The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate |
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Side 8
but the straight line c is likewise equal to AD ( Constr . ) ; whence AE and c are each of them equal to AD ; wherefore the straight line AE is equal to c ( Ax . 1. ) , and from AB , the greater of two straight lines , a part A E has ...
but the straight line c is likewise equal to AD ( Constr . ) ; whence AE and c are each of them equal to AD ; wherefore the straight line AE is equal to c ( Ax . 1. ) , and from AB , the greater of two straight lines , a part A E has ...
Side 9
... have likewise the angles contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each .
... have likewise the angles contained by those sides equal to one another , their bases shall likewise be equal , and the triangles be equal , and their other angles to which the equal sides are opposite shall be equal , each to each .
Side 12
... 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 .
... 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 13
Therefore , 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 ...
Therefore , 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 ...
Side 14
therefore , if the base Bc coincides with the base E F ; the sides BA , AC cannot but coincide with the sides E D , D F , wherefore likewise the angle BAC coincides with the angle E DF , and is equal ( Ax . 8. ) to it .
therefore , if the base Bc coincides with the base E F ; the sides BA , AC cannot but coincide with the sides E D , D F , wherefore likewise the angle BAC coincides with the angle E DF , and is equal ( Ax . 8. ) to it .
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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 |