 | Euclid, Thomas Tate - 1849 - 120 pages
...BC added together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. THEOR. If a straight line be divided into two equal, and also...square of the line between the points of section. From the point c draw (i. 11.) CE at right angles to AB, and jnake it equal to AC or CB, and join EA,... | |
 | 1852 - 314 pages
...equal to the squares of the two parts, together with twice the rectangle contained by the paits. 2. If a straight line be divided into two equal and also...square of the line between the points of section. 3. If from any point without a circle two straight lines be drawn, one of which cuts the circle and... | |
 | 1867 - 336 pages
...up of the whole and that part. Prove this also algebraically. SECTION VI. 1. If a str tight line he divided into two equal, and also into two unequal...square of the line between the points of section. , Illustrate this by Algebra. 2. Divide a given straight line into two parts, so that, the rectangle... | |
 | 1851
...straight line be d ividedinto two equal and 20 7 also into two unequal parts, the squares of the imequal parts are, together, double of the square of half the line, and of the square of the intermediate part, . 4. Explain what is meant by the term multiplica— 17 7 tion, when the factors... | |
 | Euclides - 1852 - 152 pages
...is, of AB and BC added together in one straight line. H X G T / K / / R BOOK II. PROP. IX. THEOR. If a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts: the squares of AD, DB are together... | |
 | Euclides - 1853 - 176 pages
...together in one straight line. Wherefore, if a straight Une, &c. QED PROPOSITION IX. — THEOREM. If a straight line be divided into two equal, and also...points of section. LET the straight line ab be divided at the point С into two equal, and at d into two unequal parts : the squares of ad, db are together... | |
 | Euclides - 1853 - 146 pages
...BC added together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. THEOREM. If a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts; the squares of AD, DB, are together... | |
 | Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...added together in one straight line. Wherefore, if a straight line, etc. QED PROPOSITION IX. THEOR. If a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts ; the squares of AD, DB are together... | |
 | Euclid, John Playfair - Geometry - 1853 - 317 pages
...and adding c2 to each member of this equality, we shall have, or 4a4+c2=(cf-24)2. PROP. IX. THEOR. If a straight line be divided into two equal, and also...two unequal parts are together double of the square ofhalj the line, and of the square of the line between the points of section. Let the straight line... | |
 | Euclides - Geometry - 1853 - 334 pages
...parts : then the squares of the two unequal parts shall be double of the square of half the line, and the square of the line between the points of section. Let the straight line AB be bisected in c and divided into two unequal parts AD, DB in D. Then the squares of AD, DB shall be double... | |
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IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. 
