...AND THE FIVE GROUPS OF AXIOMS. E^T us consider three distinct systems of things. The things composing the first system, we will call points and designate...planes and designate them by the Greek letters a, ft, y, . . . . The points are called the elements of linear geometry ; the points and straight lines,...

...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...planes and designate them by the Greek letters a, /?, y, . . . . The points are called the elements of linear geometry ; the points and straight lines,...

...The things composing the first system, we will call poinis and designate them by the letters A, JB, C, . . . .; those of the second, we will call straight lines and designate them by the letters #,<$,<:,....; and those of the third system, we will call planes and designate them by the Greek letters...

...language of Euclid : "Let us conceive three distinct systems of things," he said. "The things composing the first system we will call points and designate them by the letters A, B, C, " The "things" of the other two systems he called straight lines and planes. These "things" could have...

...Geometry begins as follows: "Let us consider three distinct systems of things. The things composing the first system, we will call points and designate...planes and designate them by the Greek letters a, b, c . . . ."" Hilbert continues, "We think of these points, straight lines and plains as having certain...

...language of Euclid : "Let us conceive three distinct systems of things," he said. "The things composing the first system we will call points and designate them by the letters A, B, C, . . . ." The "things" of the other two systems he called straight lines and planes. These "things"...

...consider three distinct systems of things. A point is that which has no The things composing the part. first system, we will call points and designate them by the letters A, B, C, . . . ; EUCLID ( cont. ) A line is breadthless length. The extremities of a line are points. A straight...