| P. McGregor - Logic - 1862 - 498 pages
...might do so. 41. A straight line is the shortest that can be drawn from one point to another. Hence **any two sides of a triangle are together greater than the third.** 42. Straight lines which intersect or cut one another, lie in different directions, and diverge indefinitely,... | |
| Church and social problems - 1885 - 676 pages
...nearer the reality of things, when, through the education of my intuition of space, I perceive that **any two sides of a triangle are together greater than the third,** than the brute is, who by blind impulse makes straight for his prey — so long as I believe, in the... | |
| University of Oxford - Education, Higher - 1863 - 328 pages
...the rectangle contained by the whole and that part, together with the square on the other part. 6. **Any two sides of a triangle are together greater than the third side.** 7. If two triangles have two sides of the one equal to two sides of the other, each to each, but the... | |
| Euclides - 1863 - 72 pages
...there are more than three species of quantity, — a Lini a Surface, and a Solid. PKOP. 20. — THEOK. **Any two sides of a triangle are together greater than the third side.** Cos.— Pst. 2, P. 3, Pst. 1.— DEM.— P. 8, Ax. 9, P. 19. E. C. Hyp. Cone. 1. „ 2. „ 3. by Pst.... | |
| Euclides - 1864 - 448 pages
...pass through the point A, let it fall otherwise, if possible, as FGDH, and join AF, AG. Then, because **two sides of a triangle are together greater than the third side,** (i. 20.) therefore FG, GA are greater than FA : but FA is equal to FH; (I. def. 15.) therefore FG,... | |
| Euclides - 1864 - 262 pages
...AB ; therefore AC is greater than A B. Wherefore the greater angle, &c. QED PROPOSITION XX. THEOREM. **Any two sides of a triangle are together greater than the third** lidt. Let ABC be a triangle. Then any two sides of it together shall be greater than the third side,... | |
| Hugh MacColl - Logic, Symbolic and mathematical - 1906 - 168 pages
...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... | |
| University of Sydney - 1906 - 738 pages
...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... | |
| William Henry Maxwell - English language - 1907 - 328 pages
...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 verb... | |
| 1907 - 608 pages
...sides and angles of a parallelogram are equal to one another ; and (2) the diagonal bisects it. 4. **Any two sides of a triangle are together greater than the third side.** SECTION B. 5. The base of an isosceles triangle is 54 feet, and each side is 45 feet. Find the length... | |
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