| Euclides - 1845 - 546 pages
...is one straight line. Wherefore, if a straight line, &c. QED PROPOSITION IX. THEOREM. 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... | |
| Euclid, James Thomson - Geometry - 1845 - 382 pages
...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... | |
| 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 unequal parts, the squares of the two unequal parts are together equal to twice the rectangle contained by these parts together... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...this equality, we shall have, 4aJ+c2=c2+4ic+4J2, or4ai+c2=(c4-26)2. PROP. IX. THEOR. • 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... | |
| Euclides - 1848 - 52 pages
...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 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... | |
| Euclid, Thomas Tate - 1849 - 120 pages
...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 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... | |
| 1852 - 316 pages
...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 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... | |
| 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 parts ; the squares of the two unequal parts are together double of the square of half the line, and of the square of the... | |
| Euclides - 1852 - 152 pages
...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 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... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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 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... | |
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