| 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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