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 72
... exterior angle will be 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 ...
... exterior angle will be 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 ...
Página 75
... angle BKC is equal ( 26. 3. ) to the angle ELF : also because the circles ABC , DEF are equal , their radii are ... exterior angle of the triangle ABC , is also equal ( 25. 1. ) to the two angles ABC , ACB ; therefore the angle BAC is ...
... angle BKC is equal ( 26. 3. ) to the angle ELF : also because the circles ABC , DEF are equal , their radii are ... exterior angle of the triangle ABC , is also equal ( 25. 1. ) to the two angles ABC , ACB ; therefore the angle BAC is ...
Página 93
... exterior angle BCD is equal ( 25. 1. ) to the angles CDA , DAC ; therefore also BDA is equal to BCD ; but BDA is equal to CBD , because the side AD is equal to the side ... angles , therefore five times the angle OF GEOMETRY . BOOK IV . 93.
... exterior angle BCD is equal ( 25. 1. ) to the angles CDA , DAC ; therefore also BDA is equal to BCD ; but BDA is equal to CBD , because the side AD is equal to the side ... angles , therefore five times the angle OF GEOMETRY . BOOK IV . 93.
Página 118
... is equal to the alternate angle CAD ( 21. 1 :) : Wherefore also the angle BAD is equal to the angle E A B D C CAD : Therefore the angle BAC is cut into two equal angles by the straight line AD . PROP . A. THEOR . If the exterior angle of ...
... is equal to the alternate angle CAD ( 21. 1 :) : Wherefore also the angle BAD is equal to the angle E A B D C CAD : Therefore the angle BAC is cut into two equal angles by the straight line AD . PROP . A. THEOR . If the exterior angle of ...
Página 119
... exterior angle of the triangle . Let the exterior angle CAE , of any triangle ABC , be bisected by the straight line AD which meets the base produced in D ; BD is to DC , as BA to AC . E Through C draw CF parallel to AD ( Prob . 13. 1 ...
... exterior angle of the triangle . Let the exterior angle CAE , of any triangle ABC , be bisected by the straight line AD which meets the base produced in D ; BD is to DC , as BA to AC . E Through C draw CF parallel to AD ( Prob . 13. 1 ...
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Términos y frases comunes
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