The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
Dentro del libro
Resultados 1-5 de 35
Página 9
... the base GB , and the triangle AFC to the triangle AGB , and the remaining angles of the one to the remain- ing angles of the other , each to each , to which the equal G E sides are opposite , viz . the angle ACF to BOOK I.
... the base GB , and the triangle AFC to the triangle AGB , and the remaining angles of the one to the remain- ing angles of the other , each to each , to which the equal G E sides are opposite , viz . the angle ACF to BOOK I.
Página 10
... remaining angle ABC is there- fore equal to the remaining angle ACB ( Ax . 3 ) , which are the angles at the base of the triangle ABC : And it has been proved that the angle FBC is equal to the angle GCB , which are the angles upon the ...
... remaining angle ABC is there- fore equal to the remaining angle ACB ( Ax . 3 ) , which are the angles at the base of the triangle ABC : And it has been proved that the angle FBC is equal to the angle GCB , which are the angles upon the ...
Página 18
... remaining angle ABE is equal to the remaining angle ABD ( Ax . 3 ) , the less to the greater - which is absurd : Therefore BE is not in the same straight line with BC : And in like manner it may be demon- strated that no other can be in ...
... remaining angle ABE is equal to the remaining angle ABD ( Ax . 3 ) , the less to the greater - which is absurd : Therefore BE is not in the same straight line with BC : And in like manner it may be demon- strated that no other can be in ...
Página 19
... remaining angles , each to each , to which the equal sides are opposite ; therefore the angle BAE is equal to the angle ECF : But the angle ECD is greater than the angle ECF ; therefore the angle ACD is greater than the angle BAE , or ...
... remaining angles , each to each , to which the equal sides are opposite ; therefore the angle BAE is equal to the angle ECF : But the angle ECD is greater than the angle ECF ; therefore the angle ACD is greater than the angle BAE , or ...
Página 29
... remaining angle AGH is equal to the remaining angle GHD : And they are alternate angles ; therefore AB is parallel to CD . Wherefore , If a straight line , & c . Q. E. D. PROP . XXIX . THEOR . If a straight line D 3 BOOK I. 29 like ...
... remaining angle AGH is equal to the remaining angle GHD : And they are alternate angles ; therefore AB is parallel to CD . Wherefore , If a straight line , & c . Q. E. D. PROP . XXIX . THEOR . If a straight line D 3 BOOK I. 29 like ...
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