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 TrigonometryW.E. Dean, 1839 - 318 σελίδες |
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Σελίδα 124
... altitude of any figure is the straight line drawn from its vertex perpendicular to the base . PROP . I. THEOR . Triangles and parallelograms , of the same altitude , are one to another as their bases . Let the triangles ABC , ACD , and ...
... altitude of any figure is the straight line drawn from its vertex perpendicular to the base . PROP . I. THEOR . Triangles and parallelograms , of the same altitude , are one to another as their bases . Let the triangles ABC , ACD , and ...
Σελίδα 125
... altitudes , are to one another as their bases . Let the figures be placed so as to have their bases in the same straight line ; and having drawn perpendiculars from the vertices of the triangles to the bases , the straight line which ...
... altitudes , are to one another as their bases . Let the figures be placed so as to have their bases in the same straight line ; and having drawn perpendiculars from the vertices of the triangles to the bases , the straight line which ...
Σελίδα 126
... altitude , viz . the perpen- dicular drawn from the point E to AB , they are to one another as their bases ; and for the same reason , as the triangle CDE to the tri- angle ADE , so is CE to EA . Therefore , as BD to DA , so is CE to ΕΑ ...
... altitude , viz . the perpen- dicular drawn from the point E to AB , they are to one another as their bases ; and for the same reason , as the triangle CDE to the tri- angle ADE , so is CE to EA . Therefore , as BD to DA , so is CE to ΕΑ ...
Σελίδα 136
... altitude , AB : FE :: DB : BE ( 1.6 . ) , also , BC : FE :: GB : BF ( 1. 6. ) ; therefore DB : BE :: GB : BF ( 11.5 . ) . Wherefore , the sides of the parallelograms AB , BC about their equal angles are re- ciprocally proportional . But ...
... altitude , AB : FE :: DB : BE ( 1.6 . ) , also , BC : FE :: GB : BF ( 1. 6. ) ; therefore DB : BE :: GB : BF ( 11.5 . ) . Wherefore , the sides of the parallelograms AB , BC about their equal angles are re- ciprocally proportional . But ...
Σελίδα 171
... altitudes are as their ba- ses ( 1. 6. ) , X : AO :: Y : GP , and again alternately , X : Y :: AO : GP ; wherefore , taking the doubles of each , the circumference ABD is to the circumference GHL as the diameter AD to the diameter GL ...
... altitudes are as their ba- ses ( 1. 6. ) , X : AO :: Y : GP , and again alternately , X : Y :: AO : GP ; wherefore , taking the doubles of each , the circumference ABD is to the circumference GHL as the diameter AD to the diameter GL ...
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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 definition 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 opposite angle parallel parallelogram parallelopipeds perpendicular polygon prism produced proportional 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 parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore