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 Trigonometry |
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Page 9
... angle at E. ' 7. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other , is called a ...
... angle at E. ' 7. When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other , is called a ...
Page 10
... right angled triangle is that which has a right angle . 23. An obtuse angled triangle is that which has an obtuse angle . 24. An acute angled triangle is that which has three acute angles ... angles right angles . 26. An oblong is that which ...
... right angled triangle is that which has a right angle . 23. An obtuse angled triangle is that which has an obtuse angle . 24. An acute angled triangle is that which has three acute angles ... angles right angles . 26. An oblong is that which ...
Page 18
... 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 point C at right angles to AB . F Take any point D ...
... 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 point C at right angles to AB . F Take any point D ...
Page 19
... right angles , or are together equal to two right angles . For , if the angle CBA be equal to ABD , each of them is a right angle ( Def . 7. ) ; but , if not , from the point B draw BE at right angles ( 11. 1. ) A E A D B D B to CD ; ...
... right angles , or are together equal to two right angles . For , if the angle CBA be equal to ABD , each of them is a right angle ( Def . 7. ) ; but , if not , from the point B draw BE at right angles ( 11. 1. ) A E A D B D B to CD ; ...
Page 20
... right angles ; but the angles ABC , ABD are likewise together equal to two right angles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax ...
... right angles ; but the angles ABC , ABD are likewise together equal to two right angles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining angle ABE is equal ( 3. Ax ...
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Common terms and phrases
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
Popular passages
Page 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.
Page 74 - THE angles in the same segment of a circle are equal to one another...
Page 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.
Page 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.
Page 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 '
Page 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.
Page 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.
Page 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.
Page 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.
Page 13 - BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC.