...THE FIRST BOOK. 167. Prop. 9- To cut a given Rectilinear Angle into two equal Parts. 268. Prop. ii. To draw a Perpendicular to a given Line from a given Point in it. 269. Prop. 12. To do the fame, if the given Point is cut of the Line. 270. Prop. 23. To make a...

...that is, make BF = —^.-—. Then PF will be the required line. B.—PERPENDICULARS. Problem 1.—To draw a perpendicular to a given line from a given point in it. 213. (a.) When the Point is accessible. This may be done on the ground by the methods described...

...middle of the line ....... 48 „ Second, when thepnint is at or near one extremity of theline 48 „ to draw a perpendicular to a given line from a given point without the line ; First, when the point is conveniently near the middle of the line ...... 49 „...

...convenient ; as (J, 8, and 10, or 9, 12, and 15, whether inches, feet, or any other units of length. To draw a perpendicular to a given line from a given point without the line. FIRST, When the point is conveniently near the middle of the line. 1. Let AB, Fig....

...bisect FE in G, join GC, which is the perpendicular required. SUMMARY OF PROPOSITION XII., PROBLEM 7. To draw a perpendicular to a given line from a given point without it. Cons. — With given point as centre and any point on the other side of the line as radius,...

...bisect the re-entrant angle BAC, produce the bisector of the angle BAC. 694. COROLLARY II. To erect a perpendicular to a given line from a given point in the line, bisect the straight angle at that point. PROBLEM II. 695. To bisect a given sect. With A and...

...the line would be divided into 8 equal parts ; and in a similar manner into 16, &c. PROBLEM 2. — To draw a perpendicular to a given line, from a given point in the line. Let С be the given point. With С as centre, and any radius, set off equal distances С 1 and...

...to AX, and .17 from AX equal to ^.D. Join YO ; then 7t> is perpendicular to the given line AB. (3) To draw a perpendicular to a given line from a given point on it. (Fig. 3.) Let AB be the line, and C the point. Draw a perpendicular YOZ to AB, by (2), meeting...

...less than B'C' (90). Hence ZA must be greater than Z A'. PERPENDICULARS. PROPOSITION XXI. PROBLEM. 92. To draw a perpendicular to a given line from a given point without it. F.-- --- a D\ H .--'E "- --'C Given : A point P without a straight line AB of indefinite...

...perpendicular to HK at its middle point P, and the problem is the same as 118.) r ' \ \ k 120. Problem. To draw a perpendicular to a given line from a given point without the line. \ f I—" K 6 FIG. 48. Let AB be the given line and P the given point without the...