## Chauvenet's Treatise on Elementary Geometry |

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### Common terms and phrases

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

### Popular passages

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

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 268 - Any line or plane tangent to a sphere is perpendicular to the radius drawn to the point of contact.

Page 278 - Each side of a spherical triangle is less than the sum of the other two sides.

Page 85 - At a given point in a given straight line, to construct an angle equal to a given angle. Let A be th,e given point in the straight line AB, and O the given angle.

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 285 - The shortest line that can be drawn on the surface of a sphere between two points is the arc of a great circle, not greater than a semicircumference, joining the two points.

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.