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, 1853 - 317 páginas |
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Página 3
... passing through the hands of the ancient editors during the decline of science , had suffered some diminution of their excellence , and much skill and learning have been employed by the modern mathemati- cians to deliver them from ...
... passing through the hands of the ancient editors during the decline of science , had suffered some diminution of their excellence , and much skill and learning have been employed by the modern mathemati- cians to deliver them from ...
Página 37
... passes , and let BK , KD be the other parallelograms , which make up the whole figure ABCD , and are therefore called the complements ; The complement BK is equal to the com- plement KD . Because ABCD is a parallelogram and AC its ...
... passes , and let BK , KD be the other parallelograms , which make up the whole figure ABCD , and are therefore called the complements ; The complement BK is equal to the com- plement KD . Because ABCD is a parallelogram and AC its ...
Página 63
... pass through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it . Let ABC be a circle , and let CD , a straight line drawn through the centre , bisect any straight line AB , which ...
... pass through the centre , it will cut that line at right angles ; and if it cut it at right angles , it will bisect it . Let ABC be a circle , and let CD , a straight line drawn through the centre , bisect any straight line AB , which ...
Página 64
... pass through the centre , cuts AB at right angles . Again , let CD cut AB at right angles ; CD also bisects AB ... pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in it ...
... pass through the centre , cuts AB at right angles . Again , let CD cut AB at right angles ; CD also bisects AB ... pass through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in it ...
Página 65
... passing through the centre is always greater than one more remote from it ; And from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . Let ABCD be a ...
... passing through the centre is always greater than one more remote from it ; And from the same point there can be drawn only two straight lines that are equal to one another , one upon each side of the shortest line . Let ABCD be a ...
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Términos y frases comunes
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
Pasajes populares
Página 51 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Página 74 - THE angles in the same segment of a circle are equal to one another...
Página 37 - To a given straight line to apply a parallelogram, which shall be equal to a given triangle, and have one of its angles equal to a given rectilineal angle.
Página 29 - Straight lines which are parallel to the same straight line are parallel to one another. Triangles and Rectilinear Figures. The sum of the angles of a triangle is equal to two right angles.
Página 29 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through EAF the point A, parallel to the straight line '
Página 147 - If the vertical angle of a triangle be bisected by a straight line which also cute the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Página 19 - The angles which one straight line makes with another upon one side of i't, are either two right angles, or are together eqval to two right angles.
Página 134 - IF three straight lines be proportionals, the rectangle contained by the extremes is equal to the square of the mean : and if the rectangle contained by the extremes be equal to the square of the mean, the three straight lines are proportionals.
Página 294 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Página 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.