Books Books The perpendicular is the shortest line that can be drawn from a point to a straight line. The New Practical Builder and Workman's Companion, Containing a Full Display ... - Page 22
by Peter Nicholson - 1823 - 596 pages ## Spherical Trigonometry: For Colleges and Secondary Schools

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... ## Plane [and Spherical] Trigonometry for Colleges and Secondary Schools

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... ## Elements of Plane Geometry

William Herschel Bruce, Claude Carr Cody (Jr.) - Geometry, Modern - 1910 - 286 pages
...£. Hence 2£ Cj&Z> is not a right angle. § 51 .-. CEisnot±AB. §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,... ## Elements of Solid Geometry

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.... ## Schultze and Sevenoak's Plane Geometry

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... ## Plane Geometry

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... ## Plane and Solid Geometry

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... ## Schultze and Sevenoak's Plane and Solid Geometry

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... ## Robbin's New Plane Geometry

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... 