| Charles Hutton - 1822
...be proved, or something required to be done ; and is accordingly either a Theorem or a Problem. 6. A **Theorem is a demonstrative proposition ; in which...collection of such Theorems constitutes a Theory.** I. A Problem is a proposition or a question requiring •something to be done ; either to investigate... | |
| John Playfair - 1835 - 316 sider
...; 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
...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
...; 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
...demonstrated, or something required to be done, and is accordingly either a theorem or a problem. A **theorem is a demonstrative proposition, in which some...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 - 346 sider
...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 - 346 sider
...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... | |
| John Playfair - 1846 - 317 sider
...; 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... | |
| |