Postulate (Line): two distinct points determine a single (one, and only) line that passes through them.Įxample: the distinct points $A$ and $B$ determine the line. Points $M$ and $M$ are distinct (different).The points $A, C$ and $H$ are collinear (from Latin cum + linea + ar was placed on a straight line).The points $B$ and $M$ do not belong to the line $r$.The points $A, C$ and $H$ belong to the line $r$.What does “infinite points” mean? Think of a big number, infinity is bigger than that, that is, as many points as you want. Postulate 2: In a plane, there are infinite points. Postulate 1: On a line, as well as outside it, there are infinitely many points. ![]() In this post, based on the book Elementos by Euclid, we will enunciate some postulates for point, line and plane. That is, everything that satisfies such axioms will also satisfy their consequences.With that, we deduce everything we can from such axioms. ![]() In the case of an axiom it is a statement that we assume to be true. Everything starts with the axiom, as it is the starting point of reasoning. More specifically, we have no way of proving results whose facts are accepted without a demonstration. In ancient Greece, mathematicians like Euclid used the concepts of axioms and postulates a lot.Īxioms and postulates are accepted facts without a demonstration. Next, let’s establish some notation standards for these three items: The first concepts that the Greeks initiated, for the development of geometry are the concepts of: The most important works of this period are displayed in the Elementos collection written by Euclid in Alexandria around 300 BC. These schools devoted themselves to the study of figures and numbers using methods of analysis and deduction. Pythagorean, in honor of Pythagoras of Samos.This splendid people were the first to use a deductive science, with definitions, postulates, axioms and theorems. Before the philosophical and deductive thoughts of mathematics, people such as the Egyptians, Sumerians, Hindus and Persians investigated numbers and geometric shapes without as much rigor as the Greeks. In this post specifically we will talk about the mathematics developed in this period. In this work he cites Thales of Miletus as the main person responsible for introducing Geometry in Greece, based on research studies on Egyptian works. The best known work of this period is Elements by Euclid (around 500 BC), which explains the geometry of plane shapes, circles, quadrilaterals, triangles, among others. ![]() ![]() Of the main Greeks who were very important for the contribution of geometry, we can mention Euclid, Pythagoras, Archimedes and Apollonius. The Greeks were the first to use the concept of geometry used more rigorously than in other civilizations, such as the Egyptians, Babylonians, among others.Įgyptians and other civilizations studied geometry to share fertile lands, build houses, are some examples of geometric applications. The definition of geometry is a Greek concept that comes from meters (to measure) and geo (earth), more specifically to measure the Earth. They were responsible for the heyday of philosophical, scientific, political, social and artistic ideals and had a decisive influence on the western world. The Greeks of ancient civilization were one of the most famous people in the art of thinking. In it, we will talk from very primitive concepts, to more advanced concepts, aimed at children (elementary to medium). Here we start the series of posts for plane geometry.
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