The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 286
... pyramid of which the base is the triangle ABC and its vertex the point D : the pyramid ABCD may be divided into two equal and similar pyramids having triangular bases , and similar to the whole ; and into two equal prisms which together ...
... pyramid of which the base is the triangle ABC and its vertex the point D : the pyramid ABCD may be divided into two equal and similar pyramids having triangular bases , and similar to the whole ; and into two equal prisms which together ...
Page 287
... pyramid of which the base is the triangle AEG , and of which the vertex is the point H , is equal * and * .C.11 ... ABC to the triangle AEG ; but the triangle AEG is si- milar to the triangle HKL , as before was proved ; therefore the ...
... pyramid of which the base is the triangle AEG , and of which the vertex is the point H , is equal * and * .C.11 ... ABC to the triangle AEG ; but the triangle AEG is si- milar to the triangle HKL , as before was proved ; therefore the ...
Page 289
... pyramids thus made be conceived to be divided in the like manner , and so on as the base ABC is to the base DEF , so shall all the prisms in the pyramid ABCG be to all the prisms in the pyramid DEFH made by the same number of divisions ...
... pyramids thus made be conceived to be divided in the like manner , and so on as the base ABC is to the base DEF , so shall all the prisms in the pyramid ABCG be to all the prisms in the pyramid DEFH made by the same number of divisions ...
Page 290
... ABC , OMN , as also the * 15 . 11. planes DEF , STY , are parallel , * the perpendi- culars drawn from the points G ... ABCG are equal to one another , and also the two prisms in the pyramid DEFH equal to one another ; as the prism of ...
... ABC , OMN , as also the * 15 . 11. planes DEF , STY , are parallel , * the perpendi- culars drawn from the points G ... ABCG are equal to one another , and also the two prisms in the pyramid DEFH equal to one another ; as the prism of ...
Page 291
... ABC to the base DEF ; therefore , as the base ABC to the base DEF , so are the two prisms in the pyramid ABCG to the two prisms in the pyramid DEFH : and like- wise if the pyramids now made , for example , the two OMNG , STYH , be ...
... ABC to the base DEF ; therefore , as the base ABC to the base DEF , so are the two prisms in the pyramid ABCG to the two prisms in the pyramid DEFH : and like- wise if the pyramids now made , for example , the two OMNG , STYH , be ...
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