## Elements of Plane Geometry |

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### Common terms and phrases

ABCD acute altitude angle approaches base bisector bisects called chord circle circumference circumscribed common Construct cutting describe diagonals diameter difference divided Draw drawn equal equidistant equilateral equivalent exterior extremities figure Find Find the area formed geometry given given circle given line given point Given the line greater half harmonic Hence hypotenuse included inscribed interior angle intersecting isosceles joining legs length less limit mean measured median meet mid-point parallel parallelogram passes perimeter perpendicular PROBLEM proportional PROPOSITION prove Proof quadrilateral quantities radii radius ratio rectangle regular inscribed regular polygon respectively right angle right triangle secant segments sides Similarly square straight line tangent THEOREM third trapezoid triangle variable vertex vertices

### Popular passages

Page 41 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 42 - ... if two triangles have two sides of one equal, respectively, to two sides of the other...

Page 179 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.

Page 5 - Axioms. 1. Things which are equal to the same thing are equal to each other. 2. If equals are added to equals, the wholes are equal. 3. If equals are taken from equals, the remainders are equal.

Page 135 - Conversely, if the product of two quantities is equal to the product of two other quantities, the first two may be made the extremes, and the other two the means of a proportion.

Page 67 - A Polygon of three sides is called a triangle ; one of four sides, a quadrilateral; one of five sides, a pentagon; one of six sides, a hexagon; one of seven sides, a heptagon; one of eight sides, an octagon ; one of ten sides, a decagon ; one of twelve sides, a dodecagon, &c.

Page 176 - The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side.

Page 173 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides by the projection of the other upon that side.

Page 17 - In a right triangle, the side opposite the right angle is called the hypotenuse, and the other two sides the legs.

Page 202 - Assuming that 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...