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" The enunciation of a Theorem consists of two parts, — the hypothesis, or that which is assumed, and the conclusion, or that which is asserted to follow therefrom. Thus in the typical Theorem, If A is B, then C is D, (i), the hypothesis is that A is... "
SYLLABUS OF PLANE GEOMETRY - Side 4
1876
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Elementary geometry

James Maurice Wilson - 1878
...Axioms. The two next pages, within brackets, may be omitted the first time of reading the subject. [A Theorem consists of two parts, the hypothesis,...hypothesis is that A is B, and the conclusion, that Cis D. From the truth conveyed in this Theorem it necessarily follows : If C is not D, then A is not...
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Mathematical Questions and Solutions, from the "Educational Times ..., Volum 29

W. J. C. Miller - 1878
...In the Syllabus of the Association for the Improvement of Geometrical Teaching (p. 4) we read : — "In the typical Theorem, If A is B, then C is D (i.);...conveyed in this Theorem it necessarily follows : If С is not D, then A is not B (ii.) Two such Theorems as (i.) and (n.) are said to be eontrapo3itive,...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - 1884
...propositions. These known propositions may themselves be Theorems or Axioms. 4. The enunciation of a Theorem consists of two parts, — the hypothesis,...that A is B, and the conclusion, that C is D. From this Theorem it necessarily follows that : If C is not D, then A is not B, (ii). Two such Theorems...
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The elements of plane geometry, Volum 1

Mathematical association - 1884
...propositions. These known propositions may themselves be Theorems or Axioms. 4. The enunciation of a Theorem consists of two parts, — the hypothesis,...that A is B, and the conclusion, that C is D. From this Theorem it necessarily follows that : If C is not D, then A is not B, (ii). Two such Theorems...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 312 sider
...may be demonstrated from known propositions. These propositions may themselves be theorems or axioms. A theorem consists of two parts, the hypothesis, or...follow therefrom. Thus, in the typical theorem, If X is Y, then Z is "W, (i.) the hypothesis is that X is Y, and the conclusion is that Z is W. Converse...
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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885
...may he demonstrated from known propositions. These propositions may themselves be theorems or axioms. A theorem consists of two parts, the hypothesis, or...follow therefrom. Thus, in the typical theorem, If X is T, then Z is W, (i.) the hypothesis is that X is Y, and the conclusion is that Z is W. Converse...
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THE ELEMENTS OF GEOMETRY.

GEORGE BRUCE HALSTED - 1885
...once from that of the theorem, or from what has been given in the demonstration of the theorem. 27. A theorem consists of two parts, — the hypothesis,...conclusion, or that which is asserted to follow therefrom. 28. A geometric theorem usually relates to some figure, and says that a figure which has a certain...
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The Elements of Geometry

George Bruce Halsted - 1886 - 366 sider
...once from that of the theorem, or from what has been given in the demonstration of the theorem. 27. A theorem consists of two parts, — the hypothesis,...conclusion, or that which is asserted to follow therefrom. 28. A geometric theorem usually relates to some figure, and says that a figure which has a certain...
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - 1890 - 393 sider
...as may be required to prove the truth of a theorem, or to solve a problem. 42» The enunciation of a theorem consists of two parts : the hypothesis,...Thus, in the typical theorem, If A is B, then C is D, the hypothesis is that A is B, and the conclusion that C is D. " 43. The enunciation of a problem consists...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 sider
...that is, AB is equal to AC. COROLLARY.— Hence every equiangular triangle is also equilateral. NOTE. A theorem consists of two parts, the hypothesis, or...conclusion, or that which is asserted to follow therefrom. Two theorems are said to be converse, each of the other, when the hypothesis of each is the conclusion...
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