Elements of Geometry and Conic SectionsHarper & Brothers, 1857 - 226 páginas |
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Página 7
... VIII . Polyedrons 127 BOOK IX . Spherical Geometry 148 BOOK X. The Three round Bodies . 166 Parabola Ellipse Hyperbola CONIC SECTIONS . 177 188 . 205 N.B. When reference is made to a Proposition in the same Book , only the number of the ...
... VIII . Polyedrons 127 BOOK IX . Spherical Geometry 148 BOOK X. The Three round Bodies . 166 Parabola Ellipse Hyperbola CONIC SECTIONS . 177 188 . 205 N.B. When reference is made to a Proposition in the same Book , only the number of the ...
Página 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 ...
Página 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 ...
Página 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 ...
Página 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 ...
Términos y frases comunes
ABCD AC is equal allel altitude angle ABC angle ACB angle BAC base BCDEF bisected chord circle circumference cone convex surface curve described diameter dicular draw drawn ellipse equal angles equal to AC equally distant equiangular equivalent exterior angle foci four right angles frustum given angle greater Hence Prop hyperbola inscribed intersection join latus rectum less Let ABC lines AC major axis mean proportional measured by half meet number of sides ordinate parabola parallelogram parallelopiped pendicular perimeter perpen perpendicular plane MN principal vertex prism PROPOSITION pyramid radii radius ratio rectangle regular polygon right angles Prop Scholium segment side BC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC triangle DEF vertex vertices VIII
Pasajes populares
Página 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.
Página 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Página 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.
Página 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.
Página 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Página 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.
Página 37 - Proportional, when the ratio of the first to the second is equal to the ratio of the second to the third.
Página 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.
Página 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.
Página 30 - If a side of any triangle be produced, the exterior angle is equal to the two interior and opposite angles; and the three interior angles of every triangle are together equal to two right angles.