| 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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