## Plane and Solid Geometry |

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### Common terms and phrases

ABCD altitude base bisector bisects called chord circle circumference circumscribed coincide common cone Consequently Construct contained corresponding cylinder Data diagonals diameter difference dihedral angles direction distance divide Draw drawn edges equal equidistant equivalent exterior extremities faces figure Find formed frustum given given line given point greater half Hence homologous included inscribed intercepted interior angles intersecting isosceles triangle joining lateral length less limit mean measure meet middle point opposite sides parallel parallel lines parallelogram parallelopiped pass perimeter perpendicular plane polygon prism produced Proof proportion Proposition prove pyramid quadrilateral radii radius ratio rect rectangle reference Represent respectively right angles right triangle segments sides similar sphere spherical triangle square straight line student surface tangent Theorem third triangle vertex vertical angle volume

### Popular passages

Page 67 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.

Page 47 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

Page 64 - From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other...

Page 33 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.

Page 219 - 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 217 - The. sum of the angles of any polygon is equal to twice as many right angles as the polygon has sides, less four right angles.

Page 136 - The first and fourth terms of a proportion are called the extremes, and the second and third terms, the means. Thus, in the foregoing proportion, 8 and 3 are the extremes and 4 and 6 are the means.

Page 90 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.

Page 374 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 176 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.