The Elements of Euclid |
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Page 11
... centre of the circle . XVII . A diameter of a circle is a straight line drawn through the cen- tre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the ...
... centre of the circle . XVII . A diameter of a circle is a straight line drawn through the cen- tre , and terminated both ways by the circumference . XVIII . A semicircle is the figure contained by a diameter and the part of the ...
Page 13
... centre , at any dis- tance from that centre . AXIOMS . I. THINGS which are equal to the same are equal to one another . II . If equals be added to equals , the wholes are equal . III . IV . If equals be taken from equals , the ...
... centre , at any dis- tance from that centre . AXIOMS . I. THINGS which are equal to the same are equal to one another . II . If equals be added to equals , the wholes are equal . III . IV . If equals be taken from equals , the ...
Page 15
... centre A , at the dis- tance AB , describe the circle BCD , and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in which the circles cut one the circles another , draw the straight lines b CA ...
... centre A , at the dis- tance AB , describe the circle BCD , and from the centre B , at the distance BA , describe the circle ACE ; and from the point C , in which the circles cut one the circles another , draw the straight lines b CA ...
Page 16
... centre of the circle CGH , BC is equal e to BG ; and because D is the centre of the circle GKL , e 15. Def . DL is equal to DG , and DA , DB , parts of them , are equal ; therefore the remainder AL is equal to the remainder f BG : but ...
... centre of the circle CGH , BC is equal e to BG ; and because D is the centre of the circle GKL , e 15. Def . DL is equal to DG , and DA , DB , parts of them , are equal ; therefore the remainder AL is equal to the remainder f BG : but ...
Page 23
... centre C , at the distance CD , describe the circle FDG meeting AB in F , G ; and , bi- sect FG in H , and join CF , P C A H A F D B . CH , CG ; the straight line CH , drawn from the given point C , to the given straight line AB . is ...
... centre C , at the distance CD , describe the circle FDG meeting AB in F , G ; and , bi- sect FG in H , and join CF , P C A H A F D B . CH , CG ; the straight line CH , drawn from the given point C , to the given straight line AB . is ...
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Common terms and phrases
altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore