 | Great Britain. Admiralty - 1846 - 128 σελίδες
...b, the proposition algebraically expressed is (a+b)*—a*-\-2ab + b*. PROP. XLIV. THEOR. 5 . 2 EU. If a straight line be divided into two equal parts,...points of section, is equal to the square of half the whole line. Let the str. line AB be divided into two equal parts at the pt. C, and into two unequal... | |
 | Perry Fairfax Nursey - 1846 - 536 σελίδες
...dependent on the 5th Proposition of the 2nd Book of Euclid's Elements, where it is demonstrated, that if a line be divided into two equal parts, and also into two unequal parts, the square of half the line is greater than the rectangle of the two unequal parts. Almost the whole of... | |
 | 1846 - 544 σελίδες
...dependent on the 5th Proposition of the 2nd Book of Euclid's Elements, where it is demonstrated, that if a line be divided into two equal parts, and also into two unequal parts, the square of half the line is greater than the rectangle of the two unequal parts. Almost the whole of... | |
 | Frederic A. Adams - 1846 - 230 σελίδες
...what are the numbers ? The theorem on which the solution of this question depends is this, If a number be divided into two equal parts, and also into two unequal parts, the product of the two equal parts, that is, the square of half the number, will equal the product of the... | |
 | J. Goodall, W. Hammond - 1848 - 390 σελίδες
...angle is equal to the squares described upon the sides containing the right angle. SECTION III. 1. If a straight line be divided into two equal parts,...of section is equal to the square of half the line. 2. In any triangle the square of the side subtending contained by either of these sides, and the straight... | |
 | Euclides - 1848 - 52 σελίδες
...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. EUCLID S ELEMENTS. PROP. VI. THEOREM. If a straight line be bisected, and produced to any point ; the... | |
 | Great Britain. Committee on Education - 1848 - 514 σελίδες
...right angle is equal to the square described upon the sides containing the right angle. Section 3. 1. If a straight line be divided into two equal parts,...line between the points of section is equal to the squares of half the line. 2. In any triangle the square of the side subtending any acute angle is less... | |
 | Great Britain. Council on Education - 1848 - 532 σελίδες
...right angle is equal to the square described upon the sides containing the right angle. Section 3. 1. If a straight line be divided into two equal parts,...line between the points of section is equal to the squares of half the line. 2. In any triangle the square of the side subtending any acute angle is less... | |
 | 1848 - 542 σελίδες
...Tate's Geometry," &c. page 39, where a new proof is given of this important theorem. SECTION 3. 1. If a straight line be divided into two equal parts,...parts, the rectangle contained by the unequal parts, togelher with the square of the line between the points of section, is equal to the square of half... | |
 | 1850 - 400 σελίδες
...produced, the exterior angle is greater than either of the interior opposite angles. 2. If a right line be divided into two equal parts, and also into...section, is equal to the square of half the line. 3. In every triangle, the square of the side subtending either of the acute angles, is less than 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. 
