 | Euclides - 1848 - 52 pages
...to the square of the straight line, which is made up of the whole and that part. PROP. IX. THEOREM. If a straight line be divided into two equal, and...square of the line between the points of section. PROP. X. THEOREM. If a straight line be bisected, and produced to any point, the square of the whole... | |
 | J. Goodall, W. Hammond - 1848 - 390 pages
...the square of the aforesaid part. 2. Prove that if a straight line be divided into two equal and also two unequal parts, the squares of the two unequal...square of the line between the points of section. 3. Prove that in obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...and 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...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 - 316 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
...that 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...between the 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... | |
 | Euclides - 1853 - 146 pages
...and 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...between the 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... | |
 | Euclides - Geometry - 1853 - 176 pages
...added 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...between the 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... | |
 | 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...between the 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... | |
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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. 
