The first three books of Euclid's Elements of geometry, with theorems and problems, by T. Tate1851 - 139 sider |
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Side 6
... interior angles on the same side of it taken together less than two right angles , these straight lines being continually pro- duced , shall at length meet upon that side on which are the angles which are less than two right angles ...
... interior angles on the same side of it taken together less than two right angles , these straight lines being continually pro- duced , shall at length meet upon that side on which are the angles which are less than two right angles ...
Side 20
... interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle A CD is greater than either of the interior opposite angles CBA , BA C. Bisect ( 1. 10. ) AC in E , join B E and produce it to ...
... interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle A CD is greater than either of the interior opposite angles CBA , BA C. Bisect ( 1. 10. ) AC in E , join B E and produce it to ...
Side 21
... interior and opposite angle ABC ; to each of these add the angle ACB ; there- fore the angles ACD , A CB are greater than the angles ABC , ACB ; but ACD , ACB are together equal ( 1. 13. ) to two right angles ; therefore the angles ABC ...
... interior and opposite angle ABC ; to each of these add the angle ACB ; there- fore the angles ACD , A CB are greater than the angles ABC , ACB ; but ACD , ACB are together equal ( 1. 13. ) to two right angles ; therefore the angles ABC ...
Side 23
... shown that B A , A C are greater than B E , E C ; much more then are B A , A C greater than B D , D C. Again , because the exterior angle of a triangle is greater than the interior and opposite angle ( 1. BOOK I. PROP . XXI . 23.
... shown that B A , A C are greater than B E , E C ; much more then are B A , A C greater than B D , D C. Again , because the exterior angle of a triangle is greater than the interior and opposite angle ( 1. BOOK I. PROP . XXI . 23.
Side 24
Euclides Thomas Tate. is greater than the interior and opposite angle ( 1. 16. ) , the exterior angle B DC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ...
Euclides Thomas Tate. is greater than the interior and opposite angle ( 1. 16. ) , the exterior angle B DC of the triangle CDE is greater than CED ; for the same reason , the exterior angle CEB of the triangle ABE is greater than BAC ...
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Vanlige uttrykk og setninger
A B C ABCD adjacent 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 equilateral exterior angle extremity figure fore four given point given straight line gnomon greater impossible interior join less Let ABC Let the straight likewise manner meet opposite angles opposite sides parallel parallelogram pass perpendicular PROB produced Q. E. D. PROP rectangle contained remaining remaining angle right angles segment semicircle shown sides square of AC straight line AC Take taken THEOR third touch touches the circle triangle ABC twice the rectangle vertex Wherefore whole