A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página 23
... whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Ax . 8 ] And the other angles of the one coincide with the other angles of the other , and are equal to them , namely , the angle ABC to the angle DEF ...
... whole triangle ABC coincides with the whole triangle DEF , and is equal to it . [ Ax . 8 ] And the other angles of the one coincide with the other angles of the other , and are equal to them , namely , the angle ABC to the angle DEF ...
Página 24
... whole AF is equal to the whole AG , of which the parts AB , AC are equal , [ Hyp . ] the remainder BF is equal to the remainder CG . [ Ax . 3. ] And FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two ...
... whole AF is equal to the whole AG , of which the parts AB , AC are equal , [ Hyp . ] the remainder BF is equal to the remainder CG . [ Ax . 3. ] And FC was proved to be equal to GB ; therefore the two sides BF , FC are equal to the two ...
Página 29
... whole angle BAC BGC , that is EDF . Q.E.D. Ex . 1. The diagonal of a rhombus bisects each of the angles through which it passes . Hence show that 2. The diagonals of a square bisect each other at right angles . [ Prop . 4. ] PROPOSITION ...
... whole angle BAC BGC , that is EDF . Q.E.D. Ex . 1. The diagonal of a rhombus bisects each of the angles through which it passes . Hence show that 2. The diagonals of a square bisect each other at right angles . [ Prop . 4. ] PROPOSITION ...
Página 58
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC . [ Ax . 2. ] To each of these equals add the angle ACB ; therefore , the angles ACD , ACB are equal to the three angles CBA , BAC , ACB . [ Ax . 2 ...
... whole exterior angle ACD is equal to the two interior and opposite angles CAB , ABC . [ Ax . 2. ] To each of these equals add the angle ACB ; therefore , the angles ACD , ACB are equal to the three angles CBA , BAC , ACB . [ Ax . 2 ...
Página 63
... whole , or the remainder , AE is equal to the whole , or the remainder , DF . [ Ax . 2 , 3. ] And AB is equal to DC ; [ I. 34. ] there- fore the two EA , AB are equal to the two FD , DC each to each ; and the exterior angle FDC is equal ...
... whole , or the remainder , AE is equal to the whole , or the remainder , DF . [ Ax . 2 , 3. ] And AB is equal to DC ; [ I. 34. ] there- fore the two EA , AB are equal to the two FD , DC each to each ; and the exterior angle FDC is equal ...
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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