...straight lines cannot have two points in common without having all intermediate points in common. Post. Let it be granted that a straight line may be drawn from any one point to any other point. Note — When we draw a straight line from a point A to a point B, we are said to 'join AB' ; and for...

...then A is B, is the converse of the typical theorem in (42). POSTULATES. 45. Let it be granted — 1 . That a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any distance in a straight line. 3. That a circle...

...Diagonal] is the straight line joining two of its opposite angles. POSTULATES.1 Let it be granted :— 1. That a Straight Line may be drawn from. any one point to any other point. 2. That a Terminated Straight Line may be produced to any length in a straight line. 3. And that a...

...well as practically, to carry out the processes mentioned below. POSTULATES". Let it be granted, 1. That a straight line may be drawn from any one point to any other point. When we draw a straight line from the point A to the point B, we are said to join AB. 2. That a finite,...

...elementary geometry. Of the postulates and axioms of Euclid six stand out as essentially geometrical. 1. That a straight line may be drawn from any one point to any other. 2. That a straight line may be prolonged to any length. 3. That a circle may be described about any...

...— THK THEORY or INVERSION — PE.UTELLIER'S EXACT MECHANISM. three postulates are: "I. A Ly right line may be drawn from any one point to any other point." "II. A terminated right line may he produced to any length in a right line." " III. A circle may be...

...possible, — is cut off a part equal to the less. QED " Let it be granted " by "powers" "that a railway line may be drawn from any one point to any other point," and that " profite may be produced to any amount," and the results must be satisfactory. The Chairman...

...seen in its deformity and danger. Euclid says, under the heading " Postulates :" " I. It is assumed, that a straight line may be drawn from any one point to any other point. "II. And that a terminated straight line [a sect] may be produced in a straight line continually. "...

...on a plane surface are expressed in the following construction postulates : Let it be granted: 1. ' That a straight line may be drawn from any one point to any other. 2. That a terminated straight line may be prolonged indefinitely. 3. That a circle may be described...

...is a four-sided figure which has its opposite sides parallel. THE POSTULATES. Let it be granted, 1. That a straight line may be drawn from any one point to any other point. 2. That a finite, tltat is to say a terminated, straight line may be produced to any length in that...