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, 1847 - 317 sider |
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Side 13
... PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part ...
... PROP . III . PROB . From the greater of two given straight lines to cut off a part equal to the less . Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , the greater , a part ...
Side 15
... PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB ...
... PROP . VI . THEOR . If two angles of a triangle be equal to one another , the sides which subtend or are opposite to them , are also equal to one another . Let ABC be a triangle having the angle ABC equal to the angle ACB ; the side AB ...
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 19
... PROP . XIII . THEOR . The angles which one straight line makes with another upon one side of it , are either two right angles , or are together equal to two right angles . Let the straight line AB make with CD , upon one side of it the ...
... PROP . XIII . THEOR . The angles which one straight line makes with another upon one side of it , are either two right angles , or are together equal to two right angles . Let the straight line AB make with CD , upon one side of it the ...
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Almindelige termer og sætninger
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
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Side 53 - 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 18 - If two triangles have two sides of the one equal to two sides of the...
Side 54 - If a straight line be bisected, and produced to any point, the rectangle contained by the whole line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced.
Side 82 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Side 31 - 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 11 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference, are equal to one another.
Side 21 - The angles which one straight line makes with another upon one side of it, are either two right angles, or are together equal to two right angles. Let the straight line AB make with CD, upon one side of it, the angles CBA, ABD : these shall either be two right angles, or shall together be equal to two right angles. For...
Side 101 - To describe an isosceles triangle, having each of the angles at the base double of the third angle.
Side 58 - AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part.
Side 298 - 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.