## The Eclectic School Geometry: A Revision of Evan's School Geometry |

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### Common terms and phrases

ABCD altitude Axiom axis base bisect Book called chord circle circumference coincide common Complete cone consequently construction contained convex surface definition describe diagonal diameter divided draw drawn edges equal equal to half equally distant equilateral equivalent exterior angle faces fall figure four Geometry given given line given point greater Hence hypotenuse hypothesis included inscribed intersection isosceles Join length less mean measured by half meet multiplied opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane prism PROBLEM proportional Prove pyramid quadrilateral Ques radius ratio rectangle remainder respectively right angles segment shown sides similar slant height solid sphere square straight line taken tangent Theo THEOREM third triangle triangle ABC triedral unit vertex volume whole

### Popular passages

Page 104 - If from a point without a circle, a tangent and a secant be drawn, the tangent will be a mean proportional between the secant and its external segment.

Page 32 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.

Page 54 - The circumference of every circle is supposed to' be divided into 360 equal parts, called degrees ; each degree into 60 minutes, and each minute into 60 seconds. Degrees, minutes, and seconds are designated by the characters °, ', ". Thus 23° 14' 35" is read 23 degrees, 14 minutes, and 35 seconds.

Page 42 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.

Page 107 - The areas of two circles are to each other as the squares of their radii. For, if S and S' denote the areas, and R and R

Page 147 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 140 - A cone is a solid figure described by the revolution of a right-angled triangle about one of the sides containing the right angle, which side remains fixed.

Page 50 - The area of a regular polygon is equal to half the product of its apothem and perimeter.

Page 141 - The altitude of a pyramid or cone is the perpendicular distance from the ve~rtex to the base.

Page 39 - The area of a rectangle is equal to the product of its base and altitude.