 | Harvey Goodwin - 1851 - 196 σελίδες
...divided into 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,...section, is equal to the square of half the line. 4. Equal straight lines in a circle are equally distant from the centre ; and conversely, those which... | |
 | 1851 - 502 σελίδες
...a given rectilineal angle. upon the same side together equal to two right angles. SECTION II.—1. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. 3. The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two... | |
 | Benjamin Greenleaf - 1852 - 348 σελίδες
...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 σελίδες
...the parallelograms about the diameter of a square are likewise squares. PROPOSITION V. — THEOREM. If a straight line be divided into two equal parts,...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... | |
 | Euclides - 1853 - 334 σελίδες
...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 - 534 σελίδες
...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... | |
 | Euclides - 1855 - 270 σελίδες
...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... | |
 | Cambridge univ, exam. papers - 1856 - 252 σελίδες
...triangle, and have 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,...section, is equal to the square of half the line. Prove this proposition algebraically. 6. Find the centre of a given circle. Shew that if in a circle... | |
 | Euclides - 1856 - 168 σελίδες
...of a square are likewise squares. L. — EUCLID II. 5. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained...square of half the line. Let the straight line AB (Fig. 40) be divided into two equal parts at the point C, and into two unequal parts at the point D;... | |
 | Cambridge univ, exam. papers - 1856 - 200 σελίδες
...times that on one of the sides; compare the two sides. 4. If a straight line be divided into two equal and also into two unequal parts; the rectangle contained...of section is equal to the square of half the line. State this result algebraically. 5. Draw a straight line from a given point, either without or in the... | |
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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. 
