 | Charles Hutton - 1811 - 406 σελίδες
...Definition ought to be clear, and expressed in words that are common and perfectly well understood. 5. A Proposition is something proposed to be proved,...of which is demonstrated by Geometry. —A set or collection of such Theorems constitutes a Theory. 7. A Problem is a proposition or a question requiring... | |
 | Charles Hutton - 1822 - 616 σελίδες
...and real use concerning physical objects. 3. In Mathematics are several general terms of principles j such as Definitions, Axioms, Propositions, Theorems,...of which is demonstrated by Geometry. — A set or collection of such Theorems constitutes a Theory. I. A Problem is a proposition or a question requiring... | |
 | John Playfair - 1835 - 336 σελίδες
...together ; or, two quantities that are each of them equal to a third quantity, are equal to each other. 5. A Theorem is a demonstrative proposition ; in which...it is said that the sum of the three angles of any plane triangle is equal to two right angles, this is called a Theorem ; and the method of collecting... | |
 | American Institute of Instruction - 1835 - 318 σελίδες
...his work, this author has pursued a different method in regard to parallel lines, by first proving that the sum of the three angles of any triangle is equal to two right angles ; but the demonstration is tedious and difficult for beginners, and is therefore rarely understood.... | |
 | John Playfair - 1837 - 332 σελίδες
...or, two quantities that are each of them equal to a third quantity, are equal to each other. ,. if 5. A Theorem is a demonstrative proposition ; in which...it is said that the sum of the three angles of any plane triangle is equal to two right angles, this is called.a Theorem ; and the method of collecting... | |
 | Benjamin Peirce - 1837 - 216 σελίδες
...perpendicular to its base, divides it, by art. 57, into the two equal triangles ABC and ABG. 64. Theorem. The sum of the three angles of any triangle is equal to two right angles. Demonstration. Let ABC (fig. 36) be the given triangle. Produce AC to D, and draw CE parallel to AB.... | |
 | John Playfair - 1842 - 332 σελίδες
...together ; or, two quantities that are each of them equal to a third quantity, are equal to each other. 5. A Theorem is a demonstrative proposition ; in which...it is said that the sum of the three angles of any plane triangle is equal to two right angles, this is called a Theorem; and the method of collecting... | |
 | Samuel Griswold Goodrich - 1844 - 370 σελίδες
...be demonstrated, or something required to be done, and is accordingly either a theorem or a problem. A theorem is a demonstrative proposition, in which...when it is said that the sum of the three angles of a triangle is equal to two right angles, that is a theorem, the truth of which is demonstrated by geometry.... | |
 | Elias Loomis - 1846 - 380 σελίδες
...there are many other bipeds. (7.) A theorem is the statement of some property, the truth of which is required to be proved. Thus when it is said that the...theorem, the truth of which is demonstrated by Geometry. (8.) A. problem is a question requiring something to be done. Thus, to draw one line perpendicular... | |
 | Elias Loomis - 1846 - 376 σελίδες
...there are many other bipeds. (7.) A theorem is the statement of some property, the truth of which is required to be proved. Thus when it is said that the...theorem, the truth of which is demonstrated by Geometry. (8.) A problem is a question requiring something to be done. Thus, to draw one line perpendicular to... | |
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The sum of the three angles of any triangle is equal to two right angles, this is a . Theorem, the truth of which is demonstrated by Geometry. 
