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altitude apply base becomes called chord circle circumference common conceive cone contained corresponding Cosine Cotang curve definition demonstration describe determine diameter difference direction distance divide double draw drawn ellipse equal equation expressed extremities fall figure focus four Geometry give given greater half Hence hypotenuse inscribed join length less logarithm magnitudes major axis manner means measured meet multiplied N.sine observing opposite parallel parallelogram passing perpendicular plane polygon PROBLEM produced proportion PROPOSITION prove pyramid quantities radius ratio rectangle represent right angled triangle right angles Scholium segments sides similar sin.b sine solid sphere spherical triangle square straight line subtraction supplement surface taken Tang tangent term THEOREM third triangle ABC trigonometry true units vertex vertical whole
الصفحة 62 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.
الصفحة 24 - If two triangles have two sides of the one equal to two sides of the...
الصفحة 149 - If a perpendicular be let fall from any angle of a triangle to its opposite side or base, this base is to the sum of the other two sides, as the difference of the sides is to the difference of the segments of the base.
الصفحة 48 - In place of adding unity, subtract it, and we shall find that a : a — b :: c : c — d. or a : b — a :: c : d — c. (Theorem 4.) If four magnitudes be proportional, the sum of the first and second is to their difference, as the sum of the third and fourth is to their difference.
الصفحة 110 - If a straight line stand at right angles to each of two straight lines in the point of their intersection, it shall also be at right angles to the plane which passes through them, that is, to the plane in which they are.
الصفحة 21 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
الصفحة 20 - If a side of a triangle be produced, the exterior angle is equal to the sum of the two interior and opposite angles ; and the three interior angles of every triangle are together equal to two right angles.
الصفحة 47 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.