Начертательная геометрия

4. #

51

C )) -D' 1 5. B' D' AC DE. * ) - D . @ " , "V 5 D D. (1. , AC M ) .

= . 4.31

= . 4.32

C " -" -D' 6 7. #' D' AC DF. * " D . " H , 6AC + 7 DF. ,AM AC " .

4.7. #"&"'( # "' =" %* - /

C ' + - D " .D +" ) .

!

,. B -

52

.

+ . % ) " ( " . @ D " D , + D " ) " -, + . @ D) " ' D -.

@ . 4.33 ' " AB " H V. I -V D V1, AB,D V1H. # ( AB -(ABIIV1), 11 – . @ AB (a 1b 1) " , " -" AB H.

) ( . 4.33) -D z ," H . - , ( . 4.34) :

) D x1 "AB D ;

) " a bx1;

) D x1 z -A B;

") a 1 b 1 .

= . 4.33

= . 4.34

4. #

53

" H Dy D , -) . BD D -1, D V.

/ +

, x V -

H

x2

V1

, (

D' :

H1

x

V

x

V1

x

V1

x

V

x

V

x

V1

.

2 H1

H

H

1 H

1 H1

2 H1

+ ( ( , C "( " " ( -

1. + % , -. 2 -( . 4.35 4.36).

= . 4.35

= . 4.36

+ D , , V1 ( . 4.35),, . (

54

.

" - :

x V x V1 ; V1 H; V1 // AB; x1 // ab.
H	1 H

" a b,x1, z ( x ) ). @a 1b 1 , " -" H.

" D - " ( AB. $ -D " " V " ( . 4.36).

( -) a b , y "-:

x V x V ; H1 V; H1// AB; x1// a b .
H	1 H1

2. + , , -% , , -, !(. 4.37).

$ " , D' D D, -) D V D V1. = "V1 AB. $" V1 -(a 1=b 1).

x V x V1 ; V1 H; V1 AB; x1 ab.
H	1 H

< % AB ( . 4.38) % , , , , 5 . ' %, ( ), ! % .

x V x V1 ; V1 H; V1// AB; x1//ab;
H	1 H

4. #

55

x V1 x V1 ; H1 V1; H1 AB; x2 a 1 b 1
1 H	2 H1

		= . 4.37				= . 4.38
		3. + P ( ') % -
	% (. 4.39),
	.				V D		V1. =-
		I , ,
	V1 H P.							V1 -
			P,
			-
						. C	'
			+ ( -
			"			( D, D "-
			).
			P " C1 -
			D					V1. #
			x1 D -
			"				"
			(x1 c1). D ) D -
			D			P. %		D
		= . 4.39			(c1			=11 ),
					P (	C) – D a 1c 1b 1;
	x V x V1 ; V1 H;
			V1 P( C);		V1 C1 (C1 – );			x1 (c1).
	H	1 H
		C P " -D' D
	,					H D,

56

.

V ) P ( D -( ).

4. + ( ') - % ( , ). + -(. 4.40 4.41).

= . 4.40

= . 4.41

@ . 4.40 ) -D' . I " D H D 1. =V P. @ Dx1 ) a b c -x1. $ ", y D . -D . D " - D D " , D " -ABC.

x V x V ; H1 V; H1//P( C); x1//a b c .
H	1 H1

I + " , ( ') "--D' ( . 4.41). ( ) -V D V1. # -H P. # x1 abc. z D . * ) -x1.

4. #							57
x	V	x		V1	; V1 H;	V1//P( C); x1//abc.
	H		1 H

0 % , , 1 , 5(. 4.42).

x	V		x		V1		;	V1	H; V1 P( C); V1 C1 (C1 – );
	H			1 H					x1 (c1);
x		V1		x		V1		;	H1 V1; H1//P( C); x2//a 1c 1b 1.
1 H				2 H1

= . 4.42

. ' ! ! " * *"! - ?- -" ! !"(" .

& + ' D' -, " " . = +. = , " -( , AS – " - D' ); ( , &') – ' " - , . 4.43.

58

.

AS , ( -( -D . C " -– m n, a=s -bc. # " D D " – m,) D D – m . $ (MN)//H, ) m n 1. (m n )//x.

= . 4.43

, D' ' , D,D' .

!

' % D , "-( +' " , -- ; -( . @ ( D" ( .

@ . 4.44 ' & " I, -. $ & ' " I ( . 4.44, ) , 1& , '-& ' I. $ 1 – ' &. $ & + ' " , "2, ' . M I -

4. #

59

, 2 " D. # ' – D' , .& -D, V – . "-D D & b1," , ) D D & (b1 ) - ' D . $ '2, V, ) b1& TV 2. '( D .

 

	= . 4.44

$ ' ", ' . @ -, ' , ', .

'' . @ . 4.45,' I .' & & " , ,I (i). $ & -, ) D 1,& . & , " " ab & -Ox. # V -D .

@ . 4.45, ' -V '. / ) )' I (i ) D. : c d -

60

.

CD , " Ox. #D - . $ D 'dd1, Ox.

	= . 4.45
@ . 4.46 " &' (							-
" &' V) , -
. ( " + " ( ) -
' V. # a b – -
D " &' V – ,
Ox. $ -
+ "							-
V " ,							–
, Ox. -
1 b 1
( ,
D ab1c1 " .
$ " ,
' . @
" D -
,			"
.

= . 4.46

!

' -% , -+ ' . = , -