The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |
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Side 9
Which was to be demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be produced , the angles upon the other side of the base shall be equal . DFE .
Which was to be demonstrated . PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be produced , the angles upon the other side of the base shall be equal . DFE .
Side 10
and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle Fbc is equal to the angle GCB , and the angle BCF to the angle CBG : And , since it has been demonstrated , that the whole angle ABG ...
and their remaining angles , each to each , to which the equal sides are opposite ; therefore the angle Fbc is equal to the angle GCB , and the angle BCF to the angle CBG : And , since it has been demonstrated , that the whole angle ABG ...
Side 12
to the angle BCD ; but it has been demonstrated to be greater than it ; which is impossible . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to Ad in the ...
to the angle BCD ; but it has been demonstrated to be greater than it ; which is impossible . But if one of the vertices , as D , be within the other triangle ACB ; produce AC , AD to E , F ; therefore , because AC is equal to Ad in the ...
Side 13
The case in which the vertex of the triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there cannot be two triangles , that have their sides which are terminated ...
The case in which the vertex of the triangle is upon a side of the other , needs no demonstration . Therefore , upon the same base , and on the same side of it , there cannot be two triangles , that have their sides which are terminated ...
Side 16
By help of this problem , it may be demonstrated that two straight lines cannot have a common segment . If it be possible , let the two straight lines A B C , ABD , have the segment AB common to both of them .
By help of this problem , it may be demonstrated that two straight lines cannot have a common segment . If it be possible , let the two straight lines A B C , ABD , have the segment AB common to both of them .
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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 |