The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 193
... excess of the square of AB above the square of LX , and make RX equal to its side , and join RL , RM , RN . The solid angle at R shall be the angle required . R N * 3 Def . 11 . Because RX is perpendicular to the plane of the circle LMN ...
... excess of the square of AB above the square of LX , and make RX equal to its side , and join RL , RM , RN . The solid angle at R shall be the angle required . R N * 3 Def . 11 . Because RX is perpendicular to the plane of the circle LMN ...
Page 194
... excess of the square of AB above the square of LX ; therefore the square of AB is equal to the squares of LX , XR : but the square of RL is equal to the same squares , because LXR is a right angle ; therefore the square of AB is equal ...
... excess of the square of AB above the square of LX ; therefore the square of AB is equal to the squares of LX , XR : but the square of RL is equal to the same squares , because LXR is a right angle ; therefore the square of AB is equal ...
Page 225
... excess of the circle EFGH above the space S ; because , by the preceding Lemma , if from the greater of two unequal magnitudes there be taken more than its half , and from the remainder more than its half , and so on , there shall at ...
... excess of the circle EFGH above the space S ; because , by the preceding Lemma , if from the greater of two unequal magnitudes there be taken more than its half , and from the remainder more than its half , and so on , there shall at ...
Page 231
... excess of the pyramid DEFH above the solid Q : let these , for example be the pyramids DPRS , STYH : therefore the prisms , which make the rest of the pyra- mid DEFH , are greater than the solid Q. Divide likewise the pyramid ABCG in ...
... excess of the pyramid DEFH above the solid Q : let these , for example be the pyramids DPRS , STYH : therefore the prisms , which make the rest of the pyra- mid DEFH , are greater than the solid Q. Divide likewise the pyramid ABCG in ...
Page 239
... excess * Lemma . of the cylinder above the triple of the cone : let them be those upon the segments of the circle AE , EB , BF , FC , CG , GD , DH , HA ; therefore the rest of the cylinder , that is , the prism of which the base is the ...
... excess * Lemma . of the cylinder above the triple of the cone : let them be those upon the segments of the circle AE , EB , BF , FC , CG , GD , DH , HA ; therefore the rest of the cylinder , that is , the prism of which the base is the ...
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The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |
Common terms and phrases
ABC is given AC is equal altitude angle ABC angle BAC base BC bisected centre circle ABCD circumference common logarithm cone Constr 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 gnomon greater join less Let ABC logarithm multiple opposite parallel parallelogram AC perpendicular polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle contained rectilineal figure right angles segment shewn sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore