 | 1854 - 1112 σελίδες
...product. Geometry furnishes us with a parallel to both these cases ; for, as Euclid tells us (II., 4), if a straight line be divided into any two parts,...equal to the squares of the two parts, together with twice the rectangle contained by the parts ; and, were we to represent the line as a divided into two... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...CB, together with the square of BC. If therefore a straight line, &c. QED Proposition IV. Theorem. ', If a straight line be divided into any two parts, the square or in* ELEMENTS OP KUCUD. 191 vhole line is equal to the squares of the two parts, together with twice... | |
 | Euclid - 1826 - 234 σελίδες
...and it be ag =fg + g2. Q- ED PROPOSITION IV. THEOREM. If a right line be divided into any two part:!, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained under the parts. Let the right line AB be divided into any two parts... | |
 | Jeremiah Day - 1827 - 352 σελίδες
...than 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... | |
 | Robert Simson - 1827 - 546 σελίδες
...two straight lines, &c. QE v. •11. 1. •3. 1. • 31, 1. • 31. 1. t Cons1r. • 34. 1. PROP. II. THEOR. If a straight line be divided into any two parts, the rectangles contained by the whole and each of the parts, are together equal to the square of the whole... | |
 | John Playfair - 1829 - 210 σελίδες
...-\- b. Multiply this equation by d, then sb = ab + 66, which is the prop. PROPOSITION IV. THEOREM. If a straight line be divided into any two parts, the square cf the whole line is equal to the squares of the two parts together with twice the rectangle contained... | |
 | 1833 - 412 σελίδες
...equal to the rectangle contained by the two parts together with the square of the aforesaid part. 5. If a straight line be divided into any two parts,...equal to the squares of the two parts together, with twice the rectangle contained by the parts. a. Find the value of x in x1 — a x-\-b*^0. b. Divide... | |
 | Euclides - 1834 - 518 σελίδες
...rectangle AC, CB, together with the square of BC. If, therefore, a straight line, &c. o. ED PROPOSITION IV. THEOR. — If a straight line be divided into...equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts... | |
 | Euclid - 1835 - 540 σελίδες
...the square of CB, is equal to the square of CD. Wherefore, " if a straigtd line" &c. QED PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the... | |
 | 1836 - 488 σελίδες
...equal to the rectangle contained by the two parts, together with the square of the foresaid part. IV. If a straight line be divided into any two parts,...equal to the squares of the two parts, together with twice the rectangle contained by the parts. Сок. From the demonstration, it is manifest that the... | |
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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. 
