The Foundations of GeometryOpen court publishing Company, 1902 - 132 من الصفحات |
طبعات أخرى - عرض جميع المقتطفات
عبارات ومصطلحات مألوفة
according algebra of segments allel angle BAD angle h axiom of Archimedes axiom of parallels axioms of congruence axioms of groups bers broken line called Cloth co-ordinates commutative law complex number system congruent consequently corresponding definite number demonstration denote Desargues's theorem domain ellipse equal content equation ERNST MACH etry euclidean geometry expression figure fulfilled geom geometry of space given point given straight line gruence half-ray Hence homologous sides homologous vertices integral rational joining the homologous law of multiplication line OA Mach's measures of area Mechanics ments non-euclidean geometry orem parameter Pascal's theorem PAUL CARUS perpendicular plane axioms plane geometry points of intersection polygons possible problem proposition quotient rational function real numbers right angles Science square root straight lines joining straight-edge sums of squares supplementary angle theorem 32 theorem 43 tion transferer of segments triangles ABC valid x-axis
مقاطع مشهورة
الصفحة 5 - Math. Ann., Vol. 50. THE FIVE GROUPS OF AXIOMS. 1. THE ELEMENTS OF GEOMETRY AND THE FIVE GROUPS OF AXIOMS. EiT us consider three distinct systems of things. The things composing the first system, we will call points and designate them by the letters A, B, C, . . . .; those of the second, we will call straight lines and designate them by the letters a, b, c, . . . . ; and those of the third system, we will call planes...
الصفحة 101 - The sum of the angles of a triangle is less than two right angles, and the propositions of the last chapter hold without restriction.
الصفحة 8 - II, 2. If A and C are two points of a straight line, then there exists at least one point B lying between A and C and at least one point D so situated that C lies between A and D.
الصفحة 25 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.
الصفحة ii - Geometric Exercises in Paper-Folding. By T. SUNDARA Row. Edited and revised by WW BEMAN and DE SMITH. With half-tone engravings from photographs of actual exercises, and a package of papers for folding. Pages, x, 148. Price, cloth, $1.00 net. (4s. 6d. net.) "The book is simply a revelation in paper folding.
الصفحة 7 - I, in order to distinguish them from the axioms I, 3-7, which we will designate briefly as the space axioms of this group. Of the theorems which follow from the axioms I, 3-7, we shall mention only the following : THEOREM 1. Two straight lines of a plane have either one point or no point in common ; two planes have no point in common or a straight line in common ; a plane and a straight line not lying in it have no point or one point in common. THEOREM 2. Through a straight line and a point not lying...
الصفحة 8 - Of any three points situated on a straight line, there is always one and only one which lies between the other two.
الصفحة 111 - A most fascinating volume, treating of phenomena in which all are interested, in a delightful style and with wonderful clearness. For lightness of touch and yet solid value of information the chapter ' Why Has Man Two Eyes? ' has scarcely a rival in the whole realm of popular scientific writing." — The Boston Traveller. "Truly remarkable in the insight they give into the relationship of the various fields cultivated under the name of Physics. ... A vein of humor is met here and there reminding...
الصفحة 14 - Conversely, the second part of the axiom of parallels, in its original form, follows as a consequence of theorem 8. The axiom of parallels is a plane axiom. §6. GROUP IV. AXIOMS OF CONGRUENCE. The axioms of this group define the idea of congruence or displacement. Segments stand in a certain relation to one another which is described by the word "congruent.'''' IV, 1. If A, B are two points on a straight line a, and if A...
الصفحة 108 - muscle and clothing,' and being written from the historical standpoint, introduces the leading contributors in succession, tells what they did and how they did it, and often what manner of men they were. Thus it is that the pages glow, as it were, with a certain humanism, quite delightful in a scientific book. . . . The book is handsomely printed, and deserves a warm reception from all interested in the progress of science.