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 TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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Página 25
... remaining sides will also be equal and parallel , and the figure will be a parallelogram . COR . 2. And every quadrilateral , whose opposite sides are equal , is a parallelogram , or has its opposite sides parallel . For , having drawn ...
... remaining sides will also be equal and parallel , and the figure will be a parallelogram . COR . 2. And every quadrilateral , whose opposite sides are equal , is a parallelogram , or has its opposite sides parallel . For , having drawn ...
Página 30
... remaining complement BK is equal to the remaining complement KD . PROP . XXXVII . THEOR . In any right angled triangle , the square which is described upon the side sub- tending the right angle , is equivalent to the squares described ...
... remaining complement BK is equal to the remaining complement KD . PROP . XXXVII . THEOR . In any right angled triangle , the square which is described upon the side sub- tending the right angle , is equivalent to the squares described ...
Página 37
... remaining angle EBD will be the third angle requir- ed ; because those three angles ( Cor . 6. 1. ) are together equal to two right angles . A E C B D PROP . XI . PROB . Two angles of a triangle and a side being given , to construct the ...
... remaining angle EBD will be the third angle requir- ed ; because those three angles ( Cor . 6. 1. ) are together equal to two right angles . A E C B D PROP . XI . PROB . Two angles of a triangle and a side being given , to construct the ...
Página 51
... remaining angle EFG is half a right angle ; therefore the angle GEF is equal to the angle EFG , and the side EG equal ( 4. 1. ) to the side GF ; Again , because the angle at B is half a right angle , and FDB a right angle , for it is ...
... remaining angle EFG is half a right angle ; therefore the angle GEF is equal to the angle EFG , and the side EG equal ( 4. 1. ) to the side GF ; Again , because the angle at B is half a right angle , and FDB a right angle , for it is ...
Página 52
... remaining angle DGB is half a right angle , and is therefore equal to the angle DBG ; wherefore also the side DB is equal ( 4. 1. ) to the side DG . Again , because EGF is half a right angle , and the angle at F a right angle , being ...
... remaining angle DGB is half a right angle , and is therefore equal to the angle DBG ; wherefore also the side DB is equal ( 4. 1. ) to the side DG . Again , because EGF is half a right angle , and the angle at F a right angle , being ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore