A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes, Exercises and Explanations ... By C. Mansford1874 |
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Página 22
... angle DEF , and the angle ACB to the angle DFE . For if the triangle ABC be applied to the 2 , 3. triangle DEF , so that the point A may be on the point D , and the straight line AB on the straight line DE , the point B will coincide ...
... angle DEF , and the angle ACB to the angle DFE . For if the triangle ABC be applied to the 2 , 3. triangle DEF , so that the point A may be on the point D , and the straight line AB on the straight line DE , the point B will coincide ...
Página 23
... 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 , and the angle ACB to the angle DFE . Therefore , if two triangles , & c . Q.E.D. The letters Q.E.D. = quod ...
... 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 , and the angle ACB to the angle DFE . Therefore , if two triangles , & c . Q.E.D. The letters Q.E.D. = quod ...
Página 24
... angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB , and the triangle ... ACB , which are the angles at the base of the triangle ABC . [ Ax . 3. ] And it has also been proved that the angle ...
... angle FAG common to the two triangles AFC , AGB ; therefore the base FC is equal to the base GB , and the triangle ... ACB , which are the angles at the base of the triangle ABC . [ Ax . 3. ] And it has also been proved that the angle ...
Página 25
... angle GCB , which are the angles on the other side of the base . Therefore the angles , & c . Q.E.D. Corollary ... ACB are equal to one another . 2. The opposite angles of a rhombus are equal to one another . [ Draw the diagonal ...
... angle GCB , which are the angles on the other side of the base . Therefore the angles , & c . Q.E.D. Corollary ... ACB are equal to one another . 2. The opposite angles of a rhombus are equal to one another . [ Draw the diagonal ...
Página 26
... angle ACB ; [ Hyp . ] therefore the base DC 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 , that is , it ...
... angle ACB ; [ Hyp . ] therefore the base DC 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 , that is , it ...
Otras ediciones - Ver todas
A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ... Euclides Vista completa - 1874 |
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 CBA axioms base BC BC is equal 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 Let ABC Let the straight obtuse opposite angle opposite sides parallel to CD parallelogram parallelogram ABCD perpendicular produced prop PROPOSITION 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