Elements of Geometry and Conic SectionsHarper, 1849 - 226 Seiten |
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Ergebnisse 1-5 von 47
Seite 44
... radius of a circle is a straight line drawn from the center to the circumference . A diameter of a circle is a straight line . passing through the center , and terminated both ways by the circumference . Cor . All the radii of a circle ...
... radius of a circle is a straight line drawn from the center to the circumference . A diameter of a circle is a straight line . passing through the center , and terminated both ways by the circumference . Cor . All the radii of a circle ...
Seite 46
... radius CD will coincide with the radius GH , and the point D with the point H. Therefore , the arc AID must coincide with the arc EMH , and be equal to it . Hence , in equal circles , & c . PROPOSITION IV . THEOREM . In equal circles ...
... radius CD will coincide with the radius GH , and the point D with the point H. Therefore , the arc AID must coincide with the arc EMH , and be equal to it . Hence , in equal circles , & c . PROPOSITION IV . THEOREM . In equal circles ...
Seite 48
... radius CE , per- pendicular to the chord AB , divides the arc subtended by this chord , into two equal parts in the point E. Therefore , the radius , & c . Scholium . The center C , the middle point D of the chord AB , and the middle ...
... radius CE , per- pendicular to the chord AB , divides the arc subtended by this chord , into two equal parts in the point E. Therefore , the radius , & c . Scholium . The center C , the middle point D of the chord AB , and the middle ...
Seite 49
... radius FA will pass through the three given points A , B , C. A Secondly . No other circumference can pass through the same points . For , if there were a second , its center could not be out of the line DF , for then it would be ...
... radius FA will pass through the three given points A , B , C. A Secondly . No other circumference can pass through the same points . For , if there were a second , its center could not be out of the line DF , for then it would be ...
Seite 50
... radius CF is perpendicular to the chord AB , it bisects it ( Prop . VI . ) . Hence AF is the half of AB ; and , for the same reason , DG is the half of DE . But AB is equal to DE ; therefore AF is equal to DG ( Axiom 7 , B. I. ) . Now ...
... radius CF is perpendicular to the chord AB , it bisects it ( Prop . VI . ) . Hence AF is the half of AB ; and , for the same reason , DG is the half of DE . But AB is equal to DE ; therefore AF is equal to DG ( Axiom 7 , B. I. ) . Now ...
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ELEMENTS OF GEOMETRY & CONIC S Elias 1811-1889 Loomis,Making of America Project Keine Leseprobe verfügbar - 2016 |
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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
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Seite 60 - Any two rectangles are to each other as the products of their bases by their altitudes.
Seite 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...
Seite 11 - A rhombus, is that which has all its sides equal, but its angles are not right angles.
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 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 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.
Seite 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.
Seite 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.
Seite 148 - I.), that every section of a sphere made by a plane is a circle.