 | James Maurice Wilson - 1878 - 450 pages
...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... | |
 | W. J. C. Miller - Mathematics - 1878 - 120 pages
...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,... | |
 | Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...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... | |
 | Mathematical association - 1884 - 146 pages
...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... | |
 | Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...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... | |
 | Euclides - 1885 - 340 pages
...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... | |
 | George Bruce Halsted - Geometry - 1885 - 389 pages
...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... | |
 | George Bruce Halsted - Geometry - 1886 - 394 pages
...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... | |
 | Edward Albert Bowser - Geometry - 1890 - 418 pages
...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... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...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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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... 
