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«Š’›Õ… 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.Ģ
«Š’›Õ… 13 - AXIOMS. 1. Things which are equal to the same thing are equal to one another.Ģ
«Š’›Õ… 24 - If two triangles have two sides of the one equal to two sides of the...Ģ
«Š’›Õ… 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.Ģ
«Š’›Õ… 48 - In place of adding unity, subtract it, and we shall find that a : a ó b :: c : c ó d. or a : b ó a :: c : d ó 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.Ģ
«Š’›Õ… 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.Ģ
«Š’›Õ… 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.Ģ
«Š’›Õ… 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.Ģ
«Š’›Õ… 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.Ģ
«Š’›Õ… 173 - I measured 312 yards in a right line by the side of the river, and then found that the two angles, one at each end of this line, subtended by the other end and the house, were 31į 15Ģ