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" Let it be granted that a straight line may be drawn from any one point to any other point. "
The first six books of the Elements of Euclid, with numerous exercises - Seite 4
von Euclides - 1853 - 147 Seiten
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The Philosophy of Necessity: Or, Law in Mind as in Matter

Charles Bray - 1889 - 407 Seiten
...point is that which hath no parts, or which hath no magnitude." " A line is length without breadth." " Let it be granted that a straight line may be drawn from any one point to any other point," that is, from that which has no parts and no magnitude, to that which has no parts and no magnitude...
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First and Fundamental Truths: Being a Treatise on Metaphysics

James McCosh - 1889 - 360 Seiten
...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...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 400 Seiten
...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...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 Seiten
...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...
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The Elements of Plane and Solid Geometry: With Numerous Exercises

Edward Albert Bowser - 1890 - 393 Seiten
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 Seiten
...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,...
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Journal of the Michigan Schoolmasters' Club, Band 22;Bände 31-40

Michigan Schoolmasters' Club - 1894
...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...
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Containing book II. Positive science

Shadworth Hollway Hodgson - 1898
...and also, by means of the plane, of parallel straight lines, in which use is made of the postulate " that a terminated straight line may be produced to any length in a straight line," that is, of the conception of infinity. The idea, that the direction of a straight line is not altered...
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Science and Industry: 1898-99, Band 3

1899
...— 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 described...
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Punch, Bände 116-117

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