First Mnemonical Lessons in Geometry Algebra And Trigonometry
First Mnemonical Lessons in Geometry Algebra And Trigonometry
T P Thomas Penington Kirkman
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Rad. Of semp. Is Ar'e, Are is one syl. ; of is x. (K) Four out. Is bac by Are. Bac a monosyl. . DJawictiT of out (i. E. Circumscribed) circle is the quotient or ratio ba : perc. Vitl. [11! | ; to is here equivalent to by. The inscribed mcfius of (i. E. Limes, vid. [SoC. ]) scnnjienmcicx — Arc (French for area) : four out (radii ) - bac by Area. ; or Ali = 6ac:A. § 43. ] FIRST MNEMONICAL LESSONS. 95 If DA be the bisector of the angle at A below the base AB, the perpendiculars Df, Dg, and De are ...still equal as before: and DB being then joined is proved as before to be the bisector of the angle at B, below the base. Hence a circle whose centre is D and radius De will touch the sides of the triangle below the base in ef and g. We have also (Prop. B, 20), A C x Df+ BBxDe- AB xDg = twice the a ABC, or r, (a + 6-c) = 2A, and exactly in the same manner, r 2 (a — b + c) = 2 a, r 3 (- a + b + c) = 2 a ; putting r l r 2 and r 3 for the radii of the cirles touching the sides below the bases c b and a.
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