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 42
... equal to AB , and through the point D draw DE parallel ( Prob . 13. ) to AB ... equivalent to the sum of two squares . Draw the two indefinite lines AB , AC ... similar construction which reduces two of them to one , will reduce three of ...
... equal to AB , and through the point D draw DE parallel ( Prob . 13. ) to AB ... equivalent to the sum of two squares . Draw the two indefinite lines AB , AC ... similar construction which reduces two of them to one , will reduce three of ...
Página 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 ...
Página 62
... equal . For 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 ...
... equal . For 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 ...
Página 72
... equal to the interior opposite angle . COR . 2. It follows , likewise , that a quadrilateral , of which the opposite angles are not equal to two right angles , cannot be inscribed in a circle . PROP . XXIII . THEOR Upon the same ...
... equal to the interior opposite angle . COR . 2. It follows , likewise , that a quadrilateral , of which the opposite angles are not equal to two right angles , cannot be inscribed in a circle . PROP . XXIII . THEOR Upon the same ...
Página 73
... similar ( 12 . 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 ( 12 . 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 ...
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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