Chauvenet's Treatise on Elementary Geometry

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J.B. Lippincott Company, 1889 - Geometry - 322 pages
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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.

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