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" LET it be granted that a straight line may be drawn from any one point to any other point. "
The elements of plane geometry; or, The first six books of Euclid, ed. by W ... - Σελίδα 5
των Euclides - 1863
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First and Fundamental Truths: Being a Treatise on Metaphysics

James McCosh - 1889 - 390 σελίδες
...definitions and in the propositions founded on them, such as the following, put in the form of maxims : "A straight line may be drawn from any one point to any other point ; " "A straight line may be produced to any length in a straight line ; " " There may be such a figure...

Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 442 σελίδες
...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...

The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - 420 σελίδες
...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...

The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 σελίδες
...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...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 460 σελίδες
...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,...

Journal of the Michigan Schoolmasters' Club, Τόμος 22;Τόμοι 31-40

Michigan Schoolmasters' Club - 1894 - 556 σελίδες
...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...

Punch, Τόμοι 116-117

Henry Mayhew, Mark Lemon, Tom Taylor, Shirley Brooks, Francis Cowley Burnand, Owen Seaman - 1899 - 808 σελίδες
...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...

Science and Industry: 1898-99, Τόμος 3

1899 - 676 σελίδες
...— 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...

Popular Astronomy, Τόμος 8;Τόμος 1900

1900 - 632 σελίδες
...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. "...

Elementary Geometry: Plane

James McMahon - 1903 - 380 σελίδες
...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...




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