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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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The Elements of Euclid for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - Euclid's Elements - 1880 - 400 pages
...that AF is greater than the diagonal of the square. 21. 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 tho more remote;...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 426 pages
...that AF is greater than the diagonal of the square. 21. 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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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...less than AB. Hence AC must be greater than AB. COR. — 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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Knowledge: An Illustrated Magazine of Science, Volume 5

Science - 1884 - 534 pages
...an angle, and the other on a side of the rectangle. 52. 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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First Steps in Geometry: A Series of Hints for the Solution of Geometrical ...

Richard Anthony Proctor - Geometry - 1887 - 202 pages
...an angle, and the other on a side of the rectangle. 52. 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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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 428 pages
...directions are equal. SECTION V.— OBLIQUE LINES. 34. i. DEFINITIONS. 2. PROPOSITIONS. PROP. XXI. THEOREM : A perpendicular is the shortest line that can be drawn from a given point to a given straight line. PROP. XXII. THEOREM : If a perpendicular and oblique lines are drawn from a given point...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 438 pages
...contact of its sides is equal to the semi-perimeter, minus the side lying opposite to this angle. 6. 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. 7. The longest line...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 428 pages
...given circumference of a circle passes, when produced, through the center of the circle. 7. The longest line that can be drawn from a given point to a given circumference of a circle passes through the center of the circle. 8. The radius of a circle inscribed...
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Manual of Plane Geometry, on the Heuristic Plan: With Numerous Extra ...

George Irving Hopkins - Geometry, Plane - 1891 - 204 pages
...must the other be ? If one of two supplementary angles is acute, what kind must the other one be ? 71. A perpendicular is the shortest line that can be drawn from a point to a straight line. (The analysis of this theorem has been given in the Introduction.) Post....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...and CA greater than CX. Hence obtain a proof of i. 20. 3. 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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