 | Scotland free church, gen. assembly - 1847 - 554 pages
...equal bases, and between the same parallels, are equal. 4. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of each of the parts together with twice the rectangle contained by the parts. 5. Equal straight lines... | |
 | James Bates Thomson - Algebra - 1844 - 272 pages
...in ordinary language. The proposition, (Euc. 4>. 2,) that when a straight line is divided into two parts, the square of the whole line is equal to the...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square be represented... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...rectangle AC.CB.* If, therefore, &c. PROP. IV. THEOR. — If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice their rectangle, t Let the straight line AB be divided into any two parts in C ; the square of AB is... | |
 | Euclides - 1845 - 546 pages
...line is equal to four times the square of half the line. Also, if a line be divided into any three parts, the square of the whole line is equal to the squares of the three parts, and twice the rectangle contained by every two parts. Prop. iv. Algebraically, (fig. Prop,... | |
 | Euclid - Geometry - 1845 - 218 pages
...rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided into any two parts in the point C ; the rectangle contained by AB, BC, together with the rectangle1 AB, AC, shall be equal... | |
 | Euclides - 1846 - 272 pages
...under AC and CF. PROPOSITION IV. THEOREM. If a right line (AB) be divided into any two parts, (in O) the square of the whole line is equal to the squares of the parts, together with twice the rectangle under the parts. On AB describe the square ACDB, and draw... | |
 | Euclides - 1846 - 292 pages
...equal to the rectangle contained by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into any two parts in the point C: the rectangle AB, BC shall be equal to the rectangle AC, CB, together with the square... | |
 | Jeremiah Day - Algebra - 1847 - 358 pages
...than in ordinary language. The proposition, (Euc. 4. 2.) that when a straight line is divided into two par.ts, the square of the whole line is equal to the...squares of the two parts, together with twice the product of the parts, is demonBtrated, by involving a binomial Let the side of a square be represented... | |
 | Great Britain. Committee on Education - Education - 1847 - 730 pages
...triangle. 3. A straight line being divided into two parts, prove the square of the whole line to be equal to the squares of the two parts, together with twice the rectangle contained by the parts. 4. Prove the angle in a semicircle to be a right angle. 16 10 Mr. Gordons Report on the mities 36°... | |
 | Great Britain. Committee on Education - School buildings - 1847 - 708 pages
...triangle. 3. A straight line being divided into two parts, prove the square of the whole line to he equal to the squares of the two parts, together with twice the rectangle contained by the parts. 4. Prove the angle in a semicircle to be a right angle. 518 mities 36° 20' and 60° Iff ; required... | |
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If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. 
