The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 10
... angles contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which ...
... angles contained by those sides equal to one another ; they shall likewise have their bases , or third sides , equal ; and the two triangles shall be equal ; and their other angles shall be equal , each to each , viz . those to which ...
Page 11
... equal to it ; and the other angles of the one coincide with the remaining angles of the other , and are equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the ...
... equal to it ; and the other angles of the one coincide with the remaining angles of the other , and are equal to them , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . Therefore , if two triangles have two sides of the ...
Page 12
... angle BFC was proved to be equal to the angle CGB , and the base BC is 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 : ...
... angle BFC was proved to be equal to the angle CGB , and the base BC is 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 : ...
Page 13
... equal to the two AC , CB , each to each ; and the angle DBC is equal to the ... angles , & c . Q. E. D. B DA COR . Hence every equiangular triangle is also ... equal to one another , and likewise those which are terminated in the other ...
... equal to the two AC , CB , each to each ; and the angle DBC is equal to the ... angles , & c . Q. E. D. B DA COR . Hence every equiangular triangle is also ... equal to one another , and likewise those which are terminated in the other ...
Page 15
... equal † to EF . + Hyp . Therefore BC coinciding with EF , BA and AC shall coincide with ED and DF : for , if the ... angles . Let BAC be the given rectilineal angle , it is required to bisect it . * 1.1 . Take any point D in AB , and from AC ...
... equal † to EF . + Hyp . Therefore BC coinciding with EF , BA and AC shall coincide with ED and DF : for , if the ... angles . Let BAC be the given rectilineal angle , it is required to bisect it . * 1.1 . Take any point D in AB , and from AC ...
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