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ABCD alſo be equal alſo equal alternate angle altitude angle ABC angle ACB angle BAC angle CAB angle CBD baſe becauſe biſect Book centre chord circle circle ABC circumference common Conft conſequently contained COROLL demonſtrated deſcribe diagonal diameter difference diſtance divide double draw drawn equiangular equimultiples EUCLID fall fame fide figure fince firſt four given point given right line greater half interſects leſs Let ABC line Ac magnitudes meet muſt oppoſite angle outward angle parallel parallelogram perpendicular plane polygon PROBLEM produced Prop proportional propoſition rectangle remaining angle reſpects right angles ſame ſame manner ſame multiple ſection ſegment ſhall ſhewn ſide ſide bc ſince ſome ſquare ſtand ſum taken THEOREM theſe thing third triangle triangle ABC whence whole whoſe
Page 63 - AB is the greater. If from AB there be taken more than its half, and from the remainder more than its half, and so on ; there shall at length remain a magnitude less than C. For C may be multiplied, so as at length to become greater than AB.
Page 23 - To find the centre of a given circle. Let ABC be the given circle ; it is required to find its centre. Draw within it any straight line AB, and bisect (I.
Page 63 - Lemma, if from the greater of two unequal magnitudes there be taken more than its half, and from the remainder more than its half, and so on, there shall at length remain a magnitude less than the least of the proposed magnitudes.
Page 24 - IN a given circle to inscribe a triangle equiangular to a given triangle. Let ABC be the given circle, and DEF the given triangle ; it is required to inscribe in the circle ABC a triangle equiangular to the triangle DEF. Draw* the straight line GAH touching the circle in the a 17. 3. point A, and at the point A, in the straight line AH, makeb b 23.
Page 21 - The radius of a circle is a right line drawn from the centre to the circumference.
Page 30 - To bisect a given arc, that is, to divide it into two equal parts. Let ADB be the given arc : it is required to bisect it.
Page 7 - Beciprocally, when these properties exist for 'two right lines and a common secant, the two lines are parallel.* — Through a given point, to draw a right line parallel to a given right line, or cutting it at a given angle, — Equality of angles having their sides parallel and their openings placed in the same direction.