 | 1840 - 288 pages
...fancies about numbers. All even numbers (except the duad — two — which is simply two unities) may be divided into two equal parts, and also into two unequal parts But the ODD number is only divisible into uneven parts, &c. The Antients also remarked the monad to... | |
 | Euclides - 1841 - 378 pages
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight fine be divided into two equal parts, and also into two...points of 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... | |
 | 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...points of 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... | |
 | Euclides - 1842 - 320 pages
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts,...square of the line between the points of section, is equivalent to the square of half the line. Let the straight line AB be divided into two equal parts... | |
 | 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,...points of section, is equal to the square of half the line. 7. In obtuse angled-triangles, if a perpendicular be drawn from either of the acute angles to... | |
 | Euclid, James Thomson - Geometry - 1845 - 380 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,...points of section, is equal to the square of half the line. Let the straight line AB be bisected in C, and divided unequally in D : the rectangle AD.DB,... | |
 | Euclides - 1845 - 544 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... | |
 | Scottish school-book assoc - 1845 - 434 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),... | |
 | Great Britain. Admiralty - Geometry - 1846 - 130 pages
...of the divided line be a and b, the proposition algebraically expressed is (a+b)*—a*-\-2ab + b*. PROP. XLIV. THEOR. 5 . 2 EU. If a straight line be...into two unequal parts at the point D ; then AD . DB + CD 2 = CB 8 . On CB descr. sq. CEFB, Prop. 38. join BE; , (AK, DHG || CE or BP P '°P 30 " I KLHM... | |
 | 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...points of section, is equal to the square of half the line. Let the straight line ATI be divided into two equal parts at the point C, and into two unequal... | |
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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 of the line between the points of section, is equal to the square of half the line. 
