Geometrical Drawing
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Note. — It is not possible to inscribe a circle in a rectangle, with adjacent sides unequal, or in some other symmetrical figures.
2. To inscribe a square in a Symmeirical Figure (e.g. in a Begular Pentagon).
B Draw a diagonal AG, cutting off one vertex, B. On the side oi AG remote from B, draw the perpendicular GE, equal to AG. Join EB, cutting GB in F. Draw FG parallel to GE, and EG parallel to AG, and complete the figure FGHK, which is a square.
36 GEOMETRICAL DRA WING. [Chap. IV.
* Pkoof. F...G, GH are parallel to EC, GA respectively.
.-. lFGE= Ll!GA = ^(i°.
Also from the similar triangles BGH, BGA, EG:AG::BG:BO. (Chap. v. § 2.) And from the similar triangles BGF, BOB.
BG -.BG-.-.GF-.GE.
.:HG:AG::GF:GB. (Chap. V. § 3.) But AG= CE, by construction ; :.EG=GF.
Hence, by symmetry, the figure is a square.
COK. I. " To inscribe a square, in a semicircle" is only a particular case of inscribing a square in a sector of Chap. IV.] FIGURES IN SYMMETRICAL FIGURES. 37 a circle the diagonal being AG, and the vertex, B, the centre of the semicircle.
What to read after Geometrical Drawing?
You can find similar books in the "Read Also" column, or choose other free books by Wilson, W. N to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
Note. — It is not possible to inscribe a circle in a rectangle, with adjacent sides unequal, or in some other symmetrical figures.
2. To inscribe a square in a Symmeirical Figure (e.g. in a Begular Pentagon).
B Draw a diagonal AG, cutting off one vertex, B. On the side oi AG remote from B, draw the perpendicular GE, equal to AG. Join EB, cutting GB in F. Draw FG parallel to GE, and EG parallel to AG, and complete the figure FGHK, which is a square.
36 GEOMETRICAL DRA WING. [Chap. IV.
* Pkoof. F...G, GH are parallel to EC, GA respectively.
.-. lFGE= Ll!GA = ^(i°.
Also from the similar triangles BGH, BGA, EG:AG::BG:BO. (Chap. v. § 2.) And from the similar triangles BGF, BOB.
BG -.BG-.-.GF-.GE.
.:HG:AG::GF:GB. (Chap. V. § 3.) But AG= CE, by construction ; :.EG=GF.
Hence, by symmetry, the figure is a square.
COK. I. " To inscribe a square, in a semicircle" is only a particular case of inscribing a square in a sector of Chap. IV.] FIGURES IN SYMMETRICAL FIGURES. 37 a circle the diagonal being AG, and the vertex, B, the centre of the semicircle.
What to read after Geometrical Drawing?
You can find similar books in the "Read Also" column, or choose other free books by Wilson, W. N to read onlineMoreLess
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