The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 15.
Σελίδα 4
... interior angles on the same side of it taken together less than two right angles , these straight lines being continually produced , 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 produced , shall at length meet upon that side on which are the angles which are less than two right angles .
Σελίδα 13
If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . LET a b c be a triangle , and let its side b c be produced to d , the exterior angle a cd is greater than either of the ...
If one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . LET a b c be a triangle , and let its side b c be produced to d , the exterior angle a cd is greater than either of the ...
Σελίδα 14
16 ) than the interior and opposite angle dcb ; but a db is equal ( i . 5 ) a to a b d , because the side a b is equal to the side a d ; therefore the angle abd is likewise greater than the angle a cb . Much greater then is the angle ...
16 ) than the interior and opposite angle dcb ; but a db is equal ( i . 5 ) a to a b d , because the side a b is equal to the side a d ; therefore the angle abd is likewise greater than the angle a cb . Much greater then is the angle ...
Σελίδα 15
Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle bdc of the triangle cde is greater than ced ; for the same reason , the exterior angle ceb of the triangle a be is ...
Again , because the exterior angle of a triangle is greater than the interior and opposite angle , the exterior angle bdc of the triangle cde is greater than ced ; for the same reason , the exterior angle ceb of the triangle a be is ...
Σελίδα 19
... but efd is equal to the angle bca ; therefore also the angle bha is equal to the angle b ca , that is , the exterior angle bha of the triangle a hc is equal to its interior and opposite angle bca ; which is impossible ( i .
... but efd is equal to the angle bca ; therefore also the angle bha is equal to the angle b ca , that is , the exterior angle bha of the triangle a hc is equal to its interior and opposite angle bca ; which is impossible ( i .
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angle a b c angle bac applied base base bc bc is equal bisected centre circle circumference common compounded definition demonstrated describe diameter divided double draw equal angles equal to f equiangular equilateral equimultiples exterior angle extremity fall fore four fourth given straight line greater half ILLUSTRATED inscribe interior join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION Q. E. D. PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square straight line a b Take taken third touches the circle triangle a b c wherefore whole