 | Education - 1844 - 688 pages
...and between the same parallels, the parallelogram shall be double of the triangle. 6. If a straight line be divided into two equal parts, and also into...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 - 380 pages
...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, and also into...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... | |
 | Euclides - 1845 - 544 pages
...= a2 — ma, to each of these equals add m* ; .-. (a + m) (a — m) + m' = a'. That is, if a number be divided into two equal parts, and also into two unequal parts, the product of the unequal parts and the square of half their difference, is equal to the square of half... | |
 | 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
...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, and also into...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 - 130 pages
...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, and also into...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... | |
 | Industrial arts - 1846 - 546 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... | |
 | 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... | |
 | Frederic A. Adams - Arithmetic - 1846 - 230 pages
...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... | |
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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. 
