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 64
... half the side bisected , and of the square of the line drawn from the point of bisection to the opposite an- gle of the triangle . Let ABC be a triangle , of which the side BC is bisected in D , and DA drawn to the opposite angle ; the ...
... half the side bisected , and of the square of the line drawn from the point of bisection to the opposite an- gle of the triangle . Let ABC be a triangle , of which the side BC is bisected in D , and DA drawn to the opposite angle ; the ...
Página 84
... half of the B H C E K F angle BGC , and the angle at D half of the angle EHF : therefore the angle at A is equal to the angle at D. Wherefore , in equal circles , & c . Q. E. D. PROP . XXVIII . THEOR . In equal circles , equal straight ...
... half of the B H C E K F angle BGC , and the angle at D half of the angle EHF : therefore the angle at A is equal to the angle at D. Wherefore , in equal circles , & c . Q. E. D. PROP . XXVIII . THEOR . In equal circles , equal straight ...
Página 99
... half of AD , and AF the half of AB , AE is equal to AF ; wherefore the sides opposite to these are equal , viz . FG to GE ; in the same manner , it may be demonstrated , that GH , GK , are each of them equal to FG or GE ; there- fore ...
... half of AD , and AF the half of AB , AE is equal to AF ; wherefore the sides opposite to these are equal , viz . FG to GE ; in the same manner , it may be demonstrated , that GH , GK , are each of them equal to FG or GE ; there- fore ...
Página 104
... half of the angle BCD , and CDF the half of CDE ; the angle FCD is equal F to FDC ; wherefore the side CF is equal ( 104 ELEMENTS.
... half of the angle BCD , and CDF the half of CDE ; the angle FCD is equal F to FDC ; wherefore the side CF is equal ( 104 ELEMENTS.
Página 147
... half the line . Let AB be a given straight line , which is bisected in C ; and let D be any point in it , the square on AC is C D B greater than the rectangle AD , DB . For , since the straight line AB is divided in two equal parts in C ...
... half the line . Let AB be a given straight line , which is bisected in C ; and let D be any point in it , the square on AC is C D B greater than the rectangle AD , DB . For , since the straight line AB is divided in two equal parts in C ...
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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