## Treatise on Elementary Geometry |

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ABCD adjacent altitude base bisects BOOK called centre chord circle circumference circumscribed coincide common cone consequently construct contained Corollary cylinder Definition describe diagonal diameter diedral angle difference distance divided draw drawn edges equal equivalent Exercise extremities faces fall feet figure follows formed four given circle given line given point given straight line greater half Hence hypotenuse increased indefinitely inscribed intersection joining lateral length less limit locus mean measure meet middle point number of sides one-half opposite parallel parallelogram pass perimeter perpendicular placed plane polygon prism problem proportional Proposition XIV prove pyramid radii radius ratio rectangle regular regular inscribed regular polygon respectively right angles right triangle Scholium segments sides similar sphere spherical square Suggestion surface tangent Theorem third triangle triangle ABC unit vertex vertices volume

### Popular passages

Page 137 - Two triangles having 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 117 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.

Page 63 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.

Page 38 - The sum of the three angles of any triangle is equal to two right angles.

Page 184 - If two triangles have two sides of the one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side.

Page 277 - 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 249 - 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 52 - 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 80 - An angle formed by two chords intersecting within the circumference is measured by one-half the sum of the arcs intercepted between its sides and between the sides of its vertical angle.

Page 190 - If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle : 1st.