The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 236
... polygon BCDEF : therefore all the angles at the bases of the triangles are together greater than all the angles of the polygon : and because all the angles of the triangles are together equal to * 32 1. twice as many right angles * as ...
... polygon BCDEF : therefore all the angles at the bases of the triangles are together greater than all the angles of the polygon : and because all the angles of the triangles are together equal to * 32 1. twice as many right angles * as ...
Page 237
... polygon together with four right angles : but all the angles at the bases of the triangles are greater than all the angles of the polygon , as has been proved ; wherefore the remaining angles of the triangles , viz . those of the vertex ...
... polygon together with four right angles : but all the angles at the bases of the triangles are greater than all the angles of the polygon , as has been proved ; wherefore the remaining angles of the triangles , viz . those of the vertex ...
Page 281
... polygon ABCDE be to the polygon FGHKL . Join BE , AM , GL , FN : and because the polygon ABCDE is similar to the polygon FGHKL , the angle BAE is equal to the angle B E M GFL , and as EA to AE so is GF tc FL : there- fore the two ...
... polygon ABCDE be to the polygon FGHKL . Join BE , AM , GL , FN : and because the polygon ABCDE is similar to the polygon FGHKL , the angle BAE is equal to the angle B E M GFL , and as EA to AE so is GF tc FL : there- fore the two ...
Page 282
... polygon ABCDE to the * 20 . 6. polygon FGHKL is the duplicate * of that which BA has to GF : therefore as the square of BM to the square of GN , so is the polygon ABCDE to the polygon FGHKL . Wherefore , similar polygons , & c ...
... polygon ABCDE to the * 20 . 6. polygon FGHKL is the duplicate * of that which BA has to GF : therefore as the square of BM to the square of GN , so is the polygon ABCDE to the polygon FGHKL . Wherefore , similar polygons , & c ...
Page 284
... polygon EKFLGMHN is greater than the space S. Describe likewise in the circle ABCD the polygon AXBOCPDR similar to the polygon EKFLGMHN : as therefore the square 1. 12. of BD is to the square of FH , * so is the polygon AXBOCPDR to the ...
... polygon EKFLGMHN is greater than the space S. Describe likewise in the circle ABCD the polygon AXBOCPDR similar to the polygon EKFLGMHN : as therefore the square 1. 12. of BD is to the square of FH , * so is the polygon AXBOCPDR to the ...
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