| American Association for the Advancement of Science - 1904
...Theory of Functions. Moreover, underneath all this even is the assumption of the theorem, Euclid I, 20: **"Any two sides of a triangle are together greater than the third** side;" upon which proposition, which the Sophists said even donkeys knew, Hubert has thrown brilliant... | |
| George Bruce Halsted - 1904 - 285 páginas
...than the perpendicular. Proof. Since 4 CAB is r't, .'. (by 79) 4&> 4B. :. (by 171) a> b. 174. Theorem. **Any two sides of a triangle are together greater than the third** side, Proof. On st' BC, beyond C, take CD = P1G- 73But AC is within 4 DAB, :. 4DAB> 4DAC = 4D. :. (by1j1)... | |
| American Association for the Advancement of Science - 1904
...Theory of Functions. Moreover, underneath all this even is the assumption of the theorem, Euclid I, 20: **"Any two sides of a triangle are together greater than the third** side;" upon which proposition, which the Sophists said even donkeys knew, Hubert has thrown brilliant... | |
| Hugh MacColl - 1906 - 141 páginas
...mathematical demonstrations are on lines not very dissimilar. A striking instance is Euclid's demonstration of **the proposition that any two sides of a triangle are together greater than the third** — a proposition which the Epicureans derided as patent even to asses, who always took the shortest... | |
| 1906
...contain 5, 7, and 9 units, make the construction in a carefully drawn diagram. It is proved in Geometry **that any two sides of a triangle are together greater than the third** side ; what is the corresponding property of three forces in equilibrium at a point ? The actual arrangement... | |
| Ernst Mach - 1906 - 144 páginas
...shown in Loeb's investigations on the tropisms of animals. Further, visualization alone does not prove **that any two sides of a triangle are together greater than the third** side. It is true that if the two sides be laid upon the base by rotation round the vertices of the... | |
| University of Sydney - 1906
...any formula for the roots of a quadratic. GEOMETRY. TWO HOURS AND A HALF. PAPER A. — (Eucm>.) 1. **Any two sides of a triangle are together greater than the third.** 2. If two triangles have two angles of the one equal to two angles of the other respectively and one... | |
| Herbert Spencer - 1906
...it falls within or without some other; and the like. Let us take as an example the proposition — " **Any two sides of a triangle are together greater than the third** side." " Let ABC be a triangle; any two sides of it are, together, greater than the third side; namely,... | |
| William Henry Maxwell - 1907 - 317 páginas
...is put in the present tense even when the principal verb is in a past tense ; as, It was as true as **that any two sides of a triangle are together greater than the third** side. 2. When an infinitive or a participle refers to a time coincident with, or after, that of the... | |
| David Mair - 1907 - 379 páginas
...justify your rule. The rule is important enough to be called a proposition, and may be stated thus: — **Any two sides of a triangle are together greater than the third.** 5. Points of the Compass. The terms north and east have been used. How do you know which direction... | |
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