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 sider |
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Resultat 6-10 av 63
Side 31
... square GB : And in the same manner , by joining AE , BK , it is de- monstrated , that the parallelogram CL is equal to the square HC . There- fore , the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is ...
... square GB : And in the same manner , by joining AE , BK , it is de- monstrated , that the parallelogram CL is equal to the square HC . There- fore , the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is ...
Side 41
... length be found . COR . Since a triangle may be converted into an equivalent rectangle , it follows that any polygon may be reduced to an equivalent rectangle . PROP . XVIII . PROB . To describe a square 6 OF GEOMETRY . BOOK I. 41.
... length be found . COR . Since a triangle may be converted into an equivalent rectangle , it follows that any polygon may be reduced to an equivalent rectangle . PROP . XVIII . PROB . To describe a square 6 OF GEOMETRY . BOOK I. 41.
Side 42
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . E From the point A draw ( Prob . 6. ) AC at right angles to AB ; and make ( Prob . 3. ) AD equal to AB , and through ...
... square upon a given straight line . Let AB be the given straight line ; it is required to describe a square upon AB . E From the point A draw ( Prob . 6. ) AC at right angles to AB ; and make ( Prob . 3. ) AD equal to AB , and through ...
Side 43
... square ; then , from C as centre , with a radius equal to the side of the other square , de- scribe an arc cutting AD in D : the square described upon AD will be equivalent to the difference of the squares constructed upon AC and CD ...
... square ; then , from C as centre , with a radius equal to the side of the other square , de- scribe an arc cutting AD in D : the square described upon AD will be equivalent to the difference of the squares constructed upon AC and CD ...
Side 44
... square de- scribed on the double of a line is evidently four times the square described on a single one ; on a triple line nine times that on a single one , & c . 3. In every parallelogram , any of the parallelograms about a diameter ...
... square de- scribed on the double of a line is evidently four times the square described on a single one ; on a triple line nine times that on a single one , & c . 3. In every parallelogram , any of the parallelograms about a diameter ...
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Vanlige uttrykk og setninger
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