Elements of Geometry and Conic Sections |
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Page 19
... bisected by the straight line AD ; then , in the two trian- gles ABD , ACD , two sides AB , AD , and the in- cluded angle in the one , are equal to the two B sides AC , AD , and the included angle in the other ; there fore ( Prop . VI ...
... bisected by the straight line AD ; then , in the two trian- gles ABD , ACD , two sides AB , AD , and the in- cluded angle in the one , are equal to the two B sides AC , AD , and the included angle in the other ; there fore ( Prop . VI ...
Page 20
... bisecting the vertical angle of an isosceles triangle bisects the base at right angles ; and , conversely , the line bisecting the base of an isosceles triangle at right angles bisects also the vertical angle . Cor . 2. Every ...
... bisecting the vertical angle of an isosceles triangle bisects the base at right angles ; and , conversely , the line bisecting the base of an isosceles triangle at right angles bisects also the vertical angle . Cor . 2. Every ...
Page 34
... bisect each other Let ABDC be a parallelogram whose di- agonals , AD , BC , intersect each other in E ; then will AE be equal to ED , and BE to EC . A C B Because the alternate angles ABE , ECD are equal ( Prop . XXIII . ) , and also ...
... bisect each other Let ABDC be a parallelogram whose di- agonals , AD , BC , intersect each other in E ; then will AE be equal to ED , and BE to EC . A C B Because the alternate angles ABE , ECD are equal ( Prop . XXIII . ) , and also ...
Page 48
... bisected in D , and the arc AEB will be bisected in E. Draw the radii CA , CB . The two right- angled triangles CDA , CDB have the side AC equal to CB , and CD common ; there- A fore the triangles are equal , and the base AD is equal to ...
... bisected in D , and the arc AEB will be bisected in E. Draw the radii CA , CB . The two right- angled triangles CDA , CDB have the side AC equal to CB , and CD common ; there- A fore the triangles are equal , and the base AD is equal to ...
Page 49
... bisect these lines by the perpendiculars DF , EF ; DF and EF produced wil meet one another . For , join DE ; then , because the angles ADF , AEF are together equal to two right an- gles , the angles FDE and FED are to- gether less than ...
... bisect these lines by the perpendiculars DF , EF ; DF and EF produced wil meet one another . For , join DE ; then , because the angles ADF , AEF are together equal to two right an- gles , the angles FDE and FED are to- gether less than ...
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Common terms and phrases
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diagonals diameter draw ellipse equal angles equal to AC equally distant equiangular equilateral equivalent exterior angle foci four right angles frustum given angle given point greater hyperbola hypothenuse inscribed intersect join latus rectum Let ABC lines AC Loomis major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN prism Professor of Mathematics PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side AC similar similar triangles slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Popular passages
Page 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Page 17 - If two triangles have two sides, and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal, their third sides will be equal, and their other angles will be equal, each to each.
Page 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Page 63 - IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the' rectangle contained by the parts.
Page 18 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Page 10 - 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 perpendicular to it.
Page 32 - 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 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Page 15 - Wherefore, when a straight line, &c. QED PROP. XIV. THEOR. If, at a point in a straight line, two other straight lines, upon the opposite sides of it, make the adjacent angles together equal to two right angles, these two straight lines shall be in one and the same straight line.
Page 44 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.