## A Treatise on Elementary Geometry: With Appendices Containing a Collection of Exercises for Students and an Introduction to Modern Geometry |

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### Common terms and phrases

ABCD altitude axis base bisects called centre chord circle circumference circumscribed coincide common cone constant construct contain Corollary cylinder Definition denote describe diagonals diameter diedral angle difference distance divided draw drawn edges equal equivalent expressed extremities faces figure fixed follows formed four given circles given plane given point given straight line greater hence homologous indefinitely inscribed intersection joining lateral less limit locus mean measure meet middle point one-half opposite sides parallel parallelogram pass perimeter perpendicular plane plane MN polar pole polyedron polygon preceding prism problem proportional PROPOSITION prove pyramid quadrilateral quantities radii radius ratio rectangle respectively right angles Scholium secant segment sides similar sphere spherical square suppose surface symmetrical taken tangent tetraedron theorem third triangle ABC unit vertex vertices volume

### Popular passages

Page 128 - The area of a rectangle is equal to the product of its base and altitude.

Page 348 - Three lines are in harmonical proportion, when the first is to the third, as the difference between the first and second, is to the difference between the second and third ; and the second is called a harmonic mean between the first and third. The expression 'harmonical proportion...

Page 19 - The perpendicular is the shortest line that can be drawn from a point to a straight line.

Page 79 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.

Page 29 - The sum of the three angles of any triangle is equal to two right angles.

Page 175 - If a straight line is perpendicular to each of two straight lines at' their point of intersection, it is perpendicular to the plane of those lines.

Page 263 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...

Page 219 - A truncated triangular prism is equivalent to the sum of three pyramids, whose common base is the base of the prism and whose vertices are the three vertices of the inclined section.

Page 197 - A right prism is a prism •whose lateral edges are perpendicular to the planes of the bases.

Page 127 - Any two rectangles are to each other as the products of their bases by their altitudes. Let R and R...