ballet, televised on PBS last year. Who of its viewers can forget de Mille's superb timing and sense of authority as she related the dance events of the past?

She is best when writing about the people and times she knew. Her emphatic viewpoint on Martha Graham, the descriptions of Sybil Shearer and Carmelita Maracci (less well- known but significant contributors to recent dance history), and her inclusions of Lincoln Kirstein and Lucia Chase are firsthand, fresh, and original. She gives an excellent picture of the modern dancers of the 1930s who followed Graham and others, as acolytes or Renaissance of craftsmen.

The problem with the book is the lack of accuracy. De Mille has been ill used by her editor and research assistant whom she mentions in the acknowledgments. The list of misspelled names spans the centuries from mary Ann Lee to Alison Chase, with mistakes in crucial dates. The "Historical Chronology" which precedes the text cannot be trusted when it attributes the first American performance of "Giselle" to a French dancer instead of Philadelphia-born Mary Ann Le e.