## An Elementary Treatise on Geometry: Simplified for Beginners Not Versed in Algebra. Part I, Containing Plane Geometry, with Its Application to the Solution of Problems, Part 1 |

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adjacent angles angle ABC angle ACB angle x basis bisected called centre chord circle whose radius circum circumference consequently degrees DEMON diagonal diameter dividing the product draw the lines equal angles equal sides equal triangles exterior angle feet figure ABCDEF found by multiplying fourth term geometrical proportion given angle given circle given triangle gles height hypothenuse inches isosceles triangle JOHN FARRAR length let fall line AB line AC line CD line MN mean proportional measures half number of sides parallel lines parallelogram ABCD perpendicular Plane Geometry points of division PROBLEM prove quadrilateral radii radius rectangle rectilinear figure regular inscribed regular polygon ABCDEF Remark rhombus right angles right-angled triangle second term Sect semicircle side AB side AC similar triangles smaller SOLUTION subtended tangent third line third term three angles three sides trapezoid triangle ABC triangles are equal Truth vertex

### Popular passages

Page 144 - Upon a given straight line to describe a segment of a circle, which shall contain an angle equal to a given rectilineal angle.

Page 68 - If two triangles have two sides of the one equal to two sides of the other, each to each, but the...

Page 124 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.

Page 111 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.

Page 106 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.

Page 117 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems.

Page 144 - A, with a radius equal to the sum of the radii of the given circles, describe a circle.

Page 80 - ... any two triangles are to each other as the products of their bases by their altitudes.

Page 125 - P is at the center of the circle. II. 18. The sum of the arcs subtending the vertical angles made by any two chords that intersect, is the same, as long as the angle of intersection is the same. 19. From a point without a circle two straight lines are drawn cutting the convex and concave circumferences, and also respectively parallel to two radii of the circle. Prove that the difference of the concave and convex arcs intercepted by the cutting lines, is equal to twice the arc intercepted by the radii.