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Euclid's Elements [Book 1-6] with Corrections, by J.R. Young
Sin vista previa disponible - 2018
AC is equal adjacent angles alternate angles angle ABC angle ACB angle BAC angle BCD angle EDF angles equal antecedent arc BC base BC bisected centre circle ABC circumference consequent demonstrated described diameter double draw equal angles equalf equiangular equilateral and equiangular equimultiples Euclid exterior angle fore Geometry given circle given straight line gnomon greater Hence inscribed join less Let ABC Let the straight logarithm multiple opposite angle parallel parallelogram pentagon perpendicular PROB proportion proposition q. e. d. PROP radius rectangle contained rectilineal figure remaining angle segment side BC similar similar triangles sine square of AC straight line AC tangent THEOR tHyp touches the circle triangle ABC triangle DEF Trigonometry twice the rectangle wherefore
Página 30 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Página 50 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 61 - If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line.
Página 65 - If 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.
Página 70 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Página 41 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 172 - 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.
Página 45 - TRIANGLES upon the same base, and between the same parallels, are equal to one another.
Página 38 - If a, straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another; and the exterior angle equal to the interior and opposite upon the same side; and likewise the two interior angles upon the same side together equal to two right angles.