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acute angle angles are equal arcs axis base bisecting the angle Calculus centre chord circle circumference circumscribed Cloth College cone construct conversely curve cylinder diameter difference dihedral angles distances divide drawn edges Elements ellipse equal altitudes equal bases equal respectively equivalent extremities figure focus foot formed four frustum Geometry given line given point given straight line greater homologous hyperbola hypotenuse inscribed intercepted interior angles intersection introduction joining lateral area less line drawn line parallel Mailing price mean proportional meet middle points number of sides opposite parabola parallel parallel lines parallelogram passed perimeter perpendicular placed plane plane perpendicular point of contact prism problems Professor of Mathematics proportional proposition pyramid radius ratio regular inscribed regular polygon respectively right angles right triangle segment similar sphere spherical spherical triangle square surface taken tangent THEOREMS third side triangles are equal unequal University vertex vertices volume
Side 8 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Side 9 - 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 46 INTERCEPTS BY PARALLEL LINES.
Side 15 - If four quantities are in proportion, they are in proportion by composition; that is, the sum of the first two terms is to the second term as the sum of the last two terms is to the fourth term.
Side 11 - The locus of the middle points of a system of parallel chords is the diameter perpendicular to them.
Side 24 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.
Side 8 - ... is greater than the third side of the second, then the angle opposite the third side of the first triangle is greater than the angle opposite the third side of the second.
Side 15 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.
Side 29 - If from the foot of a perpendicular to a plane a straight line is drawn at right angles to any line in the plane, the line drawn from its intersection with the line in the plane to any point of the perpendicular is perpendicular to the line of the plane. Let AB be a perpendicular to the plane MN, BE a perpendicular from B to any line CD in MN, and EA any line from E to AB.