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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 circumference consequently the angle Const Coroll demonstration diagonal diameter draw drawn equal and parallel equal angles equal bases equal to cb equi equiangular Euclid faid fame base fame manner fame multiple fame plane fame ratio fame right line fide given circle given right line inscribed intersect join the points klmn less Let abc Let the right opposite angle outward angle parallelogram perpendicular point f polygon prism proportional proposition Q.E.D. PROP radii rectangle of ac rectilineal remaining angle right angles Scholium segment shewn side ac sigure sirst solid square 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 71 - Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that part.
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 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 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. 5. If equals be taken from unequals, the remainders will be unequal.
Page 135 - If any number of magnitudes be equimultiples of as many others, each of each, what multiple soever any one of the first is of its part, the same multiple is the sum of all the first of the sum of all the rest.
Page 145 - F is greater than E; and if equal, equal; and if less, less. But F is any multiple whatever of C, and D and E are any equimultiples whatever of A and B; [Construction.