| 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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