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adapted to Book angle equal APPENDIX TO EUCLID'S base angles centre chords circles touch circular segments circum circumference circumscribing circle construct the triangle diameter equal angles equimultiples EUCLID'S ELEMENTS four magnitudes given angle given circle given in magnitude given in position given in species given magnitude given parallelogram given point given ratio given rational numbers given straight line Given the ratios Given the sum given triangle greater hypothenuse inscribed or circumscribing isosceles triangle lines be drawn multiple number of equal number of magnitudes number of sides number of straight obtuse angle opposite angles opposite sides parallel straight lines parallelogram given parallelopiped polygon PROP Propositions adapted quadrilateral inscribed radius ratio compounded regular polygon rhombus right angled triangle right cylinder sides and diagonals solid angles square straight line bisecting sum and difference sum or difference superficies tangent three angles trapezium triangle be given vertex vertical angle XVIII XXIII
Page 36 - if the segments of the base produced, have the same ratio which the other sides of the triangle have, the straight line drawn from the vertex to the point of section divides the outward angle of the triangle into two equal angles. PROP. IV.
Page 42 - the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square of the straight line bisecting the angle.
Page 31 - PROP. E. If four magnitudes be proportionals, they are also proportionals by conversion: that is, the first is to its excess above the second, as the third to its excess above the fourth. . PROP. XX.
Page 28 - of the second, or the same part of it, that the third is of the fourth; the first is to the second, aS the third is to the fourth. PROP. D.
Page 51 - .Solid parallelepipeds contained by parallelograms equiangular to one another, each to. each, that is, of which the solid angles are equal, each to each, have to one another the ratio which . is the same with the ratio compounded of > the - ratios of their sides. PROP. XXXIV.
Page 43 - The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.
Page 32 - PROP. XXIII. If there be any number of magnitudes and as many others, which, taken two and two, in cross order, have the same ratio;
Page 43 - If from any angle of a triangle a straight line be drawn perpendicular to the base; the rectangle contained by the sides of the triangle is equal to the rectangle contained by the perpendicular and the diameter of the circle described about the triangle. PROP. D. The rectangle contained by the diagonals of a quadrilateral inscribed in a circle, is equal to both the rectangles contained by its opposite sides.