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abcd ac is equal angle abc angle acb angle bad angle cab angle cba base and altitude bisect Book centre chord circle abc circumserence consequently the angle Const Coroll demonstration diagonal diameter draw drawn equal and parallel equal angles equal bases equal to bc equi equiangular Euclid faid fame base fame manner fame multiple fame plane fame ratio given circle given right line greater inscribed intersect join the points klmn less Let abc Let the right opposite angles outward angle parallelepipedons parallelogram pentagon perpendicular point f polygon prism proportional proposition Q. E. D. PROP radii rectangle of ac remaining angle right angles Scholium segment shewn side ac solid squares of ac taken tangent Theorem triangle abc triangle def twice the rectangle
Page 166 - 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.
Page 215 - 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 117 - 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 point A (III. 17), and at the point A, in the straight line AH, make the angle HAG equal to the angle DEF (I.
Page 18 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it. LET ab be the given straight line, which may be produced to any length both ways, and let c be a point without it. It is required to draw a straight line perpendicular to ab from the point c.
Page 249 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Page 102 - 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 i - Handbook to the First London BA Examination. Lie (Jonas). SECOND SIGHT; OR, SKETCHES FROM NORDLAND. By JONAS LIE. Translated from the Norwegian. [/» preparation. Euclid. THE ENUNCIATIONS AND COROLLARIES of the Propositions in the First Six and the Eleventh and Twelfth Books of Euclid's Elements.
Page 5 - AXIOM is a self-evident truth ; such as, — 1. Things which are equal to the same thing, are equal to each other. 2. If equals be added to equals, the sums will be equal. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal.