 | Mathematics - 1836 - 488 pages
...contained by the whole and each of the parts, are together equal to the square of the whole line. III. If a straight line be divided into any two parts,...parts, together with the square of the foresaid part. IV. If a straight line be divided into any two parts, the square of the whole line is equal to the... | |
 | John Playfair - Euclid's Elements - 1836 - 488 pages
...and AE = AB2. Therefore AB.AC + AB.BC = AB2. Therefore, if a straight line, &c. QED PROP. III. THEOR. If a straight line be divided into any two parts,...contained by the two parts, together with the square ofthefbresaid part. Let the straight line AB be divided into two parts in the point C ; the rectangle... | |
 | John Playfair - Euclid's Elements - 1837 - 332 pages
...both members of this equality by a, we shall have azs=ab+ad FE, 6 • F K J. H A PROP. III. THEOR. If a straight line be divided into any two parts,...'by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into two parts, in the point C ; the B E rectangle... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...showing that AB* = figures AF + CE ; and that these are = AB x AC + AB x BC. PROPOSITION III. Theorem. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. Proved by showing that AB x BC = figures AD + CE, and that these are = AC x CB + CB*.... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...equal to the square of A B. In a manner similar to this, several of the following propositions nay be IF a straight line be divided into any two parts,...by the whole and one of the parts, is equal to the square of that part, together with the rectangle contained by the two parts. Let the straight line... | |
 | Euclides - 1838 - 264 pages
...restriction of the number of parts to two is unnecessary. PROP. III. THEOR. If a straight line be dieided into any two parts, the rectangle contained by the...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... | |
 | Euclides - 1840 - 82 pages
...the sum of the rectangles contained by the whole line and each of its parts. ED f B PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by the whole line and either of its parts, is equal to the square of that part, together with the rectangle under... | |
 | Euclides - Geometry - 1841 - 378 pages
...rectangle AB, BC, is equal to the square of AB. If therefore a straight line, &c. QED PROP. III. THEOR. If a straight line be divided into any two parts,...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... | |
 | Euclides - 1842 - 316 pages
...rectangle AB, BC, is equal to the square of A B. If therefore a straight line, &c. QED PROP. III. THEOR. IF a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into two parts in the point c : the rectangle AB,... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...multiplying both members of this equality by a, we shall have a~=ab+ad FE J o $ DEC K JL B PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by tke whole and one of the parts, is equal to the rectangle contained by the two parts, together with... | |
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If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. 
