The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 6
... BC is equal to BA : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB : But things which are equal to the same are equal to one another ( Axiom 1 ) ; therefore CA is equal to CB : Where- fore ...
... BC is equal to BA : But it has been proved that CA is equal to AB ; therefore CA , CB are each of them equal to AB : But things which are equal to the same are equal to one another ( Axiom 1 ) ; therefore CA is equal to CB : Where- fore ...
Página 7
... equal to BC . Because the point B is the centre of the circle CGH , BC is equal to BG : And because D is the centre of the circle GKL , DL is equal to DG : and DA , DB , parts of them , are equal ( Construction ) ; therefore the ...
... equal to BC . Because the point B is the centre of the circle CGH , BC is equal to BG : And because D is the centre of the circle GKL , DL is equal to DG : and DA , DB , parts of them , are equal ( Construction ) ; therefore the ...
Página 8
... equal to AD : Wherefore AE is equal to C , and from AB , the greater of two given straight lines , a part AE has ... BC shall be equal to the base EF , and the triangle ABC to the triangle DEF , and the other angles shall be equal , each ...
... equal to AD : Wherefore AE is equal to C , and from AB , the greater of two given straight lines , a part AE has ... BC shall be equal to the base EF , and the triangle ABC to the triangle DEF , and the other angles shall be equal , each ...
Página 9
... BC does not coincide with EF , two straight lines would enclose a space - which is im- possible ( 4x . 10 ) ; therefore the base BC shall coincide with the base EF , and be equal to it ( Ax . 8 ) ; and the whole triangle ABC shall ...
... BC does not coincide with EF , two straight lines would enclose a space - which is im- possible ( 4x . 10 ) ; therefore the base BC shall coincide with the base EF , and be equal to it ( Ax . 8 ) ; and the whole triangle ABC shall ...
Página 11
... equal to AC the less , and join DC : Then , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both triangles , the two sides DB , BC are equal to the two AC , CB , each to each , and the angle DBC is equal to the ...
... equal to AC the less , and join DC : Then , because in the triangles DBC , ACB , DB is equal to AC , and BC common to both triangles , the two sides DB , BC are equal to the two AC , CB , each to each , and the angle DBC is equal to the ...
Términos y frases comunes
AB² ABCD AC² AD² adjacent angles angle ABC angle ACB angle BAC angle equal base BC BC is equal centre chord circle ABC circumference diameter double draw equal angles equal to F equiangular equilateral triangle equimultiples exterior angle fore given circle given line given point given rectilineal given straight line gnomon hypotenuse inscribed intersection isosceles triangle join less Let ABC lines be drawn lines drawn meet multiple opposite angles parallel to BC parallelogram perpendicular plane polygon PROB produced proportionals Q. E. D. PROP rectangle contained rectilineal figure remaining angle right angles segment semicircle shew shewn square on AC tangents THEOR touches the circle triangle ABC twice the rectangle vertex Wherefore