Elements of Geometry and Conic SectionsHarper, 1849 - 226 Seiten |
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Seite 44
... chord of an arc is the straight line which joins its two extremities . 4. A segment of a circle is the figure included between an arc and its chord . 5. A sector of a circle is the figure included between an arc , and the two radii ...
... chord of an arc is the straight line which joins its two extremities . 4. A segment of a circle is the figure included between an arc and its chord . 5. A sector of a circle is the figure included between an arc , and the two radii ...
Seite 46
... 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 drawn , the two triangles ACD , EGH will ...
... 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 drawn , the two triangles ACD , EGH will ...
Seite 47
... chord ; and , conversely , the greater chord subtends the greater arc . In the circle AEB , let the arc AE be greater than the arc AD ; then will the chord AE be greater than the chord AD . A D E B Draw the radii CA , CD , CE . Now , if ...
... chord ; and , conversely , the greater chord subtends the greater arc . In the circle AEB , let the arc AE be greater than the arc AD ; then will the chord AE be greater than the chord AD . A D E B Draw the radii CA , CD , CE . Now , if ...
Seite 48
... chord . PROPOSITION VI . THEOREM . The radius which is perpendicular to a chord , bisects the chord , and also the arc which it subtends . Let ABG be a circle , of which AB is a chord , and CE a radius perpendicular to` it ; the chord ...
... chord . PROPOSITION VI . THEOREM . The radius which is perpendicular to a chord , bisects the chord , and also the arc which it subtends . Let ABG be a circle , of which AB is a chord , and CE a radius perpendicular to` it ; the chord ...
Seite 49
... chords are equally distant from the center ; and of two unequal chords , the shortest is furthest from the center . Let the chords AB , DE , in the circle ABED , be equal to one another ; they are equally distant from the center . Take ...
... chords are equally distant from the center ; and of two unequal chords , the shortest is furthest from the center . Let the chords AB , DE , in the circle ABED , be equal to one another ; they are equally distant from the center . Take ...
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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.