 | John Playfair - Euclid's Elements - 1842 - 332 pages
...which this line is divided be denoted by a and b; then, (a-\-b)2 PROP. V. THEOR. If a straight line lie divided into two equal parts, and also into two unequal...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... | |
 | Education - 1844 - 688 pages
...the same base, and between the same parallels, the parallelogram shall be double of the triangle. 6. If a straight line be divided into two equal 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. 7. In obtuse angled-triangles,... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...being bisected, the rectangle of the parts is equal to the square of one of them. PROP. V. THEOR. — If a straight line be divided into two equal 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... | |
 | Scottish school-book assoc - 1845 - 444 pages
...be bisected in C, and divided unequally in D, 1 the rectangle AD-DB. together with the square on CD, the line between the points of section is equal to the square on (AC or CB) half the line. For AB2=AD-' + DB-+2AD-DB, (Prop. 37), but AB"=4AC2, (Prop. 37, Cor. 2),... | |
 | Euclides - 1845 - 546 pages
...that the 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 Iwo unequal parts ; the rectangle contained by the unequal parts, together with the square of the line... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...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,...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 whole line. Let the str.... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...be a and b, the proposition algebraically expressed is (a+by=a8+2ab+b8. PROP. XLIV. THEOR. 5. 2 Eu. If a straight line be divided into two equal 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 whole line. Let the str.... | |
 | Euclides - 1846 - 292 pages
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight Kne be divided into two equal parts, and also into two...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... | |
 | Perry Fairfax Nursey - Industrial arts - 1846 - 536 pages
...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... | |
 | Industrial arts - 1846 - 544 pages
...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... | |
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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. 
