Elements of Geometry and Conic SectionsHarper, 1849 - 226 Seiten |
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Seite 44
... 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 are equal ; all the diameters are equal also , and each double of the radius . 3. An ...
... 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 are equal ; all the diameters are equal also , and each double of the radius . 3. An ...
Seite 45
... diameter divides the circle and its circumference into two equal parts . A B Let ACBD be a circle , and AB its di- ameter . The line AB divides the circle and its circumference into two equal parts . For , if the figure ADB be applied ...
... diameter divides the circle and its circumference into two equal parts . A B Let ACBD be a circle , and AB its di- ameter . The line AB divides the circle and its circumference into two equal parts . For , if the figure ADB be applied ...
Seite 46
... diameter AB I D H M BE F G being equal to the diameter EF , the semicircle ADB may be applied exactly to the semicircle EHF , and the curve line AIDB will coincide entirely with the curve line EMHF ( Prop . I. ) . But the arc AID is ...
... diameter AB I D H M BE F G being equal to the diameter EF , the semicircle ADB may be applied exactly to the semicircle EHF , and the curve line AIDB will coincide entirely with the curve line EMHF ( Prop . I. ) . But the arc AID is ...
Seite 50
... diameter is the longest line that can be in- scribed in a circle . PROPOSITION IX . THEOREM . A straight line perpendicular to a diameter at its extremity , is a tangent to the circumference . Let ABG be a circle , the center of which ...
... diameter is the longest line that can be in- scribed in a circle . PROPOSITION IX . THEOREM . A straight line perpendicular to a diameter at its extremity , is a tangent to the circumference . Let ABG be a circle , the center of which ...
Seite 56
... diameter AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by half the semicircumference AFD ; also , the angle DAC is measured by half the arc DC ( Prop . XV . ) ; therefore , the sum of the angles BAD , DAC is ...
... diameter AD . The angle BAD is a right angle ( Prop . IX . ) , and is measured by half the semicircumference AFD ; also , the angle DAC is measured by half the arc DC ( Prop . XV . ) ; therefore , the sum of the angles BAD , DAC is ...
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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.