The Elements of EuclidDesilver, Thomas, 1838 - 416 páginas |
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Página 156
... prism is a solid figure contained by plane figures , of which two that are opposite are equal , similar , and parallel to one another ; and the others parallelograms . XIV . A sphere is a solid figure described by the revolution of a ...
... prism is a solid figure contained by plane figures , of which two that are opposite are equal , similar , and parallel to one another ; and the others parallelograms . XIV . A sphere is a solid figure described by the revolution of a ...
Página 181
... prism contained by the two triangles CGF , DAE , and the three parallel- ograms CA , GE , EC , is equal ( C. 11. ) to the prism contained by the two triangles CBF , DHE , and the three parallelograms BE , CH , EC ; because they are ...
... prism contained by the two triangles CGF , DAE , and the three parallel- ograms CA , GE , EC , is equal ( C. 11. ) to the prism contained by the two triangles CBF , DHE , and the three parallelograms BE , CH , EC ; because they are ...
Página 182
... prism which is contained betwixt the triangles ALG , CBH ; for the same reason because the solid AK D is cut by the plane LGHB through H K F G N the diagonals LG , BH of the oppo- site planes ALNG , CBKH , the solid AK is double of the ...
... prism which is contained betwixt the triangles ALG , CBH ; for the same reason because the solid AK D is cut by the plane LGHB through H K F G N the diagonals LG , BH of the oppo- site planes ALNG , CBKH , the solid AK is double of the ...
Página 183
... prism contained by the two triangles LMN , BHK , and the three parallelograms BM , MK , KL . If therefore the prism LMNBHK be taken from the solid of which the base is the parallelogram AB , and in which FDKN is the one opposite to it ...
... prism contained by the two triangles LMN , BHK , and the three parallelograms BM , MK , KL . If therefore the prism LMNBHK be taken from the solid of which the base is the parallelogram AB , and in which FDKN is the one opposite to it ...
Página 186
... : therefore , as the base AE to the base CF , so is the solid AB to the solid CD . Wherefore solid paral- lelopipeds , & c . Q. E. D. * See Note . COR . From this it is manifest that prisms upon 186 BOOK XI . THE ELEMENTS OF EUCLID .
... : therefore , as the base AE to the base CF , so is the solid AB to the solid CD . Wherefore solid paral- lelopipeds , & c . Q. E. D. * See Note . COR . From this it is manifest that prisms upon 186 BOOK XI . THE ELEMENTS OF EUCLID .
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Términos y frases comunes
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
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 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.
Página 9 - If one side of a triangle be produced, the exterior angle is greater than either of the interior opposite angles.
Página 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.
Página 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.
Página 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.
Página 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...
Página 131 - ... rectilineal figures are to one another in the duplicate ratio of their homologous sides.