Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |
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Page 200
... solid AB is cut into two equal prisms by the plane CDEF . Q. E. D. N. B. The insisting straight lines of a parallelepiped , mentioned in the following propositions , are the sides of the parallelograms be- twixt the base and the plane ...
... solid AB is cut into two equal prisms by the plane CDEF . Q. E. D. N. B. The insisting straight lines of a parallelepiped , mentioned in the following propositions , are the sides of the parallelograms be- twixt the base and the plane ...
Page 201
... solid there be taken the prism AGD , the remain- ing solid , viz . the parallelepiped AH is equal to the remaining parallele- piped AK . Therefore solid parallelepipeds , & c . Q. E. D. PROP . VI . THEOR . Solid parallelepipeds upon ...
... solid there be taken the prism AGD , the remain- ing solid , viz . the parallelepiped AH is equal to the remaining parallele- piped AK . Therefore solid parallelepipeds , & c . Q. E. D. PROP . VI . THEOR . Solid parallelepipeds upon ...
Page 202
... solid CP is a parallelepiped . Now the solid parallelepiped CM is equal ( 5. 2. Sup . ) to the solid parallelepiped ... parallelepipeds , & c . Q. E. D. 1 PROP . VII . THEOR Solid parallelepipeds which are upon equal bases , and of ...
... solid CP is a parallelepiped . Now the solid parallelepiped CM is equal ( 5. 2. Sup . ) to the solid parallelepiped ... parallelepipeds , & c . Q. E. D. 1 PROP . VII . THEOR Solid parallelepipeds which are upon equal bases , and of ...
Page 203
... of this proposition , they will be equal to one another ; wherefore , the solids AE and CF are also equal . Wherefore , solid parallelepipeds , & c . Q. E. D. PROP . VIII . THEOR . Solid parallelepipeds which have OF GEOMETRY . BOOK III .
... of this proposition , they will be equal to one another ; wherefore , the solids AE and CF are also equal . Wherefore , solid parallelepipeds , & c . Q. E. D. PROP . VIII . THEOR . Solid parallelepipeds which have OF GEOMETRY . BOOK III .
Page 204
... Solids ; to which are Added Elements of Plane and Spherical Trigonometry John Playfair. PROP . VIII . THEOR . Solid parallelepipeds which have the same altitude , are to one another as their bases , Let AB , CD be solid parallelepipeds ...
... Solids ; to which are Added Elements of Plane and Spherical Trigonometry John Playfair. PROP . VIII . THEOR . Solid parallelepipeds which have the same altitude , are to one another as their bases , Let AB , CD be solid parallelepipeds ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line BD THEOR third touches the circle triangle ABC triangle DEF wherefore