| John Playfair - Euclid's Elements - 1806 - 311 pages
...AD2=AC2+4BC2+4BC.AC. Now 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...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... | |
| Robert Simson - Trigonometry - 1806 - 518 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...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 - Geometry - 1810 - 518 pages
...line. WhereforCi if a straight line, &c. QED A CB G s / M / N 9 u X / • 'E F PROP. IX. THEOR. IF **a straight 'line be divided into two equal, and also...half the line, and of the square of the line between** tlie points, of section. Let the straight line AB be divided at the point C into two equal, and at... | |
| John Mason Good - 1813
...to the 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 - 1814
...the rectangle AB, BC, is equal to the gnomon AOH. To G P / K / EHJ / R N 0 , F 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 draw3 CE at right angles to AB, and • 11. i. make it equal to AC or CB, and join... | |
| Euclides - 1816 - 528 pages
...straight line. 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...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... | |
| John Playfair - Circle-squaring - 1819 - 333 pages
...AD2=AC-+4AB.BC. QED" PROP. IX. THEOR. If a straight line be divided into too equal, and also into tzeo **unequal parts ; the squares of the two unequal parts...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... | |
| John Playfair - 1819 - 317 pages
...ADs=AC3+4AB.BC. q. ED" PROP. IX. THEOR. 'If /a straight line be divided into two equal, and also into too untquai **parts ; the squares of the two unequal parts are together double of the square of half the** iinCi ahd of th-e square of the line between the points of section. • » v. Let the straight line... | |
| Miles Bland - Euclid's Elements - 1819 - 377 pages
...; then will 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... | |
| Miles Bland - Euclid's Elements - 1819 - 377 pages
....-. EB : GI :: EH . HG, whence (Eucl. v. 15.) EF : FG :: EH : HG and alt. EF . EH . FG . HG. (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... | |
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