| Peter Nicholson - Mathematics - 1825 - 1046 pages
...added together 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...points of section. Let the straight line AB be divided** at the point С into two equal, »nd at D into two unequal parts : The squares of AD, DB, are together... | |
| 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,...square of half the line, and of the square of the** Une between the points of section. 3. If two straight lines within a circle cut one another, the rectangle... | |
| John Playfair - Circle-squaring - 1826 - 326 pages
...R C. Now 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...between the points of section. Let the straight line AB** he divided at the point C into two equal, and at D into two. unequal parts ; The squares' of AD, DB... | |
| George Lees - 1826 - 266 pages
...a straight line AB be divided into two equal parts AC, CB, and also into two unequal parts AD, DB ; **the squares of the two unequal parts are together...square of half the line, and of the square of the** tine CD, between the points of section. • . ; Or, AD2 + DB2 = 2AC2 .+ 2CD2. From the point C, draw... | |
| Euclid - 1826 - 236 pages
...PROPOSITION IX. ТНЕОПЕМ. J/1 a rzgAf Kne ie any how cut into two equal and two unequal parts, then **the squares of the two unequal parts are, together, double of the square of** the half line, and the square of the intermediate part. Let any right line AB be cut into two equal... | |
| Euclides - 1826 - 226 pages
...PROPOSITION IX. THEOREM. If a right line be any how cut info two equal and two unequal parts, then **the squares of the two unequal parts are, together, double of the square of** the half line, and the square oftJie intermediate part. Let any right line AB be cut into two equal... | |
| Robert Simson - Trigonometry - 1827 - 546 pages
...BC added 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...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 line between the points... | |
| Walter Henry Burton - Astronomy - 1828 - 84 pages
...will understand this proposi-Prop. xix. tion, which is necessary for our further progress: that if **a straight line be divided into two equal, and also into two unequal parts, the** square of either of the equal parts (or the rectangle under both) is equal to the rectangle under the... | |
| John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...angle. 7. If a straight line be divided into two equal, and also into two unequal parts, prove that **the squares of the two unequal parts are, together,...square of the line between the points of section.** 8. If a straight line touch a circle, and, from the point of contact, a straight line be drawn cutting... | |
| John Playfair - Euclid's Elements - 1832 - 358 pages
...AC!+4BC'+4BC. AC. Now BC' + BC.AC = AB.BC "(3. 2.) and therefore AD = AC +4 AB.BC. QED" PROP. IX. THEOR. If **a straight line be divided into two equal, and also...two unequal parts; the squares of the two unequal** purls are together double of the square of half the line, and of the square of the line between the... | |
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