The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 11
... join FC , GB . Hyp . A * 4.1 . Because AF is equal to + AG , and AB tot AC , Const . the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two trian- gles AFC , AGB ; therefore ...
... join FC , GB . Hyp . A * 4.1 . Because AF is equal to + AG , and AB tot AC , Const . the two sides FA , AC are equal to the two GA , AB , each to each ; and they contain the angle FAG common to the two trian- gles AFC , AGB ; therefore ...
Page 12
... AB be the greater ; and from it cut * off DB equal to AC , the less , and join DC : therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC com- mon to both , the two sides , DB , 12 EUCLID'S ELEMENTS .
... AB be the greater ; and from it cut * off DB equal to AC , the less , and join DC : therefore , because in the triangles DBC , ACB , DB is equal to AC , and BC com- mon to both , the two sides , DB , 12 EUCLID'S ELEMENTS .
Page 13
... Join CD ; then , in the case in which the vertex of each of the triangles is without the other triangle , because AC is equal † to A AD , the angle ACD is equal to * * 4.1 . RtHyp . * 5 . 1 . the angle ADC : But the angle ACD is greater ...
... Join CD ; then , in the case in which the vertex of each of the triangles is without the other triangle , because AC is equal † to A AD , the angle ACD is equal to * * 4.1 . RtHyp . * 5 . 1 . the angle ADC : But the angle ACD is greater ...
Page 15
... join DE , and upon it de- scribe an equilateral triangle DEF ; then join AF : the straight line AF shall bisect the angle BAC . Because AD is equal to AE , and AF is common to the two . triangles DAF , EAF ; the two sides DA , AF , are ...
... join DE , and upon it de- scribe an equilateral triangle DEF ; then join AF : the straight line AF shall bisect the angle BAC . Because AD is equal to AE , and AF is common to the two . triangles DAF , EAF ; the two sides DA , AF , are ...
Page 16
... join FC . The straight line FC drawn from the given point C shall be at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; A D the two sides DC , CF are equal to the ...
... join FC . The straight line FC drawn from the given point C shall be at right angles to the given straight line AB . Because DC is equal to CE , and FC common to the two triangles DCF , ECF ; A D the two sides DC , CF are equal 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