| John Playfair - Euclid's Elements - 1806 - 311 pages
...BC* + BC.AC = AB.BCb ; therefore AD2=AC2+ U3.2. 4AB.BC. QED" 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... | |
| Robert Simson - Trigonometry - 1806 - 518 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... | |
| John Mason Good - 1813
...square of the straight line which is made up of the whole and that part. Prop. IX. Theor. If a straight **line be divided into two equal, and also into two unequal parts; the** tqniMN of the two unequal parts arc together double of the square of half the line, and of the square... | |
| Euclides - 1816 - 528 pages
...Wherefore, if a straight line, &c. QED TIL F ACBT z .... 6 K / P R / 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... | |
| Miles Bland - Euclid's Elements - 1819 - 444 pages
...nil lines drawn from that point meeting the three lines be harmonically divided. 23. If a straight **line be divided into two equal and also into two unequal parts,** and be |>roduced, so that the part produced may have to the whole line so produced, the same ratio... | |
| Miles Bland - Euclid's Elements - 1819 - 442 pages
...all lines drawn from that point meeting the three lines be harmonically divided. 23. If a straight **line be divided into two equal and also into two unequal parts,** and be produced, so that the part produced may have to the whole line so produced, the same ratio that... | |
| Peter Nicholson - Mathematics - 1825 - 372 pages
...in one straight line. ^herefore, 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... | |
| John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...given rectilinear figure, having an angle equal to a given rectilinear angle. 2. If a straight Hue **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... | |
| John Playfair - Circle-squaring - 1826 - 320 pages
...BO+RC.AC=\B.BC (3.2.) and therefore AD3==AC + 4\B.BC. Q, E, D," -V 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... | |
| Robert Simson - Trigonometry - 1827 - 513 pages
...together in one straight line. Wherefore, if a straight line, &c. GED 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 arc together double of the square of half the line, and of the square of the... | |
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