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 133
... similar to the triangle ABC and the triangles ABD , ADC , being each equiangular and similar to ABC , are equiangular and simi- lar to one another . Therefore , in a right angled , & c . Q. E. D. COR . From this it is manifest , that ...
... similar to the triangle ABC and the triangles ABD , ADC , being each equiangular and similar to ABC , are equiangular and simi- lar to one another . Therefore , in a right angled , & c . Q. E. D. COR . From this it is manifest , that ...
Σελίδα 138
... similar , and similarly situated to a given rectilineal figure . Let AB be the given straight line , and CDEF the given rectilineal figure of four sides ; it is required upon the given straight line AB to describe a rectilineal figure ...
... similar , and similarly situated to a given rectilineal figure . Let AB be the given straight line , and CDEF the given rectilineal figure of four sides ; it is required upon the given straight line AB to describe a rectilineal figure ...
Σελίδα 139
... similar to one another ( def . 1. 6. ) . Next , Let it be required to describe upon a given straight line AB , a rectilineal figure similar , and similarly situated to the rectilineal fi- gure CDKEF . Join DE , and upon the given ...
... similar to one another ( def . 1. 6. ) . Next , Let it be required to describe upon a given straight line AB , a rectilineal figure similar , and similarly situated to the rectilineal fi- gure CDKEF . Join DE , and upon the given ...
Σελίδα 140
... similar to one another and in the same manner a rectilineal figure of six , or more , sides may be described upon a given straight line similar to one given , and so on . Which was to be done . PROP . XIX . THEOR . Similar triangles are ...
... similar to one another and in the same manner a rectilineal figure of six , or more , sides may be described upon a given straight line similar to one given , and so on . Which was to be done . PROP . XIX . THEOR . Similar triangles are ...
Σελίδα 141
... similar , and similarly described triangle upon the second . PROP . XX . THEOR . Similar polygons may be divided into the same number of similar tri- angles , having the same ratio to one another that the polygons have ; and the ...
... similar , and similarly described triangle upon the second . PROP . XX . THEOR . Similar polygons may be divided into the same number of similar tri- angles , having the same ratio to one another that the polygons have ; and 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