| Charles Hutton - 1816
...Definitions, Axioms, Propositions, Theorems, Problems, Lemmas, Corollaries, Scholiums, &c. 4. . / Dijinition **is the explication of any term or word in a science...The sum of the three angles of any triangle is equal** lo two right angles, this is a Theorem, the truth of which is demonstrated by Geometry. —A set or... | |
| Charles Hutton - 1818
...Definition ought to be clear, and expressed in words that are common and perfectly well understood. 6. **A Proposition is something proposed to be proved,...of which is demonstrated by Geometry. — A set or** collector! of such Theorems constitutes a Theory. 7. A. Problem is a proposition or a question requiring... | |
| Charles Hutton - 1822
...Definition ought to be clear, and expressed in words that are common and perfectly well understood. 6. **A Proposition is something proposed to be proved,...collection of such Theorems constitutes a Theory.** I. A Problem is a proposition or a question requiring •something to be done ; either to investigate... | |
| Charles Hutton - 1831
...are common and perfectly well understood. 5. A Proposition is something proposed to be demonstrated, **or something required to be done ; and is accordingly...when it is said that, The sum of the three angles of** a plane triangle is equal to two right angles, that is a Theorem, the truth of which is demonstrated... | |
| John Playfair - 1835 - 316 sider
...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
...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 - 318 sider
...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 - 159 sider
...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 - 317 sider
...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 - 352 sider
...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.... | |
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