 | John Playfair - Euclid's Elements - 1837 - 332 pages
...each member of this equality, we shall have, 4aJ+c2=c2+4ic+4*2, or4ai+c2=(c-|-2i)2. PROP. IX. THEOR. If a straight line be divided into two equal, and also into twn unequal parts ; the squares of the two unequal parts are together double of the square of half... | |
 | Euclides - 1838 - 264 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...the squares of the two unequal parts are together doable of the square of half the line, and of the square of the line between the points of section.... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...each member of this equality, we shall have, 4ai+c2=c2+4ic+462, or 4ai+c2=(cr-26)2. PROP. IX. THEOR. If a straight line be divided into two equal, and also into twn unequal parts ; the squares of the two unequal parts are together double of the square of half... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...and BC added together in one straight line. Therefore, if a straight line, &c. PROP. IX. THEOR. — If a straight line be divided into two equal, and also into two unequal parts ; the squares of the unequal parts are together double of the square of half the line, and of the square of the line between... | |
 | Euclides - 1845 - 546 pages
...lines is never less than twice their rectangle. 8. If a straight line be divided into two equal and into two unequal parts, the squares of the two unequal parts are equal to twice the rectangle contained by the two unequal parts, together with four times the square... | |
 | Euclides - 1846 - 292 pages
...the rectangle ABCD is equal to twice the triangle AEF together with the rectangle BE, DF. 21. If a line be divided into two equal and also into, two...the squares of the two unequal parts are together equal to twice the rectangle contained by these parts together with four times the square of the line... | |
 | Upper Canada. Chief Superintendent of Schools - Education - 1854 - 196 pages
...of the whole line is equal to the squares of the two parts, together with twice their rectangle. 4. If a straight line be divided into two equal and also into two unequal parts ; the squares of the unequal parts are together double of the squares of half the line, and of the squares of the line between... | |
 | Euclides - 1856 - 168 pages
...manifest that the rectangles about the diameter of a square are likewise squares. L. — EUCLID II. 5. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained by the unequal parts, together with the square of the line between the points of... | |
 | Cambridge univ, exam. papers - 1856 - 200 pages
...If the square on the hypothenuse be fire times that on one of the sides; compare the two sides. 4. If a straight line be divided into two equal and also into two unequal parts; the rectangle contained by the unequal parts together with the square of the line between the points of... | |
 | Euclides - 1858 - 248 pages
...of the diagonals of a parallelogram are together equal to the squares of the four sides. 6. If a st. line be divided into two equal and also into two unequal...the squares of the two unequal parts are together equal to twice the rectangle contained by these parts, together with four tunes the square of the line... | |
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If a straight line be divided into two equal, and also into two unequal parts ; the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section. 
