A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C. Mansford1874 |
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Página ix
... common notions ' which are true of all magnitudes whatever . The twelfth axiom may be more simply expressed thus , " Two straight lines which cut one another cannot be both parallel to a third straight line . ” 6 The definitions and ...
... common notions ' which are true of all magnitudes whatever . The twelfth axiom may be more simply expressed thus , " Two straight lines which cut one another cannot be both parallel to a third straight line . ” 6 The definitions and ...
Página 24
... common to the two tri- angles AFC , AGB ; there- fore the base FC is equal D to the base GB , and the triangle AFC to the triangle AGB , and the remaining angles of the one to the remaining angles of the other , each to each , to which ...
... common to the two tri- angles AFC , AGB ; there- fore the base FC is equal D to the base GB , and the triangle AFC to the triangle AGB , and the remaining angles of the one to the remaining angles of the other , each to each , to which ...
Página 25
... and join DC . B Then , because in the triangles DBC , ACB , DB 3 . is equal to AC , [ Con . ] and BC is common to both , the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the BOOK I. 6 . 25.
... and join DC . B Then , because in the triangles DBC , ACB , DB 3 . is equal to AC , [ Con . ] and BC is common to both , the two sides DB , BC are equal to the two sides AC , CB , each to each ; and the BOOK I. 6 . 25.
Página 30
... common to A the two triangles DAF , EAF , the two sides DA , AF are equal to the two sides EA , AF , each to each ; and the base DF is equal to the base EF [ Def . 24 ] ; there- fore the angle DAF is equal to the angle EAF . [ I. 8 ...
... common to A the two triangles DAF , EAF , the two sides DA , AF are equal to the two sides EA , AF , each to each ; and the base DF is equal to the base EF [ Def . 24 ] ; there- fore the angle DAF is equal to the angle EAF . [ I. 8 ...
Página 31
... common to the two triangles ACD , BCD , the two sides , AC , CD are equal to the two sides BC , CD , each to each ; and the angle ACD is equal to the angle BCD [ Con . ] ; therefore the base AD is equal to the base DB . [ I. 4 ...
... common to the two triangles ACD , BCD , the two sides , AC , CD are equal to the two sides BC , CD , each to each ; and the angle ACD is equal to the angle BCD [ Con . ] ; therefore the base AD is equal to the base DB . [ I. 4 ...
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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