 | Harvey Goodwin - Mathematics - 1851 - 196 pages
...four equal parts. In what case will the diameter bisect the angle of a parallelogram? 3. If a straight line be divided into two equal parts, and also into...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. 4. Equal straight... | |
 | Euclides - 1852 - 152 pages
...shown of any other division of 8, as into 6 and 2, or 7 and 1.] BOOK II. PROP. V. THEOR. If a straight line be divided into two equal parts, and also into...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. Let the straight... | |
 | Benjamin Greenleaf - Algebra - 1852 - 352 pages
...c=3. Then 12=9+3; And 4Xl2X9+3 2 =(3X2X9) 2 ; 441 = 441. THEOREM XIII. 17O. If any quantity or number be divided into two equal parts, and also into two unequal parts, the sum of the squares of the two unequal parts will be double the squares of half the quantity, plus twice... | |
 | Euclides - 1853 - 176 pages
...parallelograms about the diameter of a square are likewise squares. PROPOSITION V. — THEOREM. If a straight line be divided into two equal parts, and also into...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the Une. LET the straight... | |
 | Euclides - 1853 - 146 pages
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOREM. If a straight 'line be divided into two equal parts, and also into...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. Let the straight... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...diameter of a square are likewise squares. PROPOSITION V. THEOR. If a straight line be divided inio two equal parts, and also into two unequal parts,...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. Let the straight... | |
 | Euclid, John Playfair - Geometry - 1853 - 336 pages
...line is divided be denoted by a and b; then, (a+6)* PROP. V. THEOR. If a straight line bcdividedinto two equal parts, and also into two unequal parts;...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. Let the straight... | |
 | Euclid - Geometry - 1853 - 176 pages
...the segments, together with twice the rectangle under * each pair of segments. / The rectangle under the unequal parts, together with the square on the line between the points of section, is equal in area to tho square on half the line. .The sum of the squares on the unequal parts is equal in area... | |
 | William Somerville Orr - Science - 1854 - 532 pages
...unequal parts (in D), the rectangle contained by the unequal parts, together with the square of (CD), the line between the points of section, is equal to the square of hilf the line : that is, DB H « 46 I. "upon С В describe the square С F : » draw BE ; through... | |
 | Cambridge univ, exam. papers - 1856 - 252 pages
...one of its angles equal to a given rectilineal angle. Is this a determinate problem? 6. If a straight line be divided into two equal parts, and also into...contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. Prove this proposition... | |
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If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. 
