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 sider |
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Side 17
... PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AE ...
... PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from AC cut ( 3. 1. ) off AE ...
Side 18
... PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in that line . Let AB be a given straight line , and C a point given in it ; it is requi- red to draw a straight line from the ...
... PROP . XI . PROB . To draw a straight line at right angles to a given straight line , from a given point in that line . Let AB be a given straight line , and C a point given in it ; it is requi- red to draw a straight line from the ...
Side 22
... PROP . XIX . THEOR . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is likewise ...
... PROP . XIX . THEOR . The greater angle of every triangle is subtended by the greater side , or has the greater side opposite to it . Let ABC be a triangle , of which the angle ABC is greater than the angle BCA ; the side AC is likewise ...
Side 24
... PROP . XXIII . PROB . At a given point in a given straight line , to make a rectilineal angle equal to a given ... PROP . XXIV . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , but the ...
... PROP . XXIII . PROB . At a given point in a given straight line , to make a rectilineal angle equal to a given ... PROP . XXIV . THEOR . If two triangles have two sides of the one equal to two sides of the other , each to each , but the ...
Side 27
... PROP . XXVII . THEOR . If a straight line falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight lines ...
... PROP . XXVII . THEOR . If a straight line falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight lines ...
Andre utgaver - Vis alle
Elements of Geometry: Containing the First Six Books of Euclid, with a ... Euclid,John Playfair Uten tilgangsbegrensning - 1851 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1857 |
Elements of Geometry: Containing the First Six Books of Euclid, with a ... John Playfair Uten tilgangsbegrensning - 1836 |
Vanlige uttrykk og setninger
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
Populære avsnitt
Side 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.
Side 74 - THE angles in the same segment of a circle are equal to one another...
Side 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.
Side 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.
Side 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 '
Side 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.
Side 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.
Side 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.
Side 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.
Side 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.