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" The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and... "
Elements of Geometry and Trigonometry: With Applications in Mensuration - Page 30
by Charles Davies - 1886 - 324 pages
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Exercises in Stewart's Plane and Solid Geometry: With Solutions for Teachers

Seth Thayer Stewart - Geometry - 1893 - 256 pages
...distance 0 С is greater than С G, the dist. of any other cliord from the center. (B. II., P. xIII.) 5. The shortest line that can be drawn from a given point to a given circumference of a circle passes, when produced, through the center of the circle. I. Let A В be the...
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Annual Report

1894 - 1192 pages
...the base, and the sum of the sides of a triangle, to construct the triangle. INSPECTORS' REPORT. 95 - .A. perpendicular is the shortest line that can be drawn from a given point to a given line. 7 From two points on the same side of a line given in position, r)raw two straight lines which shall...
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Proceedings of the Board of Public Instruction of the City of Albany, Volume 15

Albany (N.Y.). Board of Public Instruction - Education - 1895 - 626 pages
...complement? (6) What kind of a triangle is formed by a diagonal and two sides of a rhombus? 12. Prove that a perpendicular is the shortest line that can be drawn from a point to a line. 13. At one extremity of a line an angle of R0 is constructed, and at the other extremity...
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Plane and Solid Geometry

William James Milne - Geometry - 1899 - 398 pages
...On DG take DH= DE, and draw CO. Then, CH = CE. Why? Why? QED SOLID GEOMETRY. — BOOK VII. 448. Cor. I. A perpendicular is the shortest line that can be drawn from a point to a plane. 449. Cor. II. Equal oblique lines from a point in a perpendicular to a plane meet...
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Plane Geometry

William James Milne - Geometry, Modern - 1899 - 258 pages
...than PC, PC is the only perpendicular that can be drawn to AB from P. Therefore, etc. QED 61. Cor. A perpendicular is the shortest line that can be drawn from a point to a line. 1. Since PCF is a straight line, is PDF a straight line ? Ax. 12. 2. Which line, then,...
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A Text-book of Euclid's Elements for the Use of Schools. Books I and II, Book 1

Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...right angles to the base, the triangle is isosceles. 6. The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line ; and of others, that which is nearer to the perpendicular is less than the more remote...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - Geometry - 1903 - 384 pages
...st. line drawn from O to meet AB. .'. ON is the shortest of all such lines. QE J i. NOTE. Since the perpendicular is the shortest line that can be drawn from a given point to a given line, it is called the distance of the point from the line, Ex.668. In fig. 144, prove that OB > OP. Ex....
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Elementary Geometry: Plane

James McMahon - Geometry, Plane - 1903 - 380 pages
...circles are equal. Ex. 3. Any diameter of a circle is an axis of symmetry. 12. THEOREM 6. The least line that can be drawn from a given point to a given circle is a segment of the line that passes through the center, and the extremities of this segment...
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Elementary Geometry: Plane

James McMahon - Geometry, Plane - 1903 - 380 pages
...opposite the second angle. Perpendicular and oblique lines. 85. THEOREM 16. Of all the straight lines that can be drawn from a given point to a given line : (1) the perpendicular is the least; (2) any two that make equal angles with the perpendicular are...
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Plane Geometry by the Suggestive Method

John Alton Avery - Geometry, Modern - 1903 - 136 pages
...with the hypothesis. What theorems have already been proved by the indirect method ? THEOREM XXX 81. <A perpendicular is the shortest line that can be drawn from a point to a line. Hyp. From C, any pt. outside AB, let CD be -L AB at D. To prove that CD is the shortest...
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