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 σελίδες |
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Σελίδα 23
... equal to the remainder ( 3. Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is ...
... equal to the remainder ( 3. Ax . ) BG : But it has been shewn that BC is equal to BG ; wherefore AL and BC are each of them equal to BG ; and things that are equal to the same are equal to one another ; therefore the straight line AL is ...
Σελίδα 38
... equal sides are opposite ; therefore the angle GCB is equal to the angle DFE , but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is ...
... equal sides are opposite ; therefore the angle GCB is equal to the angle DFE , but DFE is , by the hypothesis , equal to the angle BCA ; wherefore also the angle BCG is equal to the angle BCA , the less to the greater , which is ...
Σελίδα 84
... equal to the angle at H ; therefore the base BC is equal ( 4. 1. ) to the base EF and because the angle at A is equal to the angle at D , the segment BAC is similar ( 9. def . 3. ) to the segment EDF ; and they are upon equal straight ...
... equal to the angle at H ; therefore the base BC is equal ( 4. 1. ) to the base EF and because the angle at A is equal to the angle at D , the segment BAC is similar ( 9. def . 3. ) to the segment EDF ; and they are upon equal straight ...
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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 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