 | Daniel Alexander Murray - Spherical trigonometry - 1908 - 132 pages
...a line perpendicular to a radius at its extremity is tangent to the sphere. [Suggestion for proof : The perpendicular is the shortest line that can be drawn from a point to a plane.] A tangent to an arc of a great circle at any point of the arc is perpendicular to... | |
 | Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...a line perpendicular to a radius at its extremity is tangent to the sphere. [Suggestion for proof : The perpendicular is the shortest line that can be drawn from a point to a plane.] A tangent to an arc of a great circle at any point of the arc is perpendicular to... | |
 | William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...£. Hence 2£ Cj&Z> is not a right angle. § 51 .-. CEisnotħAB. §52 PROPOSITION XV. THEOREM. 116. The perpendicular is the shortest line that can be drawn from a given point to a given line. Given the straight line AB, the point P, the _L PC, and any other line,... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...without that line. If they could, the two planes would coincide. (§ 523.) PROPOSITION I. THEOKEM. 531. The perpendicular is the shortest line that can be drawn from a point to a plane. Given the point P, the line PA J_ the plane MW, and any other line PB from P to MN.... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry, Plane - 1913 - 328 pages
...base ^i of an isos. A are equal. But this is impossible. .-. b > c. QED ZB > ZC, by hyp. 131. COR. The perpendicular is the shortest line that can be drawn from a point to a given line. (115.) NOTE. The method used in the above proof is known as the indirect method... | |
 | Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...that the hypotenuse of a right triangle is its longest side. 2. By use of Theorem XVIII, prove that the perpendicular is the shortest line that can be drawn from a point to a straight line. (Compare § 77.) 3. If the crank AB mentioned in Ex. 3, p. 59, is so arranged... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 378 pages
...that the hypotenuse of a right triangle is its longest side. 2. By use of Theorem XVIII, prove that the perpendicular is the shortest line that can be drawn from a point to a straight line. (Compare § 77.) 3. If the crank AB mentioned in Ex. 3, p. 59, is so arranged... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 488 pages
...The base A of an isos. A are equal. But this is impossible. .-. b > c. QED ^B > ZC, by hyp. 131. COR. The perpendicular is the shortest line that can be drawn from a point to a given line. (115.) NOTE. The method used in the above proof is known as the indirect method... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...(2) their sum is greater than half the sum of the sides of the triangle. PROPOSITION XXV. THEOREM 87. The perpendicular is the shortest line that can be drawn from a point to a A straight line. Given : PR _L to AB ; PC not _L. To Prove : PR < PC. Proof : Extend PR... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1918 - 486 pages
...impossible. ... b > c. 3.ED REASONS ZB > ZC, by hyp. The base 4 of an isos. A are equal. 7, by hyp. 131. COR. The perpendicular is the shortest line that can be drawn from a point to a given line. (115.) NOTE. The method used in the above proof is known as the indirect method... | |
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The perpendicular is the shortest line that can be drawn from a point to a straight line. 
