Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., EnlJ.B. Lippincott & Company, 1866 - 317 Seiten |
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Seite 63
... pass through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it . Let ABC be a circle , and let CD , a straight line drawn through the centre , bisect any straight line AB , which ...
... pass through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it . Let ABC be a circle , and let CD , a straight line drawn through the centre , bisect any straight line AB , which ...
Seite 64
... pass through the centre , cuts AB at righ angles . Again , let CD cut AB at right angles ; CD also bisects AB , that ... pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in ...
... pass through the centre , cuts AB at righ angles . Again , let CD cut AB at right angles ; CD also bisects AB , that ... pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in ...
Seite 68
... pass through A. E B COR . 1. If two circles touch each other internally , the distance be- tween their centre must be equal to the difference of their radii : for the circumferences pass through the same point in the line joining the ...
... pass through A. E B COR . 1. If two circles touch each other internally , the distance be- tween their centre must be equal to the difference of their radii : for the circumferences pass through the same point in the line joining the ...
Seite 69
... 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 , and G the centre of ADE ; the straight line which joins the points F , G shall pass ...
... 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 , and G the centre of ADE ; the straight line which joins the points F , G shall pass ...
Seite 70
... passes through the point of contact ( 11.3 ) , but it does not pass through it , because the points B , D are without the straight line GH , which is absurd : therefore one circle cannot touch another in the inside in more points than ...
... passes through the point of contact ( 11.3 ) , but it does not pass through it , because the points B , D are without the straight line GH , which is absurd : therefore one circle cannot touch another in the inside in more points than ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore