 | Daniel Alexander Murray - Plane trigonometry - 1908 - 358 pages
...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 the radius... | |
 | Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...is the shortest straight line that can be drawn from a point to a straight line ; and, conversely, the shortest line that can be drawn from a point to a straight line is perpendicular to the line. Given : PC _L AB and any oblique p line PD. To Prove :... | |
 | William Herschel Bruce, Claude Carr Cody - Geometry, Solid - 1912 - 134 pages
...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. To prove... | |
 | Walter Burton Ford, Earle Raymond Hedrick - Geometry, Modern - 1913 - 272 pages
...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 that AC... | |
 | Arthur Schultze, Frank Louis Sevenoak - Geometry - 1913 - 486 pages
...c. QED REASONS ZB > ZC, by hyp. The base 4 of an isos. A are equal. 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 or reductio... | |
 | Walter Burton Ford, Charles Ammerman - Geometry, Plane - 1913 - 376 pages
...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 that AC... | |
 | 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 or reductio... | |
 | Claude Irwin Palmer, Daniel Pomeroy Taylor - Geometry, Plane - 1915 - 320 pages
...ZC. AADC is isosceles. Why? Then AD = DC. Why? BD+DA>BA. Why? BD+DOBA. § 111 .-.BOBA. 185. Theorem. A perpendicular is the shortest line that can be drawn from a point to a straight line. Given CD drawn perpendicular to the line AB from the point C, and CE any other line... | |
 | Edward Rutledge Robbins - Geometry, Plane - 1915 - 280 pages
...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 to X, making... | |
 | Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...line through the center of the circle and perpendicular to the plane of the circle. 449. COR. 3. The perpendicular is the shortest line that can be drawn from a point to a plane. 450. The distance from a point to a plane is the perpendicular drawn from the point to the plane.... | |
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The perpendicular is the shortest line that can be drawn from a point to a straight line. 
