Titlebook: Euclidean Geometry and its Subgeometries; Edward John Specht,Harold Trainer Jones,Donald H. Book 2015 Springer International Publishing S

Fraudulent

Cabg318

甜得發(fā)膩

Pasch Geometry (PSH),s of segments, rays, and lines that are needed for a coherent geometry. The remainder of the chapter is a study of the basic interactions between lines, angles, triangles, and quadrilaterals, comprising Pasch geometry.

有特色

metropolitan

Free Segments of a Neutral Plane (FSEG),ve the trichotomy property. Addition of free segments is defined, and its elementary properties and interactions with ordering are studied. These developments are sufficient to prove the triangle inequality, and provide a first step toward defining distance on a neutral plane.

tympanometry

Euclidean Geometry Basics (EUC),xiom to arrive at Euclidean geometry. It explores many well-known elementary results from plane geometry involving parallel lines, perpendicularity, adjacent and complementary angles, parallelograms and rectangles.

Interregnum

壟斷

Similarity on a Euclidean Plane (SIM),gs are used to define the similarity of two sets. Similarity is shown to be an equivalence relation, and criteria are developed for similarity of triangles. The chapter concludes with a proof of the Pythagorean Theorem, and a proof that the product of the base and altitude of a triangle is constant.

flavonoids

Rational Points on a Line (QX), a rational multiple of a point on this line, develops the arithmetical properties of such multiples, and uses these to show the existence of an order-preserving isomorphism between the set of all rational numbers and a subset of the line.

Commodious

A Line as Real Numbers (REAL); Coordinatization of a Plane (RR),uclidean/LUB plane (which has been built into an ordered field) real multiples of points are defined and their algebraic properties derived. These properties are used to show the existence of an order-preserving isomorphism between the set of all real numbers and the whole line. The chapter ends with coordinatization of a Euclidean/LUB plane.