The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 11
... common to the two trian- gles AFC , AGB ; therefore the base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the re- maining angles of the one are equal to the remaining angles F of the other , each to each ...
... common to the two trian- gles AFC , AGB ; therefore the base FC is equal to the base GB , and the triangle AFC to the triangle AGB ; and the re- maining angles of the one are equal to the remaining angles F of the other , each to each ...
Page 12
... common to the two triangles BFC , CGB ; wherefore these triangles are equal * , and their remaining angles each to each , to which the equal sides are opposite : therefore the angle FBC is equal to the angle GCB , and the angle BCF to ...
... common to the two triangles BFC , CGB ; wherefore these triangles are equal * , and their remaining angles each to each , to which the equal sides are opposite : therefore the angle FBC is equal to the angle GCB , and the angle BCF to ...
Page 15
... common to the two . triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; * A DA E † Const . B F and the base DF , is equal to the base EF ; there- + Const . fore the angle DAF is equal to the ...
... common to the two . triangles DAF , EAF ; the two sides DA , AF , are equal to the two sides EA , AF , each to each ; * A DA E † Const . B F and the base DF , is equal to the base EF ; there- + Const . fore the angle DAF is equal to the ...
Page 16
... common to the two triangles ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is † Const . equal to the angle BCD ; there- fore the base AD is equal to the A * 4.1 . * 3.1 . * 1 . 1 . † Const ...
... common to the two triangles ACD , BCD ; the two sides AC , CD are equal to BC , CD , each to each ; and the angle ACD is † Const . equal to the angle BCD ; there- fore the base AD is equal to the A * 4.1 . * 3.1 . * 1 . 1 . † Const ...
Page 17
... common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw + BE at +11 . 1- right angles to AB ; and because ABC is a straight line , the angle CBE is ...
... common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw + BE at +11 . 1- right angles to AB ; and because ABC is a straight line , the angle CBE is ...
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