Elements of Geometry and Conic SectionsHarper, 1858 - 234 sider |
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Side 7
... VIII . Polyedrons 127 BOOK IX . Spherical Geometry 148 BOOK X. The Three round Bodies 166 CONIC SECTIONS . Parabola . Ellipse Hyperbola 177 · 188 . 205 N.B. When reference is made to a Proposition in the same Book , only the number of ...
... VIII . Polyedrons 127 BOOK IX . Spherical Geometry 148 BOOK X. The Three round Bodies 166 CONIC SECTIONS . Parabola . Ellipse Hyperbola 177 · 188 . 205 N.B. When reference is made to a Proposition in the same Book , only the number of ...
Side 18
... VIII . THEOREM . Any side of a triangle is less than the sum of the other two Let ABC be a triangle ; any one of its sides is less than the sum of the other two , viz . the side AB is less than the sum of AC and BC ; BC is less than the ...
... VIII . THEOREM . Any side of a triangle is less than the sum of the other two Let ABC be a triangle ; any one of its sides is less than the sum of the other two , viz . the side AB is less than the sum of AC and BC ; BC is less than the ...
Side 19
... VIII . ) , the side CD of the triangle CDE is less than the sum of CE and ED . To each of these add DB ; then will the sum of CD and BD be less than the sum of CE and EB . Again , because the side BE of the tri- angle BAE is less than ...
... VIII . ) , the side CD of the triangle CDE is less than the sum of CE and ED . To each of these add DB ; then will the sum of CD and BD be less than the sum of CE and EB . Again , because the side BE of the tri- angle BAE is less than ...
Side 21
... VIII . ) ; it is , therefore , less than AB . Conversely , if the side AB is greater than the side AC , then will the angle ACB be greater than the angle ABC . For if ACB is not greater than ABC , it must be either equal to it , or less ...
... VIII . ) ; it is , therefore , less than AB . Conversely , if the side AB is greater than the side AC , then will the angle ACB be greater than the angle ABC . For if ACB is not greater than ABC , it must be either equal to it , or less ...
Side 24
... VIII . ) ; hence AB , the half of ABF , is shorter than AC , the half of ACF . Therefore , the perpendicular AB is shorter than any oblique line , AC . Secondly . Let AC and AE be two oblique lines which meet the line DE at equal ...
... VIII . ) ; hence AB , the half of ABF , is shorter than AC , the half of ACF . Therefore , the perpendicular AB is shorter than any oblique line , AC . Secondly . Let AC and AE be two oblique lines which meet the line DE at equal ...
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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
Populære avsnitt
Side 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Side 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.
Side 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Side 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.
Side 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.
Side 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.
Side 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.
Side 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Side 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.
Side 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.