217112An ESSAY
and make an Angle of 22 {1/2} with the Horizon.
Let MN and GH be two Mirrours in the before-
11Fig. 72. mentioned Situation; we are to demonſtrate,
that if the Ray A B is parallel to the Horizon,
after being reflected in B and C, it ought to fall
perpendicularly upon the Machine. The Angle
A B N is 112 {1/2} Degrees; and conſequently 2211. Angle A B M, and its equal, the Angle of Re-
flection C B G, are each 67 {1/2} Degrees. The An-
gle B P Q, is the Complement of the Angle
N B A, plus the Angle P Q B, which is 22 {1/2} 3323. grees; whence the Angle B P Q is 45 Degrees.
Again, the Angle PC B is the Complement of
the two Angles C B P and B PC to 180 Degrees;
and conſequently it is 67 {1/2} Degrees, which is the
ſame as its equal, the Angle Q C a of Reflection.
And reaſoning after the ſame Manner, the An-
gle C R Q of the Triangle R C Q, is a right one.
Which was to be demonſtrated.
Let MN and GH be two Mirrours in the before-
11Fig. 72. mentioned Situation; we are to demonſtrate,
that if the Ray A B is parallel to the Horizon,
after being reflected in B and C, it ought to fall
perpendicularly upon the Machine. The Angle
A B N is 112 {1/2} Degrees; and conſequently 2211. Angle A B M, and its equal, the Angle of Re-
flection C B G, are each 67 {1/2} Degrees. The An-
gle B P Q, is the Complement of the Angle
N B A, plus the Angle P Q B, which is 22 {1/2} 3323. grees; whence the Angle B P Q is 45 Degrees.
Again, the Angle PC B is the Complement of
the two Angles C B P and B PC to 180 Degrees;
and conſequently it is 67 {1/2} Degrees, which is the
ſame as its equal, the Angle Q C a of Reflection.
And reaſoning after the ſame Manner, the An-
gle C R Q of the Triangle R C Q, is a right one.
Which was to be demonſtrated.
28.
It is not abſolutely neceſſary to give the
Mirrours the aforeſaid Inclinations; for the An-
gle A B N may be aſſumed at Pleaſure, from
which muſt be taken an Angle of 135 Degrees,
to have the Inclination of the Miror G H. Ne-
vertheleſs, the Angles we have determin’d, are
the moſt advantagious for a perpendicular Pi-
cture.
Mirrours the aforeſaid Inclinations; for the An-
gle A B N may be aſſumed at Pleaſure, from
which muſt be taken an Angle of 135 Degrees,
to have the Inclination of the Miror G H. Ne-
vertheleſs, the Angles we have determin’d, are
the moſt advantagious for a perpendicular Pi-
cture.
29.
When a Picture is inclin’d, and makes
44Fig. 73. the Angle D I A with the Horizon, the Mirrour
M N muſt keep its Situation, and the 5524. C Q R is equal to half the Angle D I A, leſs
{1/4} of a right Angle: Then I ſay, the Angle
FaC, or its equal C R Q, will be equal to the
Angle B I D. Now the Angle P B Q, is 112 {1/2}. 6611. Degrees; whence the Angle B P Q, which is the
Complement of P B Q, and P Q B to two right
Angles, is 90 Degrees, leſs the half of the 7727. gle D I A: Wherefore becauſe N B C is 67 {1/2}
44Fig. 73. the Angle D I A with the Horizon, the Mirrour
M N muſt keep its Situation, and the 5524. C Q R is equal to half the Angle D I A, leſs
{1/4} of a right Angle: Then I ſay, the Angle
FaC, or its equal C R Q, will be equal to the
Angle B I D. Now the Angle P B Q, is 112 {1/2}. 6611. Degrees; whence the Angle B P Q, which is the
Complement of P B Q, and P Q B to two right
Angles, is 90 Degrees, leſs the half of the 7727. gle D I A: Wherefore becauſe N B C is 67 {1/2}
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