The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 9
... Q. E. D. PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle ...
... Q. E. D. PROP . V. THEOR . The angles at the base of an isosceles triangle are equal to one another ; and , if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles triangle ...
Página 11
... Q. E. D. B COR . Hence every equiangular triangle is also equi- lateral . PROP . VII . THEOR . Upon the same base , and on the same side of it , there cannot be two triangles which have their sides terminated at one extremity of the ...
... Q. E. D. B COR . Hence every equiangular triangle is also equi- lateral . PROP . VII . THEOR . Upon the same base , and on the same side of it , there cannot be two triangles which have their sides terminated at one extremity of the ...
Página 12
... Q. E. D. PROP . VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have also their bases equal , the angle which is contained by the two sides of the one shall be equal to the ...
... Q. E. D. PROP . VIII . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , and have also their bases equal , the angle which is contained by the two sides of the one shall be equal to the ...
Página 13
... Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle : it is required to bisect it . A Take any point D in AB , and from AC cut off AE ...
... Q. E. D. PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . Let BAC be the given rectilineal angle : it is required to bisect it . A Take any point D in AB , and from AC cut off AE ...
Página 17
... Q. E.D. PROP . XIV . THEOR . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and the ...
... Q. E.D. PROP . XIV . THEOR . If , at a point in a straight line , two other straight lines , upon the opposite sides of it , make the adjacent angles together equal to two right angles , these two straight lines shall be in one and 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