A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 26
... less to the greater ; which is absurd . [ Ax . 9. ] Therefore AB is not unequal to AC , that is , it is equal to it . Therefore , if two angles , & c . Q.E.D. Corollary . Hence every equiangular triangle is also equilateral . If the ...
... less to the greater ; which is absurd . [ Ax . 9. ] Therefore AB is not unequal to AC , that is , it is equal to it . Therefore , if two angles , & c . Q.E.D. Corollary . Hence every equiangular triangle is also equilateral . If the ...
Página 36
... less to the greater ; which is impossible . Therefore BE is not in the same straight line with CB . there- And in like manner it may be proved that no other can be in the same straight line with it but BD ; fore BD is in the same ...
... less to the greater ; which is impossible . Therefore BE is not in the same straight line with CB . there- And in like manner it may be proved that no other can be in the same straight line with it but BD ; fore BD is in the same ...
Página 39
... less than two right angles . Let ABC be any triangle : any two of its angles are together less than two right angles . Produce BC to 1 . 2 . D. Then because 3 . ACD is the ex- terior angle of the tri- angle ABC , it is greater than the ...
... less than two right angles . Let ABC be any triangle : any two of its angles are together less than two right angles . Produce BC to 1 . 2 . D. Then because 3 . ACD is the ex- terior angle of the tri- angle ABC , it is greater than the ...
Página 40
... less side AB to E , making AE equal to AC , and joining CE . PROPOSITION 19. THEOREM . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . 1 . Let ABC be a triangle , of which ...
... less side AB to E , making AE equal to AC , and joining CE . PROPOSITION 19. THEOREM . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . 1 . Let ABC be a triangle , of which ...
Página 41
... less than AB , for then the angle ABC would be less than the angle ACB [ I. 18 ] ; but it is not [ Hyp . ] ; therefore AC is not less than AB . And it has been proved that AC is not equal to AB . Therefore AC is greater than AB ...
... less than AB , for then the angle ABC would be less than the angle ACB [ I. 18 ] ; but it is not [ Hyp . ] ; therefore AC is not less than AB . And it has been proved that AC is not equal to AB . Therefore AC is greater than AB ...
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A School Euclid, Being Books I. & II. of Euclid's Elements, with Notes by C ... Euclides Sin vista previa disponible - 2015 |
Términos y frases comunes
AC is equal adjacent angles alternate angles angle ABC angle ACB angle AGH angle BAC angle BCD angle EDF angle equal angles are equal angles CEA axioms base BC bisect centre circle coincide Const diagonals diameter double equal sides equal to BC equal to twice equilateral triangle Euclid exterior angle fore four right angles given point given rectilineal angle given straight line gnomon half a right hypotenuse interior and opposite isosceles triangle join less Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop quadrilateral rectangle AC rectangle contained remaining angle rhombus right angles right-angled triangle shew side BC sides equal square described square on AC THEOREM third angle triangle ABC triangle DEF truths twice the rectangle unequal