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Side 44
... intersect them ; it is required to prove that the alternate angles EBC , BCH are equal . L E B 7 D H C Proof . For ... intersecting lines LM , EF would be both parallel to GH ; which is impossible . ( Ax . 5. ) Therefore EBC is equal to ...
... intersect them ; it is required to prove that the alternate angles EBC , BCH are equal . L E B 7 D H C Proof . For ... intersecting lines LM , EF would be both parallel to GH ; which is impossible . ( Ax . 5. ) Therefore EBC is equal to ...
Side 45
James Maurice Wilson. THEOREM 23 . If a straight line intersects two other straight lines and makes either a pair of ... intersect the two straight lines EF , GH , and make the alternate angles EBC , BCH equal ; then will the other ...
James Maurice Wilson. THEOREM 23 . If a straight line intersects two other straight lines and makes either a pair of ... intersect the two straight lines EF , GH , and make the alternate angles EBC , BCH equal ; then will the other ...
Side 46
... intersecting lines , A B X A , B would each be parallel to a third line X , which is im- possible , by Axiom 5 . Therefore that is , A does not intersect B , A is parallel to B. * Euclid , 1. 30 . Q. E. D. REMARKS . It must be observed ...
... intersecting lines , A B X A , B would each be parallel to a third line X , which is im- possible , by Axiom 5 . Therefore that is , A does not intersect B , A is parallel to B. * Euclid , 1. 30 . Q. E. D. REMARKS . It must be observed ...
Side 58
... intersecting in A are respectively perpen- dicular to two lines intersecting in B : prove that any angle at A is equal or supplementary to any angle at B. 18. Shew that a trapezium may be divided into a parallelogram and a triangle . 19 ...
... intersecting in A are respectively perpen- dicular to two lines intersecting in B : prove that any angle at A is equal or supplementary to any angle at B. 18. Shew that a trapezium may be divided into a parallelogram and a triangle . 19 ...
Side 59
... intersect A , B and X , and using Theorems 21 , 22 . 4. Given two angles of a triangle to be respectively 72 ° . 15.47 " and 83 ° . 51 ′ . 16 " , find the third angle . 5. If one angle of a triangle is equal to the other two , prove ...
... intersect A , B and X , and using Theorems 21 , 22 . 4. Given two angles of a triangle to be respectively 72 ° . 15.47 " and 83 ° . 51 ′ . 16 " , find the third angle . 5. If one angle of a triangle is equal to the other two , prove ...
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Vanlige uttrykk og setninger
ABCD angle ABC angle APB angle BAC base bisect bisector Book called centre chord circle circumference coincide College common Constr construct converse Crown 8vo diagonals diameter difference distance divided double draw Edition ELEMENTARY equal angles Euclid Examples exterior angle extremities fall figure Find follows four Geometry given angle given point given straight line greater half Hence Illustrations included inscribed interior intersect isosceles triangle Join length less Let ABC line drawn locus magnitudes measure meet middle point minor arc opposite sides parallel parallelogram pass perpendicular placed polygon PROBLEM produced Professor Proof proportional quadrilateral radius ratio rectangle contained rectilineal figure regular required to prove respectively right angles School segment Shew sides similar Similarly square supplementary tangent THEOREM third touch triangle ABC unequal
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