| Euclides - 1863
...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.... | |
| University of Oxford - 1863
...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 - 1864
...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,... | |
| Euclides - 1864
...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 - 1865
...for the same reason, AB and BC are ~" u greater than AC, and AC and CB greater than AB; and therefore **any two sides of a triangle are together greater than the third side.** PROPOSITION IX. LEMMA. The circumferences of circles cannot cut one another in more than two points.... | |
| Hugh MacColl - 1906 - 141 sider
...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
...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 - 1907 - 317 sider
...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
...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... | |
| University of Calcutta - 1907
...of a triangle are unequal, the greater side has the greater angle opposite to it ; and the converse. **Any two sides of a triangle are together greater than the third.** Of all the straight tines that can be drawn to a given straight line from a given point outside it,... | |
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