The Elements of Euclid |
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Page 29
... centre F , at the distancè FD , de- scribe the circle DKL ; and ' from the centre G , at the distance GH , describe banother circle HLK ; and join KF , KG ; the triangle KFG has its sides equal to D the three straight lines A , B , C ...
... centre F , at the distancè FD , de- scribe the circle DKL ; and ' from the centre G , at the distance GH , describe banother circle HLK ; and join KF , KG ; the triangle KFG has its sides equal to D the three straight lines A , B , C ...
Page 30
... centre of the 15. Def . circle LKH , GH is equal to GK ; but GH is equal to C ; therefore also GK is equal to C ; and FG is equal to B ; there- fore the three straight lines KF , FG , GK , are equal to the three A , B , C ; and ...
... centre of the 15. Def . circle LKH , GH is equal to GK ; but GH is equal to C ; therefore also GK is equal to C ; and FG is equal to B ; there- fore the three straight lines KF , FG , GK , are equal to the three A , B , C ; and ...
Page 65
... centre G , at the distance GB , or GF , describe the semicircle BHF , and produce DE to H , and join GH ; therefore , because the straight line BF is divided into two equal parts in the point G , and into two unequal at E , the ...
... centre G , at the distance GB , or GF , describe the semicircle BHF , and produce DE to H , and join GH ; therefore , because the straight line BF is divided into two equal parts in the point G , and into two unequal at E , the ...
Page 67
... centre of a circle , when the perpendiculars drawn to them from the centre are equal . V. And the straight line on which the greater perpendicular falls , is said to be farther from the centre . Book III . VI . segment of a circle is THE ..
... centre of a circle , when the perpendiculars drawn to them from the centre are equal . V. And the straight line on which the greater perpendicular falls , is said to be farther from the centre . Book III . VI . segment of a circle is THE ..
Page 68
... centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw within it any straight line AB , and bisect it in D ; from the point D draw b DC at right angles to AB , and pro- duce it to E , and ...
... centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw within it any straight line AB , and bisect it in D ; from the point D draw b DC at right angles to AB , and pro- duce it to E , and ...
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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