The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |
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Side 9
... equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle
afc to the angle AGB : And E because the whole AF is equal to the whole AG , of
which the parts A B , AC , are equal : the remainder BF shall be equal ( Ax . 3. ) ...
... equal sides are opposite ; viz . the angle ACF to the angle ABG , and the angle
afc to the angle AGB : And E because the whole AF is equal to the whole AG , of
which the parts A B , AC , are equal : the remainder BF shall be equal ( Ax . 3. ) ...
Side 34
Let ABCD be a parallelogram , of which the diameter is AC , and EH , Fg the
parallelograms about A H D AC , that is , through which AC passes , and BK , KD
the other parallelograms F which make up the whole figure ABCD , which are ...
Let ABCD be a parallelogram , of which the diameter is AC , and EH , Fg the
parallelograms about A H D AC , that is , through which AC passes , and BK , KD
the other parallelograms F which make up the whole figure ABCD , which are ...
Side 43
to the complement , to each of these add DM ; therefore the whole CM A С DB is
equal to the whole DF ; but cm is L H equal ( 1. 36. ) to Al , because Ac is K M м
equal to CB ; therefore also al is equal to DF . To each of these add ch , and the ...
to the complement , to each of these add DM ; therefore the whole CM A С DB is
equal to the whole DF ; but cm is L H equal ( 1. 36. ) to Al , because Ac is K M м
equal to CB ; therefore also al is equal to DF . To each of these add ch , and the ...
Side 44
Q. E. D. PROP . VII . THEOR . H If a straight line be divided into any two parts , the
squares of the whole line , and one of the parts , are equal to twice the rectangle
contained by the whole and that part , together with the square of the other part .
Q. E. D. PROP . VII . THEOR . H If a straight line be divided into any two parts , the
squares of the whole line , and one of the parts , are equal to twice the rectangle
contained by the whole and that part , together with the square of the other part .
Side 95
But since Pg is greater than GQ , the triangle APG is greater than AGQ , and the
triangle God is greater than GQP ; therefore , the whole triangle DPA is greater
than the whole triangle DQA ; but it has been shown that the triangle DPA is
equal ...
But since Pg is greater than GQ , the triangle APG is greater than AGQ , and the
triangle God is greater than GQP ; therefore , the whole triangle DPA is greater
than the whole triangle DQA ; but it has been shown that the triangle DPA is
equal ...
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Vanlige uttrykk og setninger
ABCD alternate 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 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 AC 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 | Euclides, Thomas Tate |
| Redaktør | Thomas Tate |
| distribuert | 1849 |
| Original fra | Oxford University |
| Digitalisert | 16. okt 2006 |
| Lengde | 108 sider |
| Eksporter sitat | BiBTeX EndNote RefMan |