Books Books 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 ## 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.... ## 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... ## 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... ## 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... ## A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 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... ## 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... ## 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... ## 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... ## 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,... 