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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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Plane Geometry

Fletcher Durell - Geometry, Plane - 1904 - 382 pages
...equals be subtracted from unequals, the remainders are unequal in the same order). QED 94. COR. The perpendicular is the shortest line that can be drawn from a given point to a given line. For, in the Fig. page 31, PP'<PR + RP', Art 92. Or, 2PQ<2PR. Ax. 8. .-. PQ <PR. Ax. 10. Hence, DBF....
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Plane and Solid Geometry

Fletcher Durell - Geometry - 1911 - 553 pages
...l)e subtracted from unequals, the remainders are unequal in the same order). Q. s. D. 94. COR. The perpendicular is the shortest line that can ~be drawn from a given point to a given line. For, in the Fig. page 31, PP' <PR + RP, Art 92. Or, 2PQ<2PR. Ax. 8. /. PQ<PR. Ax. 10. Hence, DKF. The...
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Solid Geometry

Fletcher Durell - Geometry, Solid - 1904 - 232 pages
...straight line passing through the center of the circle and perpendicular to its plane. 521. COK. 3. The perpendicular is the shortest line that can be drawn from a given point to a given plane. 522. DEF. The distance from a point to a plane is the perpendicular drawn from the point to...
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Plane and Solid Geometry: Suggestive Method

George Clinton Shutts - Geometry - 1904 - 112 pages
...Zj& 3 and 4. 2. Compare lines AB and A C. Give auth. Therefore — PROPOSITION XXXVI. 130. Theorem. A perpendicular is the shortest line that can be drawn from a point to a straight line. A -D MB Let AB represent the shortest line from A to the line CD. To prove...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 484 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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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 431 pages
...constant for all positions of BC. [Show that the perimeter = AS + AT.] 370 The shortest and the longest line that can be drawn from a given point to a given circumference lie in the diameter that passes through the point. 371 Two circles intersect at A and...
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Plane and Solid Geometry

Isaac Newton Failor - Geometry - 1906 - 440 pages
...its class. Thus, the diameter of a circle is the maximum chord, and the perpendicular is the minimum line that can be drawn from a given point to a given straight line. 488 Isoperimetric figures are figures which have equal perimeters. PROPOSITION I. THEOREM...
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Plane and Solid Geometry

Elmer Adelbert Lyman - Geometry - 1908 - 364 pages
...minimum value. Thus, the maximum of all chords of a circle is the diameter and the minimum straight line that can be drawn from a given point to a given line is a perpendicular from the point to the line. What is the minimum line segment from a point within...
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Books 3-9

Euclid - Mathematics, Greek - 1908 - 456 pages
...which De Morgan proposes to introduce after i. 2i, namely, "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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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 .-. 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, as PD, from P to AB. To prove...
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