The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 218
... solid figure contained by twenty equal and equilateral triangles . Def . A. A parallelopiped is a solid figure contained by six quadrilateral figures , whereof every opposite two are parallel . 1 . PROP . I. THEOR . One part of a ...
... solid figure contained by twenty equal and equilateral triangles . Def . A. A parallelopiped is a solid figure contained by six quadrilateral figures , whereof every opposite two are parallel . 1 . PROP . I. THEOR . One part of a ...
Page 248
... solid , & c . Q. E. D. PROP . XXV . THEOR . If a solid parallelopiped be cut by a plane parallel to two of its opposite planes ; it divides the whole into two solids , the base of one of which shall be to the base of the other , as the one ...
... solid , & c . Q. E. D. PROP . XXV . THEOR . If a solid parallelopiped be cut by a plane parallel to two of its opposite planes ; it divides the whole into two solids , the base of one of which shall be to the base of the other , as the one ...
Page 251
... solid angle has been made equal to a given solid angle contained by three plane angles . Which was to be done . PROP . XXVII . THEOR . To describe from a given straight line a solid parallelopiped similar and similarly situated to one ...
... solid angle has been made equal to a given solid angle contained by three plane angles . Which was to be done . PROP . XXVII . THEOR . To describe from a given straight line a solid parallelopiped similar and similarly situated to one ...
Page 252
... solid parallelopiped . It is required from AB to describe a solid parallelopiped similar and similarly situated to CD . At the point A of the given straight line AB * 26 . 11. make * a solid angle equal to the solid angle at C , and let ...
... solid parallelopiped . It is required from AB to describe a solid parallelopiped similar and similarly situated to CD . At the point A of the given straight line AB * 26 . 11. make * a solid angle equal to the solid angle at C , and let ...
Page 253
... solid parallelopiped be cut by a plane passing through the diagonals of two of the opposite planes ; it shall be cut into two equal parts . Let AB be a solid parallelopiped , and DE , CF the diagonals of the opposite parallelograms AH ...
... solid parallelopiped be cut by a plane passing through the diagonals of two of the opposite planes ; it shall be cut into two equal parts . Let AB be a solid parallelopiped , and DE , CF the diagonals of the opposite parallelograms AH ...
Other editions - View all
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Euclid No preview available - 2015 |
The Elements of Euclid: Viz. the First Six Books, Together With the Eleventh ... Euclid No preview available - 2023 |
Common terms and phrases
AB is equal altitude angle ABC angle ACB angle BAC angle EDF base BC base DEF BC is equal bisected centre circle ABCD circle EFGH circumference cone Const cylinder described diameter draw equal angles equal to AC equiangular equilateral equimultiples exterior angle fore given rectilineal given straight line gnomon inscribed join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism PROB pyramid ABCG pyramid DEFH Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment solid angle solid CD solid parallelopiped sphere square of AC straight line AB straight line AC THEOR three plane angles tiple touches the circle triangle ABC triangle DEF triplicate ratio wherefore whole