The Elements of EuclidDesilver, Thomas, 1838 - 416 σελίδες |
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Σελίδα 156
... 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 . XIX . The axis of a cone is the fixed straight line about which the triangle revolves . XX . The base of ...
... 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 . XIX . The axis of a cone is the fixed straight line about which the triangle revolves . XX . The base of ...
Σελίδα 157
... cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is a solid figure contained by six equal squares . XXVI . A tetrahedron is a solid figure contained by four equal and ...
... cones and cylinders are those which have their axes and the diameters of their bases proportionals . XXV . A cube is a solid figure contained by six equal squares . XXVI . A tetrahedron is a solid figure contained by four equal and ...
Σελίδα 214
... Cone is a 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 a 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 ...
Σελίδα 215
... cone . Let them be those upon the segments of the circle AE , EB , BF , FC , CG , GD , DH , HA . Therefore the rest ... cone : but this prism is triple ( 1. Cor . 7. 12. ) of the pyramid upon the same base , of which the ver- tex is the ...
... cone . Let them be those upon the segments of the circle AE , EB , BF , FC , CG , GD , DH , HA . Therefore the rest ... cone : but this prism is triple ( 1. Cor . 7. 12. ) of the pyramid upon the same base , of which the ver- tex is the ...
Σελίδα 216
Euclid Robert Simson. A D G cone , which together shall be less than the excess of the cone above the third part of the cylinder . Let these be the segments upon AE , EB , BF , FC , CG , GD , DH , HA . Therefore the rest of the cone ...
Euclid Robert Simson. A D G cone , which together shall be less than the excess of the cone above the third part of the cylinder . Let these be the segments upon AE , EB , BF , FC , CG , GD , DH , HA . Therefore the rest of the cone ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gles gnomon greater join less Let ABC multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopiped square of AC square of BC straight line AB straight line BC tangent THEOR triangle ABC triplicate ratio vertex wherefore
Δημοφιλή αποσπάσματα
Σελίδα 34 - If a straight line be divided into any two parts, the squares of the whole line and of one of the parts are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts at the point C : the squares of AB, BC shall be equal to twice the rectangle AB, BC, together with the square of AC.
Σελίδα 143 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, 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 on the straight line which bisects the angle.
Σελίδα 63 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 246 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.
Σελίδα 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Σελίδα 119 - 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.
Σελίδα 19 - 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.
Σελίδα 12 - To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third (20.
Σελίδα 78 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.