Elements of geometry and trigonometry . PROPOSITION XIV. THEOREM. If the distance between the centres of two circles is equal to thedifference of their radii, the two circles will touch each otherinternally. Let C and D be the centres at a dis-tance from each other equal to AD—CA. It is evident, as before, that they willhave the point A common : they can haveno other; because, if they had, the greaterradius AD must be less than the sum ofthe radius AC and the distanceCD betweenthe centres (Prop. XIL) ; which is contraryto the supposition. Cor. Hence, if two circles touch each other, either ext
Elements of geometry and trigonometry . PROPOSITION XIV. THEOREM. If the distance between the centres of two circles is equal to thedifference of their radii, the two circles will touch each otherinternally. Let C and D be the centres at a dis-tance from each other equal to AD—CA. It is evident, as before, that they willhave the point A common : they can haveno other; because, if they had, the greaterradius AD must be less than the sum ofthe radius AC and the distanceCD betweenthe centres (Prop. XIL) ; which is contraryto the supposition. Cor. Hence, if two circles touch each other, either exteinally or internally, their centres and the point of contact willbe in the same right line. Scholium. All circles which have their centres on the righthne AD, and which pass through the point A, are tangent toeach other. For, they have only the point A common, and itthrough the point A, AE be drawn perpendicular to AD, thestraight line AE will be a common tangent to all the
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Keywords: ., bo, bookcentury1800, booksubjectgeometry, booksubjecttrigonometry
