## The Eclectic School Geometry |

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### Common terms and phrases

ABCD altitude base bisect Book called chord circle circumference circumscribed coincide common Complete cone consequently construct contained definition describe diagonal diameter difference divided draw drawn equal to half equally distant equilateral triangle equivalent exterior angles faces fall feet figure formed four given line given point greater half the product height Hence hexagon hypotenuse included inscribed intersect isosceles joining length less locus measured by half multiplied oblique opposite parallel parallelogram pass perimeter perpendicular plane PROBLEM proportional Prove pyramid quadrilateral Ques radii radius ratio rectangle regular polygon remaining respectively right angles right-angled triangle segment shown sides similar sphere square straight line taken tangent Theo THEOREM third triangle unit vertex volume whole XXVI XXXIII

### Popular passages

Page 64 - 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 31 - If two triangles have two sides of the one equal to two sides of the...

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 60 - It follows, then, that the area of a circle is equal to half the product of its circumference and its radius.

Page 67 - 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 87 - 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 40 - The area of any parallelogram is equal to the area of a rectangle having the same base and altitude.

Page 86 - 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.