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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Side
... similar to that of LEGENDRE , in his Elements of Geometry and Trigono- metry . As the properties of the sections of straight lines are easily derived from Algebra , the demonstrations of the principal propositions in the Second Book are ...
... similar to that of LEGENDRE , in his Elements of Geometry and Trigono- metry . As the properties of the sections of straight lines are easily derived from Algebra , the demonstrations of the principal propositions in the Second Book are ...
Side 42
... the sum of any number of squares ; for a similar construction which reduces two of them to one , will reduce three of them to two , and these two to one , and so of others . PROP . XX . PROB . To find the side 42 ELEMENTS.
... the sum of any number of squares ; for a similar construction which reduces two of them to one , will reduce three of them to two , and these two to one , and so of others . PROP . XX . PROB . To find the side 42 ELEMENTS.
Side 56
... Similar segments of a circle , are those in which the angles are equal , or which contain equal an- gles . PROP . I. THEOR . A diameter divides a circle and its circumference into two equal parts ; and , con- versely , the line which ...
... Similar segments of a circle , are those in which the angles are equal , or which contain equal an- gles . PROP . I. THEOR . A diameter divides a circle and its circumference into two equal parts ; and , con- versely , the line which ...
Side 62
... similar reasons FB , FC , are equal ; hence the points A , B , C , are all equally distant from the point F , and con- sequently lie in the circumference of the circle , whose centre is F , and radius FA . It is obvious , that besides ...
... similar reasons FB , FC , are equal ; hence the points A , B , C , are all equally distant from the point F , and con- sequently lie in the circumference of the circle , whose centre is F , and radius FA . It is obvious , that besides ...
Side 72
... similar to the segment ADB , and similar segments of circles contain ( 12. def . 3. ) equal angles , the angles ACB is equal to the angle ADB , the exterior to the interior , which is impossible ( 16. 1. ) PROP . XXIV . THEOR . A B Similar ...
... similar to the segment ADB , and similar segments of circles contain ( 12. def . 3. ) equal angles , the angles ACB is equal to the angle ADB , the exterior to the interior , which is impossible ( 16. 1. ) PROP . XXIV . THEOR . A B Similar ...
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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