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 TrigonometryCollins & Hannay, 1860 - 333 páginas |
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Página 228
... difference as the radius to the tangent of the difference between either of them and 45 ° . PROP . IV . The sum of any two sides of a triangle is to their difference , as the tan- gent of half the sum of the angles opposite to those ...
... difference as the radius to the tangent of the difference between either of them and 45 ° . PROP . IV . The sum of any two sides of a triangle is to their difference , as the tan- gent of half the sum of the angles opposite to those ...
Página 229
... difference ; and because BC is parallel to FG , CE : CF :: BE : BG , ( 2. 6. ) that is , the sum of the two sides of the triangle ABC is to their difference as the tangent of half . the sum of the angles oppo- site to those sides to the ...
... difference ; and because BC is parallel to FG , CE : CF :: BE : BG , ( 2. 6. ) that is , the sum of the two sides of the triangle ABC is to their difference as the tangent of half . the sum of the angles oppo- site to those sides to the ...
Página 230
... difference of the sides to the difference of the segments of the base . Q. E. D. PROP . VI . THEOR . In any triangle , twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides ...
... difference of the sides to the difference of the segments of the base . Q. E. D. PROP . VI . THEOR . In any triangle , twice the rectangle contained by any two sides is to the difference between the sum of the squares of those sides ...
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Términos y frases comunes
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 and similar 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 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 side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore