The Elements of Euclid: Explain'd in a New, But Most Easie Method: Together with the Use of Every Proposition Through All Parts of the Mathematicks

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James and John Knapton, 1726 - Euclid's Elements - 366 pages

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Page 125 - If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it.
Page 64 - The proposition which he deduces from it is, that if two angles of one triangle be equal to two angles of another, the third angles of these triangles are also equal.
Page 110 - EF, because AEF is a right angle ; therefore the square of AF is double of the squares of AC, CD : But the squares of AD, DF, are equal to the square of AF, because the angle ADF is a right angle ; therefore the squares of AD, DF are double of the squares of AC, CD : And DF is equal to DB ; therefore the squares of AD, DB are double of the squares of AC, CD.
Page 229 - Because there are three magnitudes A, B, C, and three others D, E, F, which, taken two and two, in order, have the same ratio ; ex sequali, A is to C, as D to F.
Page 218 - B shall be less than D. For C is greater than A ; and because C is to D, as A is to B...
Page 172 - BD, because EBD is a right angle : therefore the rectangle AD, DC, together with the square of EB, is equal to the squares of EB, BD : take away the common square of EB ; therefore the remaining rectangle AD, DC is equal to the square of the tangent DB.
Page 176 - One right-lined figure is Inscribed in another, or the latter circumscribes the former, when all the angular points of the former are placed in the sides of the latter. 67. A Secant is a line that cuts a circle, lying partly within, and partly without it.
Page 99 - If a straight line be divided into two parts, the square of the whole line...
Page 299 - ... angle. In the same manner, the line AB and the line PD, which represent any two straight lines not situated in the same plane, are supposed to form with each other the same angle, which would be formed by AB and a straight line parallel to PD drawn through one of the points of AB. PROPOSITION VII. THEOREM. If one of two parallel lines be perpendicular to a plane, the other will also be perpendicular to the same plane. Let...
Page 290 - Oblique circular cone 706, A circular cone is a cone whose base is a circle. The axis of a circular cone is the line drawn from the vertex to the center of the base. 707. A right circular cone is a circular cone whose axis is perpendicular to the plane of the base. An oblique circular cone is a circular cone Whose axis is oblique to the base. 708. A cone of revolution is a cone generated by the revolution of a right triangle about one of its legs as an axis.

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