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 41876Uten tilgangsbegrensning - Om denne boken
| 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... | |
| 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,... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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