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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 30
... PROP . XIV . THEOR . If , at a point in a straight line , two other straight lines , upon the oppo- site sides of it , make the adjacent angles together equal to two right angles , these two straight lines are in one and the same ...
... PROP . XIV . THEOR . If , at a point in a straight line , two other straight lines , upon the oppo- site 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
... 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 . A Produce BC to D ; and be- cause ACD is the exterior ...
... 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 . A Produce BC to D ; and be- cause ACD is the exterior ...
Página 33
... PROP : XIX . THEOR . The greater angle of every triangle is subtended by the greater - side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is ...
... PROP : XIX . THEOR . The greater angle of every triangle is subtended by the greater - side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is ...
Página 34
... PROP . XXI . THEOR . If from the ends of one side of a triangle , there be drawn two straight lines to a point within the triangle , these two lines shall be less than the other two sides of the triangle , but shall contain a greater ...
... PROP . XXI . THEOR . If from the ends of one side of a triangle , there be drawn two straight lines to a point within the triangle , these two lines shall be less than the other two sides of the triangle , but shall contain a greater ...
Página 36
... PROP . XXIV . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each . but the angle contained by the two sides of the one great- er than the angle contained by the two sides of the other ; the ...
... PROP . XXIV . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each . but the angle contained by the two sides of the one great- er than the angle contained by the two sides of the other ; the ...
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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 multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals 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 parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore