 | Euclid, James Thomson - 1845 - 382 σελίδες
...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 - 546 σελίδες
...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 - 444 σελίδες
...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 - 128 σελίδες
...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 - 128 σελίδες
...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 - 292 σελίδες
...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... | |
 | Euclid, John Playfair - 1846 - 334 σελίδες
...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 - 544 σελίδες
...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 - 536 σελίδες
...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 - 230 σελίδες
...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 of the line between the points of section, is equal to the square of half the line. 
