## Chauvenet's Treatise on Elementary Geometry |

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ABCD adjacent altitude angles are equal base 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 equal equally distant equivalent Exercise extremities faces fall figure follows formed four frustum given line given point given straight line greater half Hence increased indefinitely inscribed intersection isosceles joining lateral edges length less limit locus mean measure meet middle point one-half opposite parallel parallelogram parallelopiped pass perimeter perpendicular placed plane polyedron polygon prism problem proportional PROPOSITION Proposition VII prove pyramid radii radius ratio rectangle rectangular regular polygon respectively right angles Scholium segment sides similar sphere spherical square Suggestion surface tangent Theorem third triangle triangle ABC triangular 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 133 - The area of a rectangle is equal to the product of its base and altitude.

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 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 270 - A spherical polygon is a portion of the surface of a sphere bounded by three or more arcs of great circles. The bounding arcs are the sides of the polygon ; the...

Page 268 - A plane tangent to a sphere is perpendicular to the radius drawn to the point of contact.

Page 269 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). Let AB, AC be arcs of great circles intersecting at A; AB...

Page 128 - Find the locus of a point the sum of whose distances from two given straight lines is equal to a given constant, k.

Page 214 - The acute angle which a straight line makes with its projection upon a plane is the least angle which it makes with any line of the plane.

Page 116 - If a perpendicular is drawn from the vertex of the right angle to the hypotenuse of a right triangle : 1st.