Page:Popular Science Monthly Volume 20.djvu/875

Rh insisted on the importance of experiment as well as of observation, recalled men to the study of facts, promoted their emancipation from the bonds of authority and the enchantments of imagination, insisted on the subordination of scientific inquiries to practical aims, promoted hopefulness, and clothed his thoughts in marvelous language.

does not, like many who have written on this subject, consider Euclid's system perfect, but believes that it fails in several points to meet modern requirements, and needs remodeling. This he attempts in a few features, most noticeably in the recognition of angles of a larger measurement than 180°. He accordingly treats the sum of two right angles as itself an angle, to which he gives the name of a "straight angle," and explicitly defines it. He also uses language more in accordance with modern ideas in speaking of planes. In an introductory book, besides the usual fundamental axioms and definitions, practical exercises are given in the practice of the analysis of geometric relations by means of the eye. Some of the first principles of conic sections have been developed, as a preliminary study of that subject, or to give some knowledge of those curves to those who do not intend to study analytical geometry. In proportion, a middle course has been adopted between the rigorous and prolix treatment of Euclid and the easier and simpler, but ungeometrical, method of American works.

is the thirteenth volume of the series of documents relating to the colonial history of the State of New York, published officially under the direction of the Secretary of State. It embraces deeds, bargains, transactions of councils, memoirs, and correspondence, the general bearing of which illustrates the relations of the early settlers with the Indians. An important lesson drawn from these relations and their workings is that of the practical value of fair dealing with the Indians. It was the rule of the settlement of New Netherland, invariably enforced from the beginning, that no man could settle upon Indian land unless the Indian title was first extinguished in a manner satisfactory to the Indian proprietors. The consequence of the observance of the rule was that "the Dutch, living at the door of the powerful Five Nations, could always count upon the friendship of their Indian neighbors." This friendship had a momentous bearing upon the future of the continent, for it kept the Hudson River, the only natural route to the North and West, always open and safe for the white man, and thus greatly facilitated settlement.

the last work of the lamented author, was completed by him during the later days of his failing strength for publication in Major Powell's reports of the Geographical and Geological Survey of the Rocky Mountain region. It formed substantially the fifth part of the original manuscript of the author's "Ancient Society," but was omitted from that work on account of the size which it had reached. Parts of it have appeared in detached articles; a summary of the whole as a cyclopædia article; the substance of two of the chapters, as "Montezuma's Dinner" and the "Houses of the Mound-Builders," in the "North American Review"; and other parts, as "A Study of the houses and House-Life of the Indian Tribes," with a scheme for exploring the ruins in New Mexico, Arizona, the San Juan region, Yucatan, and Central America, in the "Transactions of the Archaeological Institute of America." The facts and views embodied in these articles being placed now in their proper connection, with others bearing upon the same point, the full force and clearness which they are capable of furnishing are given to the author's theory. That theory is that the