 | Charles Hutton - 1816 - 610 ページ
...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,...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 - 1831 - 660 ページ
...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... | |
 | Charles Hutton - 1831 - 632 ページ
...something proposed to be demonstrated, or something required to be done ; and is accordingly cither a Theorem or 'a Problem. 6. A Theorem is a demonstrative...required to be proved. Thus, when it is said that, The sun of the three angles of a plane triangle is equal to two right angles, that is a Theorem, the truth... | |
 | John Playfair - 1835 - 336 ページ
...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 ページ
...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 ページ
...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 ページ
...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 ページ
...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 ページ
...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.... | |
 | Euclid, John Playfair - 1846 - 334 ページ
...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... | |
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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. 
