## Plane and Solid Geometry |

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### Common terms and phrases

A B C adjacent Axiom base bisects BOOK chord circle circumference circumscribed coincide common Conclusion cone Construction Corollary corresponding cylinder DEFINITIONS Demonstration diagonals diameter difference direction distance divided draw drawn edges equal equal angles equally distant equilateral equivalent exterior extremities faces fall figure Find follows four given line given point given straight line greater half hypotenuse inscribed interior angles intersection isosceles triangle joining lateral surface less lines drawn measured meet middle point MISCELLANEOUS EXERCISES oblique lines opposite sides parallel parallelogram parallelopiped pass perimeter perpendicular Place plane polygon position prism problem PROP proportional PROPOSITION proved equal pyramid quadrilateral quantities radii radius rectangle regular respectively right angles right-angled triangle segments similar solid sphere spherical square Statement straight line tangent Theorem triangle unequal vertex vertical angle VIII volume

### Popular passages

Page 176 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.

Page 287 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.

Page 91 - The straight line joining the middle points of two sides of a triangle is parallel to the third side, and equal to half of it.

Page 135 - If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.

Page 154 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the center; as the figure ADB E.

Page 76 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.

Page 293 - The square of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two sides.

Page 59 - 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 60 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 139 - 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.