Elements of Geometry and Conic SectionsHarper, 1849 - 226 páginas |
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Página 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 D sides AC , AD , and the included angle in the other ; there- fore ( Prop ...
... 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 D sides AC , AD , and the included angle in the other ; there- fore ( Prop ...
Página 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 ...
Página 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 E D Because the alternate angles ABE , ECD are equal ( Prop . XXIII . ) , and ...
... 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 E D Because the alternate angles ABE , ECD are equal ( Prop . XXIII . ) , and ...
Página 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 ...
Página 49
... bisect these lines by the perpendiculars DF , EF ; DF and EF produced will 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 will 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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ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project Sin vista previa disponible - 2016 |
Términos y frases comunes
75 cents ABCD AC is equal allel altitude angle ABC angle ACB angle BAC Anthon's base BCDEF bisected chord circle circumference cone contained 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 greater Hence Prop hyperbola inscribed intersection join latus rectum Let ABC lines AC major axis mean proportional measured by half meet Muslin 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 Sheep extra side AC similar slant height solid angle sphere spherical triangle square subtangent tangent THEOREM triangle ABC vertex vertices
Pasajes populares
Página 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Página 27 - VIf 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...
Página 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
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 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 15 - 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 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 148 - I.), that every section of a sphere made by a plane is a circle.