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, 1851 - 317 σελίδες |
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Σελίδα 46
... 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 . I. PROB . · To find the side of a square equivalent to the difference of two given squares ...
... 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 . I. PROB . · To find the side of a square equivalent to the difference of two given squares ...
Σελίδα 62
... Similar segments of a circle , are those in which the angles are equal , or which contain equal an- gles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw ...
... Similar segments of a circle , are those in which the angles are equal , or which contain equal an- gles . PROP . I. PROB . To find the centre of a given circle . Let ABC be the given circle ; it is required to find its centre . Draw ...
Σελίδα 76
... similar to the segment ADB , and similar segments of circles contain ( 9. def . 3. ) equal angles , the angle 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 ( 9. def . 3. ) equal angles , the angle ACB is equal to the angle ADB , the exterior to the interior , which is impossible ( 16. 1. ) . PROP . XXIV . THEOR . A B Similar ...
Σελίδα 78
... similar ( 9. def . 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore the segment BAC is equal to the ...
... similar ( 9. def . 3. ) to the segment EDF ; and they are upon equal straight lines BC , EF ; but similar segments of circles upon equal straight lines are equal ( 24. 3. ) to one another , therefore the segment BAC is equal to the ...
Σελίδα 87
... similar reasons FB , FC , are equal ; hence the points A , B , C , are all equally distant from the point F , and consequently 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 consequently lie in the circumference of the circle , whose centre is F , and radius FA . It is obvious , that besides ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal 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 PROB PROP proportional 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 touches the circle triangle ABC triangle DEF wherefore