| 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 - 382 pages
...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 - 336 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... | |
| |