The Elements of EuclidLongmans, Green and Company, 1866 - 376 páginas |
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Página 7
... Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Q. E. F. PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the ...
... Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC . Q. E. F. PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the ...
Página 9
... Wherefore , If two triangles , & c . 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 ...
... Wherefore , If two triangles , & c . 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 ...
Página 10
... Wherefore , The angles at the base , & c . Q. E.D. COROLLARY . equiangular . C G E Hence every equilateral triangle is also PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides also which subten l , or are ...
... Wherefore , The angles at the base , & c . Q. E.D. COROLLARY . equiangular . C G E Hence every equilateral triangle is also PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides also which subten l , or are ...
Página 11
... Wherefore , If two angles , & c . 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 ...
... Wherefore , If two angles , & c . 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 ...
Página 12
... Wherefore , Upon the same base , & c . 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 ...
... Wherefore , Upon the same base , & c . 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 ...
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