| Robert Simson - Trigonometry - 1775 - 520 pages
...likcwife fquares. PROP. Book II. PRO PV THEO R. Fa ftraight line be divided into two equal parts, and alfo **into two unequal parts ; the rectangle contained by the unequal parts, together with the** fquare of the line between the points of fection, is equal to the fquare of half the line. Let the... | |
| Robert Simson - Trigonometry - 1804
...'• . c- 43. '• PROP. V. THE OR. • IF a ftraight line be divided into two equal parts, and alfo **into two unequal parts ; the rectangle contained by the unequal parts, together with the** fquare of the line between the points of fe&ion, is equal to the fquare of half the line. Let the ftraight... | |
| John Playfair - Euclid's Elements - 1804 - 440 pages
...are likewife fquares. PROP. V. THEO R. IF a ftraight line be divided into two 'equal parts, and alfo **into two unequal parts ; the rectangle contained by the unequal parts, together with the** fquare of the line between the points of fection, is equal to the fquare of half the line. Let the... | |
| John Playfair - Euclid's Elements - 1806 - 311 pages
...manifest that the parallelograms about the diameter of a square are likewise squares. . PROP. V. THEOR. IF **a straight line be divided into two equal parts, and...square of the line between the points of section,** are equal to the square of half the line. Let the straight line AB be divided into two equal parts... | |
| John Mason Good, Olinthus Gilbert Gregory - 1813
...squares of the two parts, together •with twice the rectangle contained by the parts. Prop. V. Theor. If **a straight line be divided into two equal parts, and...section, is equal to the square of half the line.** Prop. VI. Theor. If a straight line be bisected, and produced to any point; the rectangle contained... | |
| Charles Butler - Mathematics - 1814
...product a+or.a— «•= aa — xx ; to each of these equals add xx, and a+xa — x+xx=aa, that b, **the rectangle contained by the unequal parts, together with the square of** (x) the line between the points of section is equal to the square of (a) half the line. QED In the... | |
| Euclides - Euclid's Elements - 1816 - 528 pages
...manifest, that the parallelograms about the diameterof a square are likewise squares. PROP. V. THEOR. IF **a straight line be divided into two equal parts, and...section, is equal to the square of half the line.** Let the straight line AB be divided into two e qual parts in the point C, and into two unequal parts... | |
| John Playfair - 1819 - 317 pages
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If **a straight line be divided into two equal parts, and...section, is equal to the square of half the line.** Let the straight line AB be divided into%two equal parts in the point C, and into two unequal parts... | |
| John Mason Good, Olinthus Gilbert Gregory - 1819
...parts, and also into two um quäl parts j the rectangle contained by the unequal parts, togotherVrith **the square of the line between the points of section, is equal to the square of half the line.** Prop. VI. Theor. If a straight line be bisected, and produned to any point; the rectangle contained... | |
| John Playfair - Circle-squaring - 1819 - 333 pages
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If **a straight line be divided into two equal parts, and also into two** uneqtial parts ; the rectangle contained by the unequal parts, together with the square of the line... | |
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