The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, The Book of Euclid's Data, in Like Manner Corrected. viz. the first six books, together with the eleventh and twelfthMathew Carey, and sold by J. Conrad & Company, S. F. Bradford, Birch & Small, and Samuel Etheridge. Printed by T. & G. Palmer, 116, High-Street., 1806 - 518 sider |
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Side 197
... cone is called a right angled cone ; if it be less than the other side , an obtuse angled , and if greater , an acute angled cone . Book XI . XIX . The axis of a cone OF EUCLID . 197.
... cone is called a right angled cone ; if it be less than the other side , an obtuse angled , and if greater , an acute angled cone . Book XI . XIX . The axis of a cone OF EUCLID . 197.
Side 198
... cone is the circle described by that side containing the right angle , which revolves . XXI . A cylinder is a solid ... cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is ...
... cone is the circle described by that side containing the right angle , which revolves . XXI . A cylinder is a solid ... cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is ...
Side 269
... cone is the third part of a cylinder which has the same base , and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude . The cone is the third part of the ...
... cone is the third part of a cylinder which has the same base , and is of an equal altitude with it . Let a cone have the same base with a cylinder , viz . the circle ABCD , and the same altitude . The cone is the third part of the ...
Side 270
... segments of the cylinder which together are less c than the excess of the cylinder above the triple of the cone . Let them be those upon the segments of the circle AE , EB , BF , ma . E A H D G FC , CG , GD 270 THE ELEMENTS.
... segments of the cylinder which together are less c than the excess of the cylinder above the triple of the cone . Let them be those upon the segments of the circle AE , EB , BF , ma . E A H D G FC , CG , GD 270 THE ELEMENTS.
Side 271
... cone , of which the base is the circle ABCD : but it is also less , for the pyramid is contained within the cone ; which is impossible . Nor can the cylinder be less than the triple of the cone . Let it be less , if possible : therefore ...
... cone , of which the base is the circle ABCD : but it is also less , for the pyramid is contained within the cone ; which is impossible . Nor can the cylinder be less than the triple of the cone . Let it be less , if possible : therefore ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given point given ratio given straight line gnomon greater join less Let ABC meet multiple opposite parallel parallelogram perpendicular point F polygon prisms proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure right angles segment sides BA similar sine solid angle solid parallelepipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore
Populære avsnitt
Side 30 - Any two sides of a triangle are together greater than the third side.
Side 64 - 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.
Side 30 - IF, from the ends of the side of a triangle, there be drawn two straight lines to a point within the triangle, these shall be less than the other two sides of the triangle, but shall contain a greater angle. Let...
Side 59 - PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour 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.
Side 28 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Side 165 - 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.
Side 19 - THE angles at the base of an isosceles triangle are equal to one another : and, if the equal sides be produced, the angles upon the other side of the base shall be equal.
Side 191 - In right angled triangles, the rectilineal figure described upon the side opposite to the right angle, is equal to the similar, and similarly described figures upon the sides containing the right angle.
Side 39 - 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 sidef. For any rectilineal figure ABCDE can be divided into as many triangles as the figure has sides, by drawing straight lines from a point F within the figure to each of its angles.
Side 180 - Therefore, universally, similar rectilineal figures are to one another in the duplicate ratio of their homologous sides.