 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.  Elements of Plane Geometry - Page 64by Thomas Hunter - 1878 - 132 pagesFull view - About this book
 | Euclides - Euclid's Elements - 1837 - 112 pages
...and that these are = AC x CB + CB*. PROPOSITION IV. Theorem. 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. * By the rectangle... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...with the 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... | |
 | Charles Reiner - Geometry - 1837 - 246 pages
...M.- — Express this truth as a general proposition. P. — 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. The master will,... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...CB, together with the square of BC. PROPOSITION TV. THEOREM. 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. Let the straight... | |
 | Euclides - 1840 - 194 pages
...the divided line. PROP. II. THEOR. If a straight line (AB) be divided into any two parts (AF, FB), the square of the whole line is equal to the sum of...rectangles contained by the whole line and each of its parts. On AB describe the square ACDB a Prop. 46), and from F draw FE parallel to AC or BD. Then... | |
 | Euclides - 1840 - 82 pages
...together with the rectangle under the parts. 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 parts, together with twice the rectangle contained by the parts. COR.—Thus it appears... | |
 | John M'Nevin - Arithmetic - 1841 - 300 pages
...and 2 over. Hence, from the properties of Euclid. 4, Lib. 2. "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." Thus, let AB be... | |
 | John M'Nevin - Arithmetic - 1841 - 300 pages
...and 2 over. Hence, from the properties of Euclid. 4, Lib. 2. "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." Thus, let AB be... | |
 | Euclides - Geometry - 1841 - 378 pages
...square of BC. If therefore a straight, &c. QED 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 the rectangle contained by the parts. Let the straight... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...members of this equality by c, we shall have ac= 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 the rectangle contained by the parts. Let the straight... | |
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