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ABCD according angle BAC antecedent base bisected Book called centre chord circumference circumscribed coincide common consequent Conversely corresponding denoted described diagonals diameter difference distances divided draw drawn duplicate ratio equal equal circles equiangular externally extremes fall fixed four fourth given circle given point given ratio given straight line greater Hence homologous sides inscribed internally intersect kind less lies line joining magnitudes manner meet minor arc multiple parallel parallelogram passes perpendicular polygon PROB produced proportional Prove quadrilateral radii radius ratio compounded rectangle BD rectangle contained rectilineal figure regular respectively right angles sector segment Shew sides similar similarly square standing straight line taken tangent THEOR third triangle ABC vertical angle whole
Pagina 167 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Pagina 169 - If four straight lines be proportionals, the rectangle contained by the extremes is equal to the rectangle contained by the means...
Pagina 30 - In the same circle, or in equal circles, equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Pagina 171 - ... are to one another in the duplicate ratio of their homologous sides.
Pagina 150 - 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.
Pagina 115 - IF any number of magnitudes be proportionals, as one of the antecedents is to its consequent, so shall all the antecedents taken together be to all the consequents. Let...
Pagina 101 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.
Pagina 96 - ... if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle be equal to the square of the line which meets it, the line which meets shall touch the circle.
Pagina 150 - When there are any number of magnitudes of the same kind, the first is said to have to the last of them the ratio compounded of the ratio which the first has to the second, and of the ratio whi.ch the second has to the third, and of the ratio which the third has to the fourth, and so on unto the last magnitude. For example, if A, B, C, D be four magnitudes of the same kind, the first...