| Euclid, James Thomson - 1845 - 352 sider
...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, and...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, together... | |
| Euclides - 1845
...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
...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 - 1846
...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, and...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... | |
| Great Britain. Admiralty - 1846
...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, and...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... | |
| Euclides - 1846
...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...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 parts... | |
| John Playfair - 1846 - 317 sider
...PROP. V. THEOR. If a straight line le dividedinto two equal parts, and also into two unequalparts ; **the rectangle contained by the unequal parts, together...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 parts... | |
| 1846
...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 - 1846
...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 - 212 sider
...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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