A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 26
... equal to the angle ACB ; [ Hyp . ] therefore the base DO is equal to the base AB , and the triangle DBC is equal to the triangle ACB , [ I. 4. ] the less to the greater ; which is absurd . [ Ax . 9. ] Therefore AB is not unequal to AC ...
... equal to the angle ACB ; [ Hyp . ] therefore the base DO is equal to the base AB , and the triangle DBC is equal to the triangle ACB , [ I. 4. ] the less to the greater ; which is absurd . [ Ax . 9. ] Therefore AB is not unequal to AC ...
Página 27
... equal to one another , and likewise their sides CB , DB , that are terminated in B. 2 . 3 . A Join CD . Then in the case in which the vertex of each triangle is without the other triangle ; because AC is equal to AD [ Hyp . ] , the ...
... equal to one another , and likewise their sides CB , DB , that are terminated in B. 2 . 3 . A Join CD . Then in the case in which the vertex of each triangle is without the other triangle ; because AC is equal to AD [ Hyp . ] , the ...
Página 28
... AC equal to the two sides DE , DF , each to each , namely AB to DE and AC to DF , and also the base BC equal to the base EF ; the angle BAC shall be equal to the angle EDF . A B For if the triangle ABC be applied to the 2 , 3. triangle ...
... AC equal to the two sides DE , DF , each to each , namely AB to DE and AC to DF , and also the base BC equal to the base EF ; the angle BAC shall be equal to the angle EDF . A B For if the triangle ABC be applied to the 2 , 3. triangle ...
Página 29
... equal to one another , and like- wise their sides which are terminated in the other extremity . But this is impossible . [ I. 7. ] Therefore if the base BC coincides with the base EF , the sides BA , AC must coincide with the sides ED ...
... equal to one another , and like- wise their sides which are terminated in the other extremity . But this is impossible . [ I. 7. ] Therefore if the base BC coincides with the base EF , the sides BA , AC must coincide with the sides ED ...
Página 30
... equal angles . 1 . Let BAC be the given recti- lineal angle . It is required to bisect it . 2 . Take any point D in AB , and from AC cut off AE equal to AD [ I. 3 ] ; join DE , and on DE on the side remote from A describe the ...
... equal angles . 1 . Let BAC be the given recti- lineal angle . It is required to bisect it . 2 . Take any point D in AB , and from AC cut off AE equal to AD [ I. 3 ] ; join DE , and on DE on the side remote from A describe the ...
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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