The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |
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Side 71
If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; and , if it cuts it at right angles , it shall bisect it .
If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre , it shall cut it at right angles ; and , if it cuts it at right angles , it shall bisect it .
Side 72
If in a circle two straight lines cut one another which do not both pass through the centre , they do not bisect each the other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do ...
If in a circle two straight lines cut one another which do not both pass through the centre , they do not bisect each the other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do ...
Side 79
If two circles touch each other internally , the straight line which joins their centres being produced shall pass through the point of contact . Let the two circles ABC , ADE , touch each other internally in the point A , and let F be ...
If two circles touch each other internally , the straight line which joins their centres being produced shall pass through the point of contact . Let the two circles ABC , ADE , touch each other internally in the point A , and let F be ...
Side 80
B E D For , if not , let it pass otherwise , if possible , as F C D G , and join FA , AG : And because F is the centre of the circle ABC , AF is equal to FC : Also because G is the centre of the circle ADE , AG is equal to GD ...
B E D For , if not , let it pass otherwise , if possible , as F C D G , and join FA , AG : And because F is the centre of the circle ABC , AF is equal to FC : Also because G is the centre of the circle ADE , AG is equal to GD ...
Side 81
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 on the inside in more points than one . Nor can two circles touch one another on ...
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 on the inside in more points than one . Nor can two circles touch one another on ...
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Vanlige uttrykk og setninger
A B C ABCD adjacent angle ABC angle ACB angle BAC angle equal base BC BC is equal bisect centre circle ABC circumference coincide common construct demonstrated describe diameter divided double draw equal angles equal to FB equilateral exterior angle extremity figure fore four given point given straight line greater impossible interior join less Let ABC likewise lines AC manner meet opposite angles opposite sides parallel parallelogram pass perpendicular PROB produced Q. E. D. PROP rectangle A B rectangle contained remaining remaining angle right angles segment semicircle shown sides squares of AC straight line A B Take taken THEOR third touch touches the circle triangle ABC twice the rectangle Wherefore whole
Bibliografisk informasjon
| Tittel | The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate Gleig's sch. series |
| Forfatter | Euclides |
| Redaktør | Thomas Tate |
| distribuert | 1851 |
| Original fra | Oxford University |
| Digitalisert | 30. jan 2009 |
| Lengde | 139 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |