Elements of Geometry and Conic SectionsHarper, 1849 - 226 páginas |
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Página 14
... fall on the point C ; and the line EG , coinciding with AC , the line GH will coincide with CD . For , if it could have any other position , as CK , then , because the angle EGH is equal to FGH ( Def . 10 ) , the angle ACK must be equal ...
... fall on the point C ; and the line EG , coinciding with AC , the line GH will coincide with CD . For , if it could have any other position , as CK , then , because the angle EGH is equal to FGH ( Def . 10 ) , the angle ACK must be equal ...
Página 18
... fall at their intersection , D. Hence the two triangles ABC , DEF coincide throughout , and are equal to each other ; also , the two sides AB , AC are equal to the two sides DE , DF , each to each , and the angle A to the angle D ...
... fall at their intersection , D. Hence the two triangles ABC , DEF coincide throughout , and are equal to each other ; also , the two sides AB , AC are equal to the two sides DE , DF , each to each , and the angle A to the angle D ...
Página 26
... be two perpendicu lars , OA , OB , let fall from the same point , on the same straight line , which is impossible ( Prop . XVI . ) . Therefore , two straight lines , & c . PROPOSITION XXI . THEOREM . If a straight line , 26 GEOMETRY .
... be two perpendicu lars , OA , OB , let fall from the same point , on the same straight line , which is impossible ( Prop . XVI . ) . Therefore , two straight lines , & c . PROPOSITION XXI . THEOREM . If a straight line , 26 GEOMETRY .
Página 45
... fall either within or without the curve ADB , there would be points in one or the other unequally distant from the center , which is contrary to the definition of a circle . Therefore , every diameter , & c . D PROPOSITION II . THEOREM ...
... fall either within or without the curve ADB , there would be points in one or the other unequally distant from the center , which is contrary to the definition of a circle . Therefore , every diameter , & c . D PROPOSITION II . THEOREM ...
Página 46
... fall on the point H , and therefore the chord AD is equal to the chord EH ( Axiom 11 , B. I. ) . Conversely , if the chord AD is equal to the chord EH , then the arc AID will be equal to the arc EMH . For , if the radii CD , GH are ...
... fall on the point H , and therefore the chord AD is equal to the chord EH ( Axiom 11 , B. I. ) . Conversely , if the chord AD is equal to the chord EH , then the arc AID will be equal to the arc EMH . For , if the radii CD , GH are ...
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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.