A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 30
... produced in order to bisect the angle , and the proof would require modification . The restriction introduced insures that F shall fall within BAC as in the figure . If BA and AC were in one straight line the construction and proof ...
... produced in order to bisect the angle , and the proof would require modification . The restriction introduced insures that F shall fall within BAC as in the figure . If BA and AC were in one straight line the construction and proof ...
Página 32
... producing the line . A method of drawing a line at right angles to a given line from its extremity and without producing the ... produced to any length both ways , and let C be a given point without it . It is required 32 EUCLID'S ELEMENTS .
... producing the line . A method of drawing a line at right angles to a given line from its extremity and without producing the ... produced to any length both ways , and let C be a given point without it . It is required 32 EUCLID'S ELEMENTS .
Página 38
... 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 to D : the exterior angle ACD shall be greater than either of the interior opposite ...
... 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 to D : the exterior angle ACD shall be greater than either of the interior opposite ...
Página 39
... 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 . B [ I. 16. ] To each of these add the angle ACB . There- fore the angles ACD , ACB ...
... 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 . B [ I. 16. ] To each of these add the angle ACB . There- fore the angles ACD , ACB ...
Página 40
... producing the 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 ...
... producing the 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 ...
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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