Elements of Geometry and Conic SectionsHarper & brothers, 1861 - 234 Seiten |
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Seite 7
... VIII . Polyedrons BOOK IX . Spherical Geometry BOOK X. The Three round Bodies . Parabola . Ellipse Hyperbola • CONIC SECTIONS . Fage 38 44 ! 67 89 98 112 • 127 148 C 166 • 1.77 • 188 205 N.B. - When reference is made to a Proposition in ...
... VIII . Polyedrons BOOK IX . Spherical Geometry BOOK X. The Three round Bodies . Parabola . Ellipse Hyperbola • CONIC SECTIONS . Fage 38 44 ! 67 89 98 112 • 127 148 C 166 • 1.77 • 188 205 N.B. - When reference is made to a Proposition in ...
Seite 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 ...
Seite 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 ...
Seite 21
... VIII . ) ; it is , therefore , less than AB . Conversely , if the side AB is greater than the side AC , ther 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 , ther 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 ...
Seite 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 CA² chord circle circumference cone contained 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 point given straight line greater hyperbola hypothenuse inscribed intersect join latus rectum 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 quadrant radii radius ratio rectangle regular polygon right angles Prop right-angled triangle Scholium segment side AC similar similar triangles solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Beliebte Passagen
Seite 27 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
Seite 157 - The sum of the angles of a spherical triangle is greater than two and less than six right angles ; that is, greater than 180° and less than 540°. (gr). If A'B'C' is the polar triangle of ABC...
Seite 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Seite 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.
Seite 101 - When you have proved that the three angles of every triangle are equal to two right angles...
Seite 10 - CHG; and they are adjacent angles; but when a straight line standing on another straight line makes the adjacent angles equal to one another, each of them is a right angle; and the straight line which stands upon the other is called a perpendicular to it; therefore from the given point C a perpendicular CH has been drawn to the given straight line AB.
Seite 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.
Seite 22 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Seite 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.
Seite 41 - It follows that either couplet of a proportion may be multiplied or divided by any quantity, and the resulting quantities will be in proportion. And since by...