...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. "III. And that a circle may be described with any center and radius." From these Euclid rigidly deduces...

...of which is self-evident. EXAMPLES OF POSTULATES. Let it be granted — I. That a straight line can be drawn from any one point to any other point; II. That a straight line can be produced to any distance, 01 terminated at any point; III. That the circumference...

...problem, the solution of which is self-evident. • Let it be granted — I. That a straight line can be drawn from any one point to any other point ; II. That a straight line can be produced to any distance, or terminated at any point ; III. That the circumference...

...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...

...a problem, the solution of which is self-evident. Let it be granted — I. That a straight line can be drawn from any one point to any other point ; II. That a straight line can be produced to any distance, or terminated at any point ; III. That the circumference...

...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...

...anti-Common-Sense principles ! 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) that a circle may be described from any centre at any distance from that centre, — we must...

...assume that with their help the processes mentioned below may be duly performed. Let it be granted : 1. That a straight line may be drawn from any one point to any other point. 2. That a FINITE (or terminated) straight line may be PRODUCED (that is, prolonged] to any length in...

...Engineers say to a man who should ask admittance to their society on auti-Common-Sense principles ! 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) that a...