A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 28
... triangle is a rigid figure ; ie . , its sides cannot be forced into any ... ABC , DEF be two triangles , having the two sides AB , AC equal to the two ... triangle ABC be applied to the 2 , 3. triangle DEF , so that the point B may be on ...
... triangle is a rigid figure ; ie . , its sides cannot be forced into any ... ABC , DEF be two triangles , having the two sides AB , AC equal to the two ... triangle ABC be applied to the 2 , 3. triangle DEF , so that the point B may be on ...
Página 29
... triangles equal in this prop . When triangles are to be proved equal , he always appeals to prop . 4. The demonstration of this prop . may be conducted thus : For let the triangle DEF be applied to ABC so that the bases may coincide ...
... triangles equal in this prop . When triangles are to be proved equal , he always appeals to prop . 4. The demonstration of this prop . may be conducted thus : For let the triangle DEF be applied to ABC so that the bases may coincide ...
Página 31
... triangle ABC [ I. 1 ] , and bisect the angle ACB by the straight line CD . [ I. 9. ] AB shall be cut into two equal A parts at the point D. D Because AC is equal to CB [ Def . 24 ] , and CD 3 . is common to the two triangles ACD , BCD ...
... triangle ABC [ I. 1 ] , and bisect the angle ACB by the straight line CD . [ I. 9. ] AB shall be cut into two equal A parts at the point D. D Because AC is equal to CB [ Def . 24 ] , and CD 3 . is common to the two triangles ACD , BCD ...
Página 38
Euclides Charles Mansford. PROPOSITION 16 . THEOREM . If one side of a triangle be produced , the exterior angle shall be greater than either of the interior opposite angles . Let ABC be a triangle , and let one side BC be 1 . produced ...
Euclides Charles Mansford. PROPOSITION 16 . THEOREM . If one side of a triangle be produced , the exterior angle shall be greater than either of the interior opposite angles . Let ABC be a triangle , and let one side BC be 1 . produced ...
Página 39
... 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 interior and opposite angle ABC ...
... 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 interior and opposite angle ABC ...
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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