| Charles Hutton - Mathematics - 1811
...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 - Mathematics - 1822 - 618 pages
...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 - Euclid's Elements - 1835 - 316 pages
...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 - Education - 1835 - 318 pages
...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 - Geometry - 1837 - 332 pages
...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 - Geometry - 1837 - 216 pages
...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 - Euclid's Elements - 1842 - 332 pages
...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 - Astronomy - 1844 - 370 pages
...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 - Algebra - 1846 - 346 pages
...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 - Algebra - 1846 - 380 pages
...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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