The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 8
... AB be the given straight line ; it is re- quired to describe an equilateral triangle upon AB . From the centre A ... equal * to AB ; and because the point B is the centre of the circle ACE , BC is equal to BA : But it has been proved ...
... AB be the given straight line ; it is re- quired to describe an equilateral triangle upon AB . From the centre A ... equal * to AB ; and because the point B is the centre of the circle ACE , BC is equal to BA : But it has been proved ...
Page 9
... equal to BC . Because the point B is the centre of the circle CGH , BC is equal to BG ; and because D is the centre ... AB and C be the two given straight lines , whereof AB is the greater . It is re- quired to cut off from AB , the ...
... equal to BC . Because the point B is the centre of the circle CGH , BC is equal to BG ; and because D is the centre ... AB and C be the two given straight lines , whereof AB is the greater . It is re- quired to cut off from AB , the ...
Page 10
... equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles , which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and B the angle BAC ...
... equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles , which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; and B the angle BAC ...
Page 11
... equal to it ; and the other angles of the one coincide with the remaining angles of the other , and are equal to ... AB is equal to AC , and let the straight lines AB , AC be produced to D and E : the angle ABC shall be equal to the ...
... equal to it ; and the other angles of the one coincide with the remaining angles of the other , and are equal to ... AB is equal to AC , and let the straight lines AB , AC be produced to D and E : the angle ABC shall be equal to the ...
Page 13
... equal to the angle + ACB ; therefore the + IIyp . base DC is equal to the base AB , and the triangle DBC is equal to the triangle * ACB , the less to the greater , which is absurd . There- fore AB is not unequal to AC , that is , it is ...
... equal to the angle + ACB ; therefore the + IIyp . base DC is equal to the base AB , and the triangle DBC is equal to the triangle * ACB , the less to the greater , which is absurd . There- fore AB is not unequal to AC , that is , it 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