Elementary Geometry ... |
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Página 11
... coincide are equal . 2. Two straight lines that have two points in common lie wholly in the same straight line . 3. A finite straight line has one and only one point of bisection . 4. An angle has one and only one bisector . POSTULATES ...
... coincide are equal . 2. Two straight lines that have two points in common lie wholly in the same straight line . 3. A finite straight line has one and only one point of bisection . 4. An angle has one and only one bisector . POSTULATES ...
Página 13
... coincides with , and is equal to , the angle QRS . ( Ax . 1. ) But by Def . 14 , the angle ABC is half the angle DBC ; and the angle PRS is half the angle QRS ; and the halves of equals are equal ; therefore the right angle ABC is equal ...
... coincides with , and is equal to , the angle QRS . ( Ax . 1. ) But by Def . 14 , the angle ABC is half the angle DBC ; and the angle PRS is half the angle QRS ; and the halves of equals are equal ; therefore the right angle ABC is equal ...
Página 18
... coincide with one another are said to be identically equal ; and every part of one being equal to a correspond- ing part of the other , they are said to be equal in all respects . THEOREM 5 . If two triangles have two sides of the one ...
... coincide with one another are said to be identically equal ; and every part of one being equal to a correspond- ing part of the other , they are said to be equal in all respects . THEOREM 5 . If two triangles have two sides of the one ...
Página 19
... coincide with the point F. Therefore BC would coincide with EF , ( Ax . 2. ) and therefore BC = EF : ( Ax . 1. ) and the angles B and C respectively coincide with and are equal to the angles E and F , and the area of the triangle BAC ...
... coincide with the point F. Therefore BC would coincide with EF , ( Ax . 2. ) and therefore BC = EF : ( Ax . 1. ) and the angles B and C respectively coincide with and are equal to the angles E and F , and the area of the triangle BAC ...
Página 21
... in one point only ; ( Ax . 2. ) and therefore the triangles coincide and are equal in all respects , AB being equal to DE , AC to DF , and the * Eucl . I. 26. Part 1 . angle A to the angle D , and the area SECT . II . ] 21 TRIANGLES .
... in one point only ; ( Ax . 2. ) and therefore the triangles coincide and are equal in all respects , AB being equal to DE , AC to DF , and the * Eucl . I. 26. Part 1 . angle A to the angle D , and the area SECT . II . ] 21 TRIANGLES .
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Términos y frases comunes
AB² ABCD alternate angles angle ABC angle APB angle BAC angles are equal angles equal bisector centre chord circumference coincide College Constr construct contrapositive Crown 8vo describe a circle diagonals diameter divided draw Edition equal angles equal circles equiangular Euclid exterior angle fcap Find the locus four right angles Geometry given angle given circle given line given point given rectilineal figure given straight line hypotenuse included angle inscribed intersect isosceles triangle less Let AB Let ABC locus magnitudes meet middle point minor arc opposite angles opposite sides parallel parallelogram perpendicular polygon PROBLEM produced Proof Q. E. D. THEOREM quadrilateral radius rectangle contained reflex angle required to prove rhombus right angles segment semicircle Shew square subtend supplementary supplementary angles tangent THEOREM trapezium triangle ABC triangles are equal unequal
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