Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids ; to which are Added, Elements of Plane and Spherical TrigonometryW.E. Dean, 1839 - 318 páginas |
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Página 25
... Q. E. D. COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to them , are also equal to one another ...
... Q. E. D. COROLLARY . Hence every equilateral triangle is also equiangular . PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend , or are opposite to them , are also equal to one another ...
Página 30
... 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 are in one and the same ...
... 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 are in one and the same ...
Página 32
... Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the ...
... Q. E. D. PROP . XVII . THEOR . Any two angles of a triangle are together less than two right angles . Let ABC be any triangle ; any two of its angles together are less than two right angles . Produce BC to D ; and because ACD is the ...
Página 33
... PROP . XIX . THEOR . The greater angle of every triangle is subtended by the greater side , or has the greater side ... Q. E. D. E PROP . XXI . THEOR . If from the ends OF GEOMETRY . BOOK I. 33.
... PROP . XIX . THEOR . The greater angle of every triangle is subtended by the greater side , or has the greater side ... Q. E. D. E PROP . XXI . THEOR . If from the ends OF GEOMETRY . BOOK I. 33.
Página 34
... Q. E. D. PROP . XXII . PROB . To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third ( 20. 1. ) Let A , B , C be the three given ...
... Q. E. D. PROP . XXII . PROB . To construct a triangle of which the sides shall be equal to three given straight lines ; but any two whatever of these lines must be greater than the third ( 20. 1. ) Let A , B , C be the three given ...
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ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes meet opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism PROB produced proportional proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelopipeds spherical angle spherical triangle square straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore