| 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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