 | University of Oxford - Education, Higher - 1863 - 316 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 - 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,... | |
 | Robert Potts - 1865 - 528 pages
...AB ; therefore AC is greater than AB. Wherefore the greater angle, &c. QED PROPOSITION XX. THEOREM. Any two sides of a triangle are together greater than the third side. Let ABC be a triangle. Then any two sides of it together shall be greater than the third side, viz. the sides BA, AC greater... | |
 | Queensland. Department of Public Instruction - Education - 1866 - 336 pages
...extremity. Construct the figure for the third case, and shew why it " needs no demonstration." 3. Prove that any two sides of a triangle are together greater than the third side. Show from this proposition that the difference of any two sides of a triangle is less than the third... | |
 | Euclides - 1865 - 80 pages
...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.... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
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Any two sides of a triangle are together greater than the third side. 
