| Euclides - 1852
...may be 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...section, is equal to the square of half the line.** Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts... | |
| Benjamin Greenleaf - 1852 - 336 sider
...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
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOREM. If **a straight 'line be divided into two equal parts,...section, is equal to the square of half the line.** Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts... | |
| Euclides - 1853 - 147 sider
...parallelograms about the diameter of a square are likewise squares. PROPOSITION V. — THEOREM. If **a straight line be divided into two equal parts, and...points of section, is equal to the square of half the** Une. LET the straight line ab be divided into two equal parts in the point С, and into two unequal... | |
| Euclid, John Playfair - 1853 - 317 sider
...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;...section, is equal to the square of half the line.** Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts... | |
| Royal Military Academy, Woolwich - 1853
...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,...section, is equal to the square of half the line.** Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts... | |
| Euclides - 1853
...proved. PEOP. V. THEOE. If a straight line be bisected, and also divided into two unequal parts : then **the rectangle contained by the unequal parts together with the square of the** part of the line intercepted between the points of section, shall be equal to the square of half the... | |
| William Somerville Orr - 1854
...л straight line (AB) be divided into two equal parts (inC), and also info two 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... | |
| John Playfair - 1855 - 318 sider
...T) B PROP. V. THEOR. If a straight linele divided into two equal parts, andalsointo twounequalparts; **the rectangle contained by the unequal parts, together...section, is equal to the square of half the line.** Let the straight line AB be divided into two equal parts in the- point C, and into two unequal parts... | |
| Euclides - 1855
...into turn equal parts, and also into two unequal part'; the rectangle contained by the unequal parta, **together with the square of the line between the points of section** (or division), is equal to the square of half the line. Let the straight line AB be divided into two... | |
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