The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 18
... Const . * 8 . 1 . * Join CF , CG : and because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base * 15 Def . CF is equal * to the base CG ...
... Const . * 8 . 1 . * Join CF , CG : and because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH , HC are equal to the two GH , HC , each to each ; and the base * 15 Def . CF is equal * to the base CG ...
Page 21
... Const . * 15. 1 . CEF , because they are opposite vertica , angles ; therefore the base AB is equal to the base CF , * 4 . 1 . and the triangleAEB to the triangle CEF , and the remaining , angles to the reinairing angles , each to each ...
... Const . * 15. 1 . CEF , because they are opposite vertica , angles ; therefore the base AB is equal to the base CF , * 4 . 1 . and the triangleAEB to the triangle CEF , and the remaining , angles to the reinairing angles , each to each ...
Page 22
... Const . because the side AB is equal to the side AD ; therefore the angle ABD is likewise greater than the angle ACB : therefore much more is the angle ABC greater than ACB . Therefore the greater side , & c . Q. E. D. PROP . XIX ...
... Const . because the side AB is equal to the side AD ; therefore the angle ABD is likewise greater than the angle ACB : therefore much more is the angle ABC greater than ACB . Therefore the greater side , & c . Q. E. D. PROP . XIX ...
Page 23
... than BC . In the same manner it may be Because AD is equal † to AC , add BA to each , therefore † Const the whole BD is equal † to the two BA and AC . +2 Ax . demonstrated , that the sides AB , BC are greater BOCK I PROP . XX . 23.
... than BC . In the same manner it may be Because AD is equal † to AC , add BA to each , therefore † Const the whole BD is equal † to the two BA and AC . +2 Ax . demonstrated , that the sides AB , BC are greater BOCK I PROP . XX . 23.
Page 25
... Const . Again , because G is the centre of the circle LKH , GH is equal to GK ; but GH is equal to * 15 Def . C ; therefore also GK is equal to C : and FG is equal to B : therefore the three straight lines + Const . KF , FG , GK , are ...
... Const . Again , because G is the centre of the circle LKH , GH is equal to GK ; but GH is equal to * 15 Def . C ; therefore also GK is equal to C : and FG is equal to B : therefore the three straight lines + Const . KF , FG , GK , are ...
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