The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |
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Side 63
If two circles touch each other externally , the straight line which joins their centres shall pass through the point of ... One circle cannot touch another in more points than one , whether it touches it on the inside or outside .
If two circles touch each other externally , the straight line which joins their centres shall pass through the point of ... One circle cannot touch another in more points than one , whether it touches it on the inside or outside .
Side 67
From this it is manifest that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it , touches the circle ; and that it touches it only in one point , because , if it did meet the circle in ...
From this it is manifest that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it , touches the circle ; and that it touches it only in one point , because , if it did meet the circle in ...
Side 68
BF Because E is the centre of the circles BCD , AFG , E A is equal to EF , and ED to EB ; therefore the two sides A E , EB are D. equal ... Therefore AB touches the circle ; and it is drawn from the given point A. Which was to be done .
BF Because E is the centre of the circles BCD , AFG , E A is equal to EF , and ED to EB ; therefore the two sides A E , EB are D. equal ... Therefore AB touches the circle ; and it is drawn from the given point A. Which was to be done .
Side 69
A If a straight line touches a circle , and from the point of contact a straight line be drawn at right angles to the touching line , the centre of the circle shall be in that line . Let the straight line de touch the circle ABC in • c ...
A If a straight line touches a circle , and from the point of contact a straight line be drawn at right angles to the touching line , the centre of the circle shall be in that line . Let the straight line de touch the circle ABC in • c ...
Side 78
If a straight line touches a circle , and from the point of contact a straight line be drawn cutting the circle , the angles made by this line with the line touching the circle , shall be equal to the angles which are in the alternate ...
If a straight line touches a circle , and from the point of contact a straight line be drawn cutting the circle , the angles made by this line with the line touching the circle , shall be equal to the angles which are in the alternate ...
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Vanlige uttrykk og setninger
ABCD 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 gnomon greater impossible interior isosceles triangle join less Let ABC likewise line be drawn lines AC meet opposite angles opposite sides parallel parallelogram pass perpendicular PROB produced PROP Q.E.D. PROP rectangle contained 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 vertex wherefore whole
Populære avsnitt
Side 6 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 5 - Let it be granted that a straight line may be drawn from any one point to any other point.
Side 20 - If two triangles have two sides of the one equal to two sides of the...
Side 30 - Parallelograms upon equal bases, and between the same parallels, are equal to one another.
Side 17 - Any two angles of a triangle are together less than two right angles. Let ABC be any triangle ; any two of its angles together are less than two right angles.
Side 84 - IF from a point without a circle there be drawn two straight lines, one of which cuts the circle, and the other meets it; if the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets it shall touch the circle.
Side 82 - If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Side 11 - UPON the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.
Side 19 - To make a triangle of which the sides shall be equal to three given straight lines, but any two whatever of these must be greater than the third, (i.
Side 7 - From the greater of two given straight lines to cut off a part equal to the less. Let AB and C be the two given straight lines, whereof AB is the greater.
Bibliografisk informasjon
| Tittel | The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |
| Forfattere | Euclid, Thomas Tate |
| Redaktør | Thomas Tate |
| Utgiver | Longman, Brown, Green, and Longmans, 1849 |
| Original fra | Oxford University |
| Digitalisert | 16. okt 2006 |
| Lengde | 108 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |