The first six books of the Elements of Euclid, with numerous exercises |
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Αποτελέσματα 1 - 5 από τα 47.
Σελίδα 10
... in the same manner , because a bd is a straight line , d . the angle d be is equal to the angle e ba ; wherefore the angle d be is a b equal to the angle cbe , the less to the greater , which is impossible ; therefore two straight ...
... in the same manner , because a bd is a straight line , d . the angle d be is equal to the angle e ba ; wherefore the angle d be is a b equal to the angle cbe , the less to the greater , which is impossible ; therefore two straight ...
Σελίδα 12
And in like manner it may be demonstrated , that no other can be in the same straight line with it but b d , which therefore is in the same straight line with cb . Wherefore , if at a point , & c . Q. E. D. ز ز PROPOSITION XV .
And in like manner it may be demonstrated , that no other can be in the same straight line with it but b d , which therefore is in the same straight line with cb . Wherefore , if at a point , & c . Q. E. D. ز ز PROPOSITION XV .
Σελίδα 13
In the same manner it can be demonstrated , that the angles ceb , a ed are equal . Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that , if two straight lines cut one another , the angles they ...
In the same manner it can be demonstrated , that the angles ceb , a ed are equal . Therefore , if two straight lines , & c . Q. E. D. Cor . 1. From this it is manifest , that , if two straight lines cut one another , the angles they ...
Σελίδα 14
In like manner it may be demonstrated , that bac , a cb , as also ca b , a b c , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROPOSITION XVIII . - THEOREM . The greater side of every triangle is opposite ...
In like manner it may be demonstrated , that bac , a cb , as also ca b , a b c , are less than two right angles . Therefore any two angles , & c . Q. E. D. PROPOSITION XVIII . - THEOREM . The greater side of every triangle is opposite ...
Σελίδα 15
In the same manner it may be demonstrated , that the sides a b , bc , are greater than ca , and b C bc , ca greater than a b . Therefore any two sides , & c . Q. E. D. & PROPOSITION XXI . — THEOREM . e If from the ends of the side of a ...
In the same manner it may be demonstrated , that the sides a b , bc , are greater than ca , and b C bc , ca greater than a b . Therefore any two sides , & c . Q. E. D. & PROPOSITION XXI . — THEOREM . e If from the ends of the side of a ...
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a b c angle a b c angle bac 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 join less likewise magnitudes manner meet multiple parallel parallelogram pass perpendicular produced proportionals PROPOSITION ratio reason rectangle contained rectilineal figure remaining angle right angles segment shewn sides similar square square of a c straight line a b Take taken third touches the circle triangle triangle a b c wherefore whole