Plane and solid geometry . 4. With A as center and with AC as radius draw CP, cuttingAB at P. 6. AB:AP=AP: FB. II. Proof Argument1. AB is tangent to circle 0. 9 .-. AD: AB = AB: AC, .-. ^D — ^P : ^P = ^P — ^C: ^C. .-. AD— CD: AB = AB — ^P : AP, .-. ^P : .4P = PB : AP. .-. AB: AP = AP: PB, Reasons 1. §314. 0 §461. 00. § 399. 4. §309. 5. §309. 6. § 395. III. The discussion is left as aL exercise for the student. 206 PLANE GEOMETRY Ex. 763. Divide a line AB externally in extreme and mean In the figure for Prop. XXXIII prolong BA to P, makingP^A = AD. Then prove AB : P^
Plane and solid geometry . 4. With A as center and with AC as radius draw CP, cuttingAB at P. 6. AB:AP=AP: FB. II. Proof Argument1. AB is tangent to circle 0. 9 .-. AD: AB = AB: AC, .-. ^D — ^P : ^P = ^P — ^C: ^C. .-. AD— CD: AB = AB — ^P : AP, .-. ^P : .4P = PB : AP. .-. AB: AP = AP: PB, Reasons 1. §314. 0 §461. 00. § 399. 4. §309. 5. §309. 6. § 395. III. The discussion is left as aL exercise for the student. 206 PLANE GEOMETRY Ex. 763. Divide a line AB externally in extreme and mean In the figure for Prop. XXXIII prolong BA to P, makingP^A = AD. Then prove AB : P^A = P^A : PB, Ex. 764. If the line I is divided internally in extreme and mean ratio,and if s is the greater segment, the value of s in terms of I : s = s \l — s. Ex. 765. A line 10 inches long is divided internally in extreme andmean ratio. Find the lengths of the two segments. Ex. 766. A line 8 inches long is divided externally in extreme andmean ratio. Find the length of the longer MISCELLANEOUS EXERCISES Ex. 767. Explain how the accompanyingfigure can be used to find the distance from^ to J5 on opposite sides of a hill. CE = \BC^CD = \AC. ED is found by measurement tobe 125 feet. What is the distance AB ? Ex. 768. A little boy wished to obtain theheight of a tree in his yard. He set up a ver-tical pole 6 feet high and watched until theshadow of the pole measured exactly 6 feet. Hethen measured quickly the length of the trees shadow and called this theheight of the tree. Was his answer correct ? Draw figures and this method for measuring the height of your school building and flagpole. Ex. 769. If light from a tree,as AB^ is allowed to pass through asmall aperture 0, in a window shutterW^ and strike a white screen or wall,an inverted image of the tree, as CD^is formed on the screen. If the dis-tance 0£= 30 feet, 0F = 8 feet, andthe length of the tree ^5=35 feet, findth3 length of the image CD. Underwhat condition will the
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Keywords: ., bookcentury1900, bookdecade1910, booksubjectgeometr, bookyear1912
