Teorema sull'INTERSEZIONE

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Teorema sull'INTERSEZIONE

Tg (AB)= XB-XA/ YB-YA

AB¯=XB-XA/ sen(AB)

APˉ=ABˉ/ senγ·senβ 636c28g

BPˉ= ABˉ/ senγ·senα

(AP)=(AB)-α

(BP)=(AB)±180+β

(XP)_A=APˉ sen(AP)

(YP)_A= APˉ cos(AP)

(XP)_B=BPˉ·sen(BP)

(YP)_B= BPˉ·cos(BP)

XP=XA+(XP)_A

YP=YA+(YP)_A

XP=XB+(XP)_B

YP=YB+(YP)_B

Teorema di SNELLIUS

Tg(BA)=XA-XB/YA-YB

Tg(BC)=XC-XB/YC-YB

BAˉ= XA-XB/sen(BA)

BCˉ= XC-XB/sen (BC)

ω=(BA)-(BC)

PÂB=x

PĈB=y

x+y/2=180-½ (α+β+ω)

x-y/2=inv tg[tg x+y/2 ·cotg (θ+45)]

θ=inv tg AB¯·senβ/BC¯ sen

x=M+N

y=M-N

ω₁=180-(α+x)

+y)

AP¯=AB¯/senα·senω₁

CP¯=BC¯/senβ· senω₂

BP¯=BC¯/senβ·seny

BP¯=BA¯/senα·senx

(AP)=(BA)±180+x

(BP)=(BC)+ ω2

(CD)=(BC)±180-Y

(XP)_A=AP¯·sen(AP)

(YP)_A= AP¯·cos(AP)

(XP)_B=BP¯·sen(BP)

(YP)_B= BP¯·cos(BP)

(XP)_C=CP¯·sen(CP)

(YP)_C= CP¯·cos(CP)

XP=XA+(XP)_A

YP=YA+(YP)_A

XP=XB+(XP)_B

YP=YB+(YP)_B

XP=XC+(XP)_C

YP=YC+(YP)_C

Teorema di HANSEN

α₁=APQ  =AQP  =BPQ  β₂=BQP

Tg (AB)= XB-XA/ YB-YA

AB¯=XB-XA/ sen(AB)

x+y/2=90- ½ (α₁-β₁)

x-y/2=inv tg[tg x+y/2 ·cotg (θ+45)]

θ=inv tg senα₂·senβ₁+β₂/sen sen

x=M+N

y=M-N

(AP)=(AB)+x

(AQ)=(AP)-[180-(

(BP)=(AB)±180-y

(BQ)= (BP)-[180-(β₁+β₂ )]

AP¯=AB¯/sen (α₁- sen y

BP¯= AB¯/sen (α₁- sen x

AQ¯= AB¯/sen ( sen y+180-(

BQ¯= AB¯/sen ( sen x-180-(α₁+

(XP)_A=AP¯·sen(AP)

(YP)_A= AP¯·cos(AP)

(XQ)_A=AQ¯·sen(AQ)

(YQ)_A= AQ¯·cos(AQ)

(XP)_B=BP¯·sen(BP)

(YP)_B= BP¯·cos(BP)

(XQ)_B =BQ¯·sen(BQ)

(YQ)_B= BQ¯·cos(BQ)

XP=XA+(XP)_A

YP=YA+(YP)_A

XQ=XA+(XQ)_A

YQ=YA+(YQ)_A

XP=XB+(XP)_B

YP=YB+(YP)_B

XQ=XB+(XQ)_B

YQ=YB+(YQ)_B