225120An ESSAY, &c.
A Demonſtration of the Inclination of the Looking-
Glaſs.
Glaſs.
48.
Let A B be a Ray, proceeding from ſome
11Fig, 75. Point of an Object. We are to demonſtrate, 2219. if the Line D I hath the Inclination given to a
Picture, and the Looking-Glaſs G H hath the In-
clination we have preſcribed, that the Angle
B a F, will be equal to the Angle B C D. Now to
prove this, draw the Line F I parallel to the Ho-
rizon, then the two Angles I D F and D F I, of
the Triangle I D F, are together equal to the
Angle D I E; but the Angle D F I, which is the
Inclination of the Looking-Glaſs, is equal 3316. 47. half the Angle D I E, leſs half the Angle I F a;
and conſequently it is leſs than the Angle F D I,
by the Quantity of the whole Angle I F a:
Therefore if the Angle I F a be added to the An-
gle D F I, we ſhall have the Angle D F a, equal
to the Angle F D I: Therefore the Angle
Fa B will be likewiſe equal to the Angle BCD. 4419. Which was to he demonſtrated.
11Fig, 75. Point of an Object. We are to demonſtrate, 2219. if the Line D I hath the Inclination given to a
Picture, and the Looking-Glaſs G H hath the In-
clination we have preſcribed, that the Angle
B a F, will be equal to the Angle B C D. Now to
prove this, draw the Line F I parallel to the Ho-
rizon, then the two Angles I D F and D F I, of
the Triangle I D F, are together equal to the
Angle D I E; but the Angle D F I, which is the
Inclination of the Looking-Glaſs, is equal 3316. 47. half the Angle D I E, leſs half the Angle I F a;
and conſequently it is leſs than the Angle F D I,
by the Quantity of the whole Angle I F a:
Therefore if the Angle I F a be added to the An-
gle D F I, we ſhall have the Angle D F a, equal
to the Angle F D I: Therefore the Angle
Fa B will be likewiſe equal to the Angle BCD. 4419. Which was to he demonſtrated.
In reaſoning nearly after the ſame Manner,
we demonſtrated what is mentioned 5547. ning the Inclination of the Mirrour, when the
Box is inclin’d a little backwards.
we demonſtrated what is mentioned 5547. ning the Inclination of the Mirrour, when the
Box is inclin’d a little backwards.
FINIS.