...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....

...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...

...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...

...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...

...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...

...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...

...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...

...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...

...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,...

...Hence 2£ Cj&Z> is not a right angle. § 51 .-. CEisnot±AB. §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...