John D. NortonDepartment of background and approach of ScienceUniversity of chathamtownfc.netsburgh

The 5 postulates on i beg your pardon Euclid based his geometry are:

1. To draw a right line native any allude toany point.2. To create a finite right linecontinuously in a straight line.3. To describe a one with any kind of centerand distance.4. That all appropriate angles are equal come oneanother.5. That, if a straight line falling ontwo straight lines makes the internal angles on the same side less than tworight angles,the two straight lines, if produced indefinitely, meet on that side top top whichare the angles less than the two ideal angles.

You are watching: Five basic postulates of euclidean geometry

Playfair"s postulate, identical to Euclid"s fifth, was:

5ONE. Through any given point can bedrawn precisely one straightline parallel come a given line.

In trying to show that the fifth postulate had actually to hold, geometersconsidered the other feasible postulates that might replace 5". The twoalternatives as given by Playfair are:

5MORE. Through any kind of given point an ext thanone right line deserve to be drawn parallel to a given line.5NONE. Through any kind of given suggest NO right lines can be drawnparallel come a given line.

Once you see that this is the geometry of an excellent circles top top spheres, friend alsosee the postulate 5NONE cannot live happily with the first fourpostulates after all. They need some young adjustment:

1". Two unique points determine at least one straightline.2". A right line is boundless (i.e. Has no end).

Each of the three alternate forms that the 5th postulate are connected witha unique geometry: