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 σελίδες |
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Σελίδα 31
... right angles ; therefore the two angles CEA , AED are equal to the two AED , DEB . Take a- way the common angle AED , and the remaining angle CEA it A- -B E D is equal ( 3. Ax . ) to the remaining angle DEB . In the same manner may be ...
... right angles ; therefore the two angles CEA , AED are equal to the two AED , DEB . Take a- way the common angle AED , and the remaining angle CEA it A- -B E D is equal ( 3. Ax . ) to the remaining angle DEB . In the same manner may be ...
Σελίδα 32
... 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 angle of the triangle ABC ...
... 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 angle of the triangle ABC ...
Σελίδα 39
... right angles ; the two straight lines are parallel to one another . Let the straight line EF , which falls upon the ... angles on the same side BGH , GHD together equal to two right angles ; AB is paral- lel to CD . Because the angle EGB ...
... right angles ; the two straight lines are parallel to one another . Let the straight line EF , which falls upon the ... angles on the same side BGH , GHD together equal to two right angles ; AB is paral- lel to CD . Because the angle EGB ...
Σελίδα 40
... angle EGB is equal to the interior and opposite , upon the same side , GHD ; and the two interior angles BGH , GHD upon the same side are together equal to two right angles . For if AGH be not equal to GHD , let KG be drawn making the angle ...
... angle EGB is equal to the interior and opposite , upon the same side , GHD ; and the two interior angles BGH , GHD upon the same side are together equal to two right angles . For if AGH be not equal to GHD , let KG be drawn making the angle ...
Σελίδα 41
... angles ; therefore AB is parallel ( 27.1 . ) to CD . Where- fore straight lines , & c . Q. E. D. A Ꮐ B E I T K D ... right angles . Let ABC be a triangle , and let one of its sides BC be produced to D ; the exterior angle ACD is equal ...
... angles ; therefore AB is parallel ( 27.1 . ) to CD . Where- fore straight lines , & c . Q. E. D. A Ꮐ B E I T K D ... right angles . Let ABC be a triangle , and let one of its sides BC be produced to D ; the exterior angle ACD is equal ...
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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