The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |
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Page 67
... touch a circle , when it meets the circle , and being produced does not cut it . III . O Circles are said to touch one another , which meet , but do not cut one another . IV . Straight lines are said to be equally distant 67 ...
... touch a circle , when it meets the circle , and being produced does not cut it . III . O Circles are said to touch one another , which meet , but do not cut one another . IV . Straight lines are said to be equally distant 67 ...
Page 73
... touch one another internally , they shall not have the same centre . Let the two circles ABC , CDE touch one another internally in the point C : they shall not have the same centre . For , if they have , let it be F : join FC and draw ...
... touch one another internally , they shall not have the same centre . Let the two circles ABC , CDE touch one another internally in the point C : they shall not have the same centre . For , if they have , let it be F : join FC and draw ...
Page 78
... touch each other internally , the straight line which joins their centres being produced shall pass through the point of con- tact . Let the two circles ABC , ADE touch each other internally in the point A ; and let F 78 EUCLID'S ELEMENTS .
... touch each other internally , the straight line which joins their centres being produced shall pass through the point of con- tact . Let the two circles ABC , ADE touch each other internally in the point A ; and let F 78 EUCLID'S ELEMENTS .
Page 79
... touch each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE , touch each other externally in the point A ; and let F be the centre of the circle ABC ...
... touch each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE , touch each other externally in the point A ; and let F be the centre of the circle ABC ...
Page 80
... touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle EBF touch the circle ABC in more points than one , and first on the inside , in the points B , D : join BD ...
... touch another in more points than one , whether it touches it on the inside or outside . For , if it be possible , let the circle EBF touch the circle ABC in more points than one , and first on the inside , in the points B , D : join BD ...
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