 | Adrien Marie Legendre - Geometry - 1822 - 394 pages
...two right angles APQ, AQP, which is impossible. PROPOSITION V. THEOREM. Oblique lines equally distant from the perpendicular are equal ; and, of two oblique lines unequally distant from, the perpendicular, the more distant is the longer. For the angles APB, APC, APB, being right,... | |
 | Adrien Marie Legendre, John Farrar - Geometry - 1825 - 280 pages
...would have two right angles APQ, AQP, which is impossible. THEOREM. 329. Oblique lines equally distant from the perpendicular are equal ; and of two oblique lines unequally distant from the perpendicular, that which is at the greater distance is the greater. Fig. 184 Demonstration.... | |
 | Adrien Marie Legendre - Geometry - 1825 - 276 pages
....4PQ would have two right angles APQ, AQP, which is impossible. 329. Oblique lines equally distant from the perpendicular are equal ; and of two oblique lines unequally distant from the perpendicular, that which is at the greater distance is the greater. F,g. 184. Demonstration.... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...BA is less than any oblique line BE, and measures 'the distance of the point B, from the plane. 319. Theorem. Oblique lines drawn from a point to a plane...unequally distant the more remote is the greater. Demonstration, a. The oblique lines BC, BD, BE &c. (fig. 149) at the equal distances AC, AD, AE &c.... | |
 | Benjamin Peirce - Geometry - 1841 - 186 pages
...E' upon E, and AE' upon AE. Therefore, the angle BAE' is equal to the angle BAE, and each is, by 5) 20, a right angle. 319. Corollary. The perpendicular...perpendicular BA are equal ; for the triangles BAC, fl -J Oblique Lines drawn to a Plane. BAD, BAE, &c. are equal, by § 51, since the angles BAC, BAD,... | |
 | Adrien Marie Legendre - Geometry - 1841 - 288 pages
...would have two right angles .#PQ, AQP, which is impossible. THEOREM. 329. Oblique lines equally distant from the perpendicular are equal ; and of two oblique lines unequally distant from the perpendicular, that which is at the greater distance is the greater. Fig. 184. Demonstration.... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...at the same point and in the same plane, which is impossible (Prop. XVI., Cor., BI). PROPOSITION V. THEOREM. Oblique lines drawn from a point to a plane,...equal; and of two oblique lines unequally distant from the perpendicular, the more remote is the longer. Let the straight line AB be drawn perpendicular... | |
 | Benjamin Peirce - Geometry - 1855 - 184 pages
...The perpendicular BA. is less than any oblique line JBEy and measures the distance of the point jB, from the plane. 320. Theorem. Oblique .lines drawn...unequally distant the more remote is the greater. Oblique Lines drawn to a Plane. BAD, BAE, &c. are equal, by § 51, since the angles BAC, BAD, BAE,... | |
 | Elias Loomis - Conic sections - 1858 - 256 pages
...triangle ABG will have two right angles, which is impossible (Prop. XXVII., Cor. 3, BI). PROPOSITION V. THEOREM. Oblique lines drawn from a point to a plane,...equal ; and of two oblique lines unequally distant from the perpendicular, the more remote is the longer. Let the straight line AB be drawn perpendicular... | |
 | Benjamin Greenleaf - Geometry - 1862 - 518 pages
...angles, ABG, AGB, which is impossible (Prop. XXVIII. Cor. 3, Bk. I.). PROPOSITION V. — THEOREM. 405. Oblique lines drawn from a point to a plane at equal distances from a perpendicular drawn from the same point to it, are equal; and of two oblique lines unequally distant... | |
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B, from the plane. 320. Theorem. Oblique lines drawn from a point to a plane at equal distances from the perpendicular are equal; and of two oblique lines unequally distant the more remote is the greater. 
