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ABCD altitude approach axis base bisect bisector called centre chord circle circumscribed coincide common Comparing Conclusion cone construction contained Corollary corresponding curve definition describe diagonals diameter difference dihedral angle direction distance divided draw drawn edges ellipse equal angles equally distant expressed exterior angle faces fall figure four geometry given greater half Hence hyperbola Hypothesis identically equal indefinitely inscribed intersection Join lateral length less limit magnitude mean measured meet pair parallel parallelogram pass perpendicular plane poles polygon position prism PROBLEM produced Proof proportion pyramid Q.E.D. THEOREM radius ratio rectangle regular respectively right angles segments shown sides similar solid sphere spherical square straight angle straight line suppose surface tangent THEOREM third touch triangle turned vertex vertices volume whence whole
Pagina 146 - In an obtuse-angled triangle the square on the side opposite the obtuse angle is greater than the sum of the squares on the other two sides by twice the rectangle contained by either side and the projection on it of the other side.
Pagina 44 - Every point in the bisector of an angle is equally distant from the sides of the angle...
Pagina 149 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Pagina 45 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Pagina 103 - A rectilineal figure is said to be described about a circle, when each side of the circumscribed figure touches the circumference of the circle. V. In like manner, a circle is said to be inscribed...
Pagina 235 - ten decimals are sufficient to give the circumference of the earth to the fraction of an inch, and thirty decimals would give the circumference of the whole visible universe to a quantity imperceptible with the most powerful microscope.
Pagina 90 - The sum of the three straight lines drawn from any point within a triangle to the three vertices, is less than the sum and greater than the half sum of the three sides of the triangle (I . 33, 66).
Pagina 168 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.